Computer Interpretation of Selected Labanotation Commands

Zella Wolofsky

MSc, Dept Kinesiology

April 1974

Simon Fraser University

ABSTRACT

A computer program which converts selected movement notation symbols into numerical representations of the body's positions and prints out the results in the form of graphic output was developed. The notation system chosen for conversion was Labanotation.

Gestural movement commands were analyzed and a program was written which interpreted these forms of commands. Both methods of describing gestural movements available in Labanotation were programmed. In addition, modifications of final positions - through specific contractions and intermediate positions and knowledge about the amount of rotation within each limb were programmed. Once spherical coordinates for each bodypart were calculated for every unit of time, the program interpolated the movements for each interval (frame) to be used in the dynamic displays of the computer outputs. These were plotted as stickfigure drawings for each frame These plots were photographed one at a time, using the standard animation technique of doubling, to produce an animated film of the computer derived movements.

In order to examine the coherence and comprehensibility of the animated films produced from the computer outputs, assessors were asked to compare the computer derived drawings to similar drawings derived from cinematographic analysis of a dancer doing the same movements as were entered into the computer. The assessors were asked to rate the quality of the animation in general, the timing of the movements, the clarity of the drawings and the usefulness such films would have as cursory methods visalizing movements.

The results of the assessments indicated that the interpolation formulae which calculated the timing of the movements in the conversion program seemed to be oversimplified, as the timing factor for the computer produced film was rated significantly poorer. In general, the assessment results seemed to indicate that both films showed the movements in a sufficiently clear and comprehensible manner for use by dancers.

ACKNOWLEDGEMENT

I wish to express my thanks to John Montgomery who has been my research supervisor and an untiring source of encouragement. I would, also like to thank him for helping with the draft of this manuscript and offering valuable criticisms. Tom Calvert and Iris Garland. also, deserve a special thanks for serving on my research committee and for helping me formulate this research. In addition, I would like to thank Ms. Garland for allowing me to film her dancing and to use her Kinesiology class as film assessors. John Dunn provided me with information about animation that I could never find in the literature, and Jaan Pill and Rudy Wrench, of the Simon Fraser University Film Workshop donated their time and expertise in helping me prepare the animated films. My thanks also goes to Mrs. Ellis who typed the manuscript.

Finally, the positive feedback that I received from David Lach made me realize that anything was possible.

TABLE OF CONTENTS

• I. INTRODUCTION
  • Purpose of Research
• II. RELATED LITERATURE
  • Summary
• III. THEORY OF LABANOTATION
  • Introduction
  • Description of Labanotation Commands Used in Computer Analysis
• IV. MACHINE REPRESENTATIONS OF MOVEMENTS
  • Development of Coding Protocol
  • LABAN Interpreter Program
  • Evaluation Procedure
  • Analysis of Data
• V. CONCLUSIONS
  • Discussion of Results
  • Conclusions
• BIBLIOGRAPHY
• APPENDIX A - PROGRAM LISTING OF LABAN
• APPENDIX B - FLOWCHART OF LABAN
• APPENDIX C - EVALUATION QUESTIONNAIRE AND SIGN TEST
• APPENDIX D - SAMPLE DRAWINGS FROM THE PLOTTER
• APPENDIX E - LABANOTATION PHRASE USED AS INPUT TO PROGRAMME

LIST OF TABLES

1. BODYPART COMPONENTS

2. TOTALS FOR COMPUTER DERIVED FILM ASSESSMENTS AND MOTION ANALYSER FILM ASSESSMENTS FOR EACH RATING

3. DATA FROM THE SIGN TEST (5% LEVEL OF SIGNIFICANCE)

4. ASSESSMENT OF QUESTION NINE OF THE QUESTIONNAIRE

LIST OF FIGURES

Figure 1 - Labanotation Symbols

Figure 2 - Directional Descriptions with Level Shading

Figure 3 - Specific Contractions

Figure 4 - Labanotation Staff

Figure 5 - Basic Bodypart Signs in Labanotation

Figure 6 - Numbering of Bodyparts in the Program LABAN

Figure 7 - Labanotation Description / Input into the LABAN Program

Figure 8 - Intersection of Planes

Figure 9 - Defining Coordinates of a Line

Figure 10 - Flex Calculation

Figure 11 - Fold Calculation

Figure 12 - Current Time Calculations for Torso and/or Upper Sections of Limbs

Figure 13 - Current Time Calculations for Lower Sections of Limbs

Figure 14 - Projection of a Point onto a Plane

Figure 15 - Sample Drawing from the Plotter (1)

Figure 16 - Sample Drawing from the Plotter (2)

Figure 17 - Labanotation Phrase used as Input to Program

I. INTRODUCTION

Dance is an art form which concerns itself with space and time. For its development as a major form, it requires some method of recording and preserving the works of people engaged in making dances.

It required several centuries for music notation to become a uniform system. Because of its recent development dance notation has not yet reached the stage of having one acceptable form. However, dance is more complex than music for it deals with both space and time, and the human body has many potential simultaneous actions. Consequently, there are many more problems involved in the formulation of a notation system in dance than in music.

There are several criteria for a dance qotation system to be useable. Firstly, a notation system for movement must be capable of recording movement from a variety of styles, such as ballet, modern dance, jazz, folk dance and tap dancing, as well as the movements of ordinary life, such as walking and runnihg. Secondly, it must be economical. Since there are often several parts of the body to be notated, the system must be moderately quick to write. Thirdly, it must be accurate. Dancers and choreographers who have never seen a notated work should be able to read a score and get an adequate idea of the movements.

Three major systems of movement notation exist today [Turnbaugh, 1970]. One is based oh a stickfigure notation, the other two, on analytical descriptions of body movements. Benesh notation, invented by Joan and Rudolph Benesh in 1958 [Causley, 1967], is used extensively by ballet companies but has not been successfully used in other dance forms. The notation is based on an abstract stick-figure drawing. The second notation system was developed by Noa Eshkol and Abraham Wachmann [Eshkol and Wachmann, 1958]. The movements are placed on a cumbersome and complicated staff, and are expressed in terms of degrees of planar, rotary, and conical movements, not in terms ordinarily used in dance. The third system is Labanotation, invented by Rudolph Laban in 1926 [Laban, 1956]. This system is capable of recording changes in angles of the limbs, dynamic changes, and spatial qualities. It too, deals with movement in terms foreign to dancers, however, it allows the widest range of movement description of the three notation systems described [Hutchinson, 1972].

Because notation systems should be able to record any human movement, not just a very formalized subset called dance, the need for economy is extremely important. Labanotation combines the space-time elements into one Symbol. The length of a symbol in Labanotation is proportional to the time required to complete the movement.

As a means of preserving choreography, a notation system must be able to give to the reader information concerning spatial changes and the dynamics of the notated works. Video tape and film are useful for the preservation of dances but just as phonographic recordings are not enough for the serious study of a piece of music, then too, film is not enough for the serious reconstruction of a work by someone other than the choreographer.

Movement notation systems are difficult to learn and require several years of advanced study to develop proficiency in their use. Consequently, dancers and choreographers have been very reluctant to learn any notation, although most understand the need for a recording system in dance.

The use of computers in aiding the study of notation is feasible. There are two criteria for the selection of the notation system to be used in such a computer system. First, the notation system would have to be well known, in use and fully developed. Secondly, the notation system would have to be a general movement description system, as opposed to those that notate only movements of a specific style of dance.

The first criterion limits the selection to the notation systems listed above. The Benesh system is used extensively among ballet companies [Turnbaugh, 1970]. Despite its extensive use, this system of notation has several drawback. It is used primarily for ballet and is not an analytical system [Hutchinson, 1972] and would prove to be very difficult to computerize [Eshkol, et al.,1970]. The two remaining systems approach movement in a similar analytical fashion. Each has advantages and disadvantages.

Eshkol/Rachmann notation treats joint movement as spatial coordinates designating them in numbers. They stress the independence of their notation system from the stylistic approach which is characteristic and special [Eshkol and Wachmann, 1958, p. vii] and that it expresses pure movement, not just dance. However, to notate dance, the ability to notate a broader range of movement qualities is desirable.

The essence of the movement being notated must be captured if the notation is to be useful to anyone who has not seen the original dance. The reason for performing a certain movement and the manner in which it is performed are often stressed by the choreographer when setting dances; these subtleties must be written in the notation, otherwise the reconstructed dance would be only a series of positions. Labanotation has the potential of describing the process of movement as well as the spatial positions.

[Eshkol et al 1970] used computer technology to help interpret movements of one limb notated in Eshkol/Wachmann notation. There was no attempt at dynamic display of the movement nor was there any significant work on total body movement using their notation.

Works of several contemporary choreographers have been notated in Labanotation and this system is taught in many American universities. However, many dancers do not know, or feel qualified enough, to make use of the available notated scores. If a computer system were operational which read Labanotation symbols and produced a dynamic display of the movements, interpretations of scores could be simplified.

The use of Labanotation in a computer system such as the one suggested by the Eshkol study has never been attempted. Because of the analytical treatment of limb movements in Labanotation and because Laban's work formed the basis for Eshkol/Wachmann notation, the fundamental premises of the Eshkol work would be applicable to the development of a computer system using Labanotation as input.

Such a computer system would not develop into an art form itself but would be a tool of dance. It would be a rough tool and could never replace the use of film or video tape as a preserving and recording medium. Its purposes would be to aid in the reconstruction of dances and the visualization of notated work. Most important would be the usefulness of such a system in providing an overall view of a dance.

The basic problem when using a notation is in getting the feel of a dance. A computer system which interpreted notation symbols and produced dynamic displays of the notated movements would provide the cursory view needed when initially looking at a dance score.

Purpose of Research

It is proposed to develop a computer system which would interpret a subset of Labanotation symbols, and produce graphic outputs of the realized movements. The drawings would be in the form of a stickfigure, and by photographing the drawings produced by the computer, a conventional animated film of the movements would be produced. The comprehensibility and clarity of the film and the movements would be tested, and in this way, information regarding the validity of the computer program assumptions could be obtained.

II. RELATED LITERATURE

The desirability of establishing dance as a literary form has been noted by many authors [Morris, 1928; Tetley, 1948; Laban, 1956; Jay, 1957; Eshko1 and Wachman, 1958; McGraw, 1964; Hutchinson, 1970; Turnbaugh, 1970]. Choreographers, without the benefit of a movement notation system have had to rely on esoteric notes or good memories in order to shape a dance. The use of notation systems and the potential applications of computer technology in composition has been noted by Hutchinson [1967]:

Recently, Cunningham [1973], an American choreographer, also expressed the potential use he could see for computer help in the visualization of movement patterns and ideas. However, he was unclear as to how the man-machine interface could be accomplished. Notation as the language of conmunication between man and machine has the potential of solving the problem raised by Cunningham.

Preston-Dunlop[1969] provided a comprehensive listing of the current notation systems; however, the most publiCized ones have proved to be difficult to master. Although notation is now a part of many university dance programs [Dance Notation Bureau, 1973], there is still resistance to incorporate dance notation into dance training.

Work by Eshkol et al. [1970] has provided the basis for a method of reducing this problem by utilizing computer technology. In proving that kinematic descriptions of movement could be derived from coded notation, the need for educated guesses as to the meaning of a notated piece could be replaced by objective analysis by a computer.

Three areas of research are required to produce a computer system which could interpret notation. First, the movement notation must be translated into machine readable forms. Secondly, the computer program which would execute the movements by calculating the numerical representaions of the movements would have to be formulated. Thirdly, the results of the program would have to be printed out in numerical or graphic form.

The first area was successfully accomplished by Eshkol's group [1970]. Input in the study was 100% keyboard entry. An attempt at entering Labanotation symbols into a computer was investigated by Fulkerton [no date, ca, 1967]. He called for the use of a light pen and cathode ray tube for entering Labanotation scores into a computer. Unfortunately, this project was never implemented. Implementation on a small scale was done through the manipulation of symbols on a cathode ray tube by Shapiro [1972]. She produced a short Labanotation score. From the point of view of simplicity, manipulation of Labanotation symbols on a screen, rather than remembering an alphameric code (needed with 100% card entry). for each symbol is a desirable attribute of a system such as the one proposed.

In the second area of research, the conversion of notation symbols into machine representations of body positions, virtually no work has been done prior to this time. The Eshkol work was limited to one limb and the STKMAN program of whole body movements did not use Eshkol/Wachmann notation. Eshkol/Wachmann notation uses an external coordinate system which is only effective for the moving limb; any limb attached to the moving limb would change its angles and orientation in the external fixed reference system. This created problems for the authors of the STKMAN program. Also, the rotational state of the limbs was not always uniquely defined. The authors suggested a solution to the latter problem. They felt that by specifying the normal by two polar angles or a rotational angle, a solution to the non-uniqueness of some rotational states could be overcome.

Initial work on developing a computer program which would use Labanotation has been done by the present author. Progranming allowed for the description of any number of moving bodyparts. Due to notational features, the handling of locomotor descriptions (motion) was not attempted. The same problem was encountered by the Eshkol group, with no solution of the problem achieved.

Information on the joint movements [American Academy of Orthopaedic Surgeons, 1965] and general infonnation on selected areas of analytical geometry [eg. McCrae, 1953] was obtained for solutions of specific problems in the Labanotation conversion program. However, this area is an entirely new area of research.

The third area of research relates to the display of the computer movements. Given the purpose of the present research project, a visual display of the movements is essential. Animated films, when properly produced relay sufficient information to be satisfactory replications. of movement [Kallis, 1969]. However film, whether real or animated, is not totally satisfactory method for the observation and analysis of movement. Preston-Dunlop [1969] presented the drawbacks when using film to study movements. She stated that spatial changes were visible, but dynamics were not. However, in the system proposed the use of some sort of two-dimensional viewing medium is the only possible choice.

Summary

Notation systems exist today but are extremely difficult to master. A potential aid in improving this situation could be through the use of computer technology. Work using Eshkol/Wachmann notation as input into a computer system was undertaken, but the project was confined to motion of one limb.

Another notation system, Labanotation, is in extensive use. in North America. This system has been used to notate much contemporary choreography, and was the basis for many of the premises of the Eshkol/Wachmann notation. As of yet, however, no work has been done to produce a computer compatible set of Labanotation. Because of the growing number of notated works using this notation system, computer assistance in the reconstruction of scores would be extremely useful. Literature on the conversion of Labanotation symbols into numerical representations of a body does not exist, but the work done in the Eshkol study has applications.

A shortcoming of the Eshkol project was the lack of dynamic displays of tha graphic output produced by the computer. Animated film is a good choice for conveying the motion realized by the computer system, and can provide sufficient information to be useful. When cathode ray tube devices are not available, animated film is the only option which can display the movements in real-time.

III. THEORY OF LABANOTATION

Introduction

The problems involved in translating a three-dimensional art form into a two dimensional representation are many sided. In addition to the obvious loss of the third dimension, the interrelationship between time and space must be considered. Dance is primarily concerned with this interrelationship and keeping it intact is of fundamental importance. In film and video representations of dance, this interrelationship is visible although somewhat distorted because of the flatness of the view, but it is reproducible. When translating motion into an abstract notational form, the problem of the time-space relationship must be recognized as being the singularly most important aspect to convey to the viewer.

Nikolais [7948, p. 64] summarized the factors inherent in human movement which must be represented in any notation system. They are: (1) the nature of the body as a moving entity, (2) the space in which the body exists and moves, (3) the time in which the movement takes place, (4) the dynamic energies behind the movement. Others [Eshkol and Wachmann, 1958; Hutchinson, 1970] have also recognized these factors as being the major factors for consideration in movement notation systems.

Labananalysis is an umbrella term which describes the system of notations developed by Laban. There are three areas involved in labananalysis. They are:

1. Labanotation: This is a description of movement using spatial orientations. Basically, Labanotation identifies the bodypart moving, the timing of the movements, the direction and degree of movement and defines the system of reference from which is based the direction of the movement.
2. Motif Writing: This is the description. of movement which identifies the underlying theme or most important feature of the movement being notated. When using Motif Writing the reader is concerned with keeping to a theme, not a particular movement pattern. One might think of Labanotation and Motif Writing as being at opposite ends of a continuum of movement specificity. Motif Writing is used when recording improvisational studies.
3. Effort/Shape: This is the term for the description of the qualitative aspects of movement. It concerns itself with the qualities of tension, body weight, spatial focus and time utilization, as well as the shaping of the body [Hackney, Manno, Topaz, 1970, Part X].

Bodypart is a technical term used in labanotation to represent a predefined section or segment of a body.

Description of Labanotation Commands Used in Computer Analysis

Laban, in the development of his movement notation system, clearly had a firm grasp of the need to represent the factors of space, time and bodypart identification. Each symbol in Labanotation can potentially describe these three factors of movement.

1. Space Factor

Bodypart is a general term used to indicate a limb or a part of a limb. Each bodypart has a bound end, or base, and a free end; these have been defined for reference by Hutchinson [1970, p. 227] and are represented in Table 1.

1. BODYPART COMPONENTS

When calculating spatial directions, Labanotation has adopted a certain frame of reference for measurement.

(a) Direction

The directions are taken from the relationship of the bound to free ends of limbs with specific directional names given to specific relationships, and have been specially shaped to show the directions:

When movement is described in terms of final position, the position is calculated from the relationship between the bound and free ends of the moving body part. This type of description is called destinational description in Labanotation. It is used mainly when dealing with gestural movements. A gestural movement (or gesture) is chiefly movement which involves parts of the body not supporting the weight of the body. When movement is described in terms of direction of movement, rather than final position, it is called motional description. Usually this type of movement description is used for locomotor activities, and descriptions of the state of the weight-bearing bodyparts. Motional description is a less fundamental description than destinational description and can only be reduced to destinational description with great effort.

(b) Level

The description of direction must be a three-dimensional representation. To do this, shading of the symbol is used and is referred to, in Labanotation, as the level of the movement. Level refers to the direction of movement in three dimensions. When the bound and free ends are in the same horizontal plane, this level is called Middle. High level is when the free end of a limb is 45° above the bound end; Low level is when it is 45° below the bound end of the limb.

(c) Rotary Motion

The action of a limb or bodypart moving about its axis is called rotary motion. The axes of the limb and of the movement coincide so that no appreciable change in tht position of the limb in space occurs [Eshkol and Wachmann, 1958; Hutchinson, 1970], unlike destinational movements, where the axis of the limb is at right angles to the axis of the movement.

(d) Contractions

Movement which shortens the distance between two points is referred to, in Labanotation, as either flexing or folding. A flexion is movement at two joints, while a fold is movement at one joint. The free end of a bodypart in flexion draws in towards the bound end on a straight path, while in a fold, it approaches the bound end on a curved path. In a flexion, the central joint of a limb is displaced while in a fold it is the extremity which moves. Figure 3 displays the differences between flexes and folds.

2. Bodypart Factor

As with music notation, Labanotation utilizes a staff on which to write the, symbols. Unlike music, the staff runs vertically, and is read from the bottom upward. There can be up to fifteen columns in a staff, each column representing a bodypart, or group of bodyparts. Certain columns of the staff have definite bodyparts assigned, while other columns can have more liberal usage. When the latter case occurs, a presign (a symbol used before a direction command on the staff to indicate which bodypart is moving) is used.

The placement on a staff, or the use of a presign, therefore, indicates which bodypart is being referred to. It must be noted that this convention is used for destinational descriptions. The most often used presigns are shown in Figure 5. When the whole body moves (as in walking or running} the central two columns of the staff are used exclusively to indicate this.

3. Time Factor

Time is marked off on the central line of the staff, the space between the marks represents the duration of the unit of time (either in beats, measures or seconds), usually predetermined. The length of any symbol is proportional to the time required for the movement of the bodypart. Simultaneous actions are described in the same horizontal space on the staff. In Labanotation, the elements of time and space have been combined into one symbol, a factor not found in other notation systems [Hutchinson, 1972]. When both elements of space and time are combined into one symbol, there is an economy of the language, which is important when dealing with.the complexities of human movement.

4. Summary

A description of the factors of movement as defined by Nikolais and others have been mentioned. Labanotation includes three of the four factors necessary in any movement notation system. A destinational description symbol in Labanotation has three built-in factors:- (using Laban's terminology)

1. identification of the bodypart moving
2. identification of the starting time and duration of the movement.
3. direction and level of the movement.

Additional information to the above is required to describe rotary motion and contractions. In addition, a full explanation of all the Labanotation Symbols has not been included in the above discussion, but can be found in Hutchinson [1970]. 0nly those symbols which have been used in the computer analysis were dealt with.

IV. MACHINE REPRESENTATIONS OF MOVEMENTS

Development of Coding Protocol

A computer program was written to interpret suitably coded information concerning movements and to produce drawings which, when made into an animated film, showed the realized movements in real-time. The optimum data format would allow the user to enter Labanotation symbols directly into the computer. Since the hardware which would allow this was not available, an alternate coding system was devised.

1. Coding Procedure

In Labanotation there are limbs and joints, these not necessarily coinciding with the conventions of anatomy, but representing some convenient point of reference. In the program, the Labanotation convention of bodypart identification was maintained as closely as possible.

The body was divided up into segments (limbs) which were either simple or complex. The simple limbs were defined as having no internal movement capabilities. For example, the arm is a complex limb and is composed of the upper arm, lower arm and hand, which are all considered simple limbs. In this research, the hand and foot was each treated as a unit - there was no finger or toe movement. The trunk, or torso, was divided up according to the Labanotation convention: the chest region consisted of the region of the torso bounded by the thoracic vertebrae, the waist region bordered by the first and third lumbar vertebrae, and the pelvis, by the fourth vertebrae and the coccyx.

At the start of the program, this data was entered, as well as other relevant information about each bodypart. In addition to the limbs, the joints were numbered to accommodate the problem of hierarchy of movement.

[Whenever a bodypart moves, it takes all the other bodyparts attached to its moving end along with it. There is, then, a hierarchy of bodyparts, the closer the bodypart to the torso, the higher on the hierarchy. In the calculation of the position of each limb, at each time interval, a specific order had to be followed so that those limbs closer to the torso were calculate first.]

The lower end of the torso was set as 1 and the other joints of the torso (here defined as the free end of each torso section) were numbered consecutively. The right side of the body was numbered evenly, the left had odd numbers. Figure 6 shows the numbering of the bodyparts (both joints and limbs).

Two examples representing the same movements are shown in Figure 7. The first example will describe the movements using Labanotation symbols, the second uses the coding protocol developed for the program.

The movements - The initial position is a standing position, facing forward, both feet together. On the first beat, the left leg goes to forward hip level, taking one entire beat to complete the movement. On the second beat, the left leg goes to the left side, also at hip level, taking one half beat. 0n the third beat, the left leg, lowers by 45° and the movement requires an entire beat to complete.

Labanotation representation - The Labanotation representations of the above movements are shown in Figure 7.

Coded input of LABAN program -- Bodypart, timing and spatial identifications are inherent in any Labanotation symbol by virtue of the fact that the symbol is placed on a staff (which defines the starting point and the bodypart moving), has a certain size (the duration of the movement), shape (direction of the movement) and shading (level of the movement). This information had to be explicitly given in the program. The following format was chosen.

LABAN is the name givento the computer program developed for this research. The listing is given in Appendix A and a flowchart provide in Appendix B.

The first column represents the type of movement, 2 for a support (a bodypart which bears weight), 1 for a gesture, 0 for the end of the input. The second column of the input data represents the starting time of a particular movement. The third column represents the bodypart (either a joint or a limb) moving or acting as a support. The fourth column represents the duration of the movement or support. The fifth column represents the direction and level of the movement. Often there: can be more than one entry in the last column. This is how intermediate positions (those directions not defined by a specific symbol) are entered. Appendix E shows the actual dance entered into LABAN.

Additional Data

Additional data needed for the final animation drawings had to be entered. The cine rate (desired frames per second) and timing (beats per minute) were required as data to calculate the number of frames per beat. In addition, information used to calculate the apparent angle of viewing of the final plotter drawings and the two-dimensional projections, was given at the outset of the program.

It was decided that each limb would be described in terms of spherical coordinates. Thus, translation of Labanotation direction and level symbols into angular measure had to be done. Front direction (in Labanotation) was considered to be zero radians, backwards, to be π radians, the right side (perpendicular to front) π/2 radians, the left side 3π/2 radians. Middle level was chosen to be zero radians, high level to be 3π/4 radians and low level to be π/4 radians.

Each position in Labanotation could be described by using two angles, φ for direction measure and ψ for level measure. A problem arose when qualifying Place. Because Place is the longitudinal axis of the body in gestural movements, certain changes had to be made to the values of φ (direction) when moving to or from this position. In order to keep the movements in one plane, when the origin (or destination) of a movement was Place, the φ value of the destination (or origin) had to be adopted instead of the value of 2π radians normally given to Place.(This measure of 2π radians is an arbitrary measure ; it could have been any other.) Thus Place has a measure of ±π/2 radians, but a non-unique φ.

Although the drawings produced by the computer were stick-figure drawings, the facings of palms, feet, and the rotation of each limb about its longitudinal axis had to be known and this was also part of the initial data. The angle of rotation was called θ.

LABAN Interpreter Program

1. General Overview

The program LABAN interprets: (1) coded bodyparts and commands to those bodyparts, and computes the spherical coordinates describing the final position of each bodypart, (2) computes the duration left to complete each command at the end of each beat, (3) computes by interpolation, the rectangular coordinates of certain points, at specific intervals of time, (4) plots a stickfigure drawing of the moves, and prints the rectangular coordinates of the points at each time interval desired. The program can move as many bodyparts as must be moved at any given time. Any gestural movement, described in terms of destinational movements can be interpreted by LABAN .

The original plan was to have the program on a Digital PDP 8e, a minicomputer, with initial debugging to be done on a larger machine, the IBM 370/50. The program, in order to fit into the minicomputer, was divided up into three sections, each section calling up the next when completed. However, the size of the program and the lack of adequate plotting facilities on the PDP 8e made the use of this computer quite impractical, and the final work was done exclusively on the IBM 370.

2. Translation of labanotation into Machine Readable forms

The first section of the program primarily read in and stored data concerning coded bodyparts, tempo of the dance, cine rate and plotting information. The smallest fraction of a beat used in any particular dance was referred to as the beat-step. This value. of the beat-step was constant, and all duration information was converted into beat step units. This allowed for the use of integer, rather than real values, thus providing economy of memory space requirements.

(a) Outline of LABAN1 (Section one of LABAN)

This routine read in the coded dance, decided if a bodypart was a limb or joint, and if the destinational command was modified by some sort of contraction or intermediate position. These modifications were stored in arrays to be used later in the program.

(i) Directional angle conversion - The Direction and level commands were then translated into directional angles of φ and ψ respectively. The φ and ψ values for each bodypart and the duration needed to complete the movement of each bodypart were stored in arrays at each beat-step.

Labanotation commands have nine specific directions, intermediate positions are specially mdified positions, and are given in the coded commands as a series of components of the desired position. The average of the components' directions is taken to give the correct φ and ψ. Differences of 7.5° in direction and level are possible in LABAN.

If no new command was given for a particular bodypart at a specific time, the previous values of φ and ψ were retained. If no command was ever given for a particular bodypart, the initial default position value (the value read in before information about a dance is read) for the bodypart was stored in the arrays. If no direction and level commands were given, but a flex or fold command was, the previous φ and ψ values were assumed and stored.

(ii) Support bodyparts -- Arrays specifying which bodypart was supporting the body weight were also stored as well as arrays indicating the duration of these supports.

(iii) Complex to simple bodypart conversion -- Certain limbs were treated as complex composed of a series of bodyparts (e.g. arm). Movement of these complex limbs had to be described as movements of the component parts. The values of φ and ψ and the duration of the movement for each of the component parts of a complex limb were stored in arrays as if there had been movement commands for these component parts individually.

(iv) Calculations of angle of rotation of a bodypart -- Because of the nature of the human body, contractions normally occur in one direction, toward the inner surface of the limb. The facing of the inner surface (i.e., the rotation of the limb) then had to be calculated before any flex or fold calculations could be done.

Theory used to calculate the angle of rotation: If the rotation of each limb could be defined as an angle of rotation about an axis, then it could be treated in the same way as the directional angles. An imaginary set of axes at each joint of the stickfigure is assumed to exist, with the positive X-axis to the right of the figure (viewers' left), the positive Y-axis coming out of the page, and the Z-axis having its positive direction upwards.

If the end of an element is described by the three dimensional vector u, then a general rotation can be produced by an application of a transformation matrix A, so that

u' = A u 

Rotation about the Z-axis in a clockwise direction, looking down the positive axis towards the origin, yields a positive φ and a matrix D which describes the rotation.

     |  cosφ   sinφ    0  |
D =  | -sinφ   cosφ    0  |
     |    0     0      1  |

Rotation about the X-axis in a clockwise direction looking towards the origin along the positive axis, yields a positive φ and a matrix C which describes the rotation.

     |   1       0      0    |
C =  |   0     cosψ   sinψ   |
     |   0    -sinψ   cosψ   |

Rotation about the Y-axis in a counterclockwise direction, looking down the positive axis towards the origin, yields a positive θ and a matrix B which describes the rotation

     |  cosθ   0    sinθ  |
B =  |   0     1      0   |
     | -sinθ   0    cosθ  |
     
   
A = DCB                               (1)

A is a transformation matrix representing a general rotation through angles φ, ψ and θ from an initial position with φ = ψ = θ = 0.

This represents an impossible position, but was chosen to allow the normals of the head, torso, and arms to be off to the right and the normal of the legs, to the left.

Because of the appropriate choice of angles in describing direction and level Labanotation commands, the φ and ψ are known. The θ is unknown in most cases except for that of a bent complex limb.

The degree of rotation of a complex limb can be determined from the coordinates of the normal to the plane of the complex limb. The coordinates of this normal can be found in two ways:

(i) by taking the cross-product of the vectors which represent the vectors of the positions of each of the component limbs.

(ii) by applying the transformation matrix A representing rotations of the normal through the angles φ, ψ and θ.

By equating these two sets of coordinates., we can solve for θ, The angle of rotation.

Matrix A is

| cosφcosθ-sinφsinψsinθ  sinφcosψ   cosφsinθ+sinφsinψcosθ  |
|-sinφcosθ-cosφsinψsinθ  cosφcosψ  -sinφsinθ-cosφsinψcosθ  |
|-cosψsinθ               -sinψ             cosψcosθ        |

Multiplying matrix A by the vector X (the normal to the limb in its initial position of φ=ψ=θ=0), where

  |1|
X=|0|
  |0|

results in the vector P, where L, M, and N represent the elements of the vector P.

  |L|      | cosφcosθ-sinφsinψsinθ|
P=|M|  = - |-sinφcosθ-cosφsinψsinθ|
  |N|      | cosψsinθ             |

If there are two component limb parts, with directional angles φ and ψ and φ' and ψ' respectively, then the cross-product of the vectors which represent the component parts is

|l|      | cosφ'cosψ'sinψ-sinφ'cosφcosψ  |
|m|  = - |-sinφ'cosψ'sinψ+sinφ'sinφcosψ  |
|n|      |-cosψ'cosφ(sinφ'cosφ-cosφ'sinφ)|

These two vectors (l, m, n) and (L, N, N) are identical except for magnitude and therefore

 l = kL              (1)
 m = kM              (2)
 n = kN              (3)

where k is an unknown positive constant.

This unknown constant can be found by substituting k=n/N into the equations (2) or (1). The value of k is unique.

For computational sanity let

Mn = Nm              (4)
Lm = Ml              (5)
Ln = Nl              (6)

Using (4) yields

                -n⋅cosφ
tan θ = -----------------------                  (7)
          -m⋅cosψ + n⋅cosφ sinψ 
          

Let θ be a solution to this equation, where -π/2 < θ₀ < π/2. Then θ=θ₀ or θ=θ₀+ π. One of these two solutions yields a vector (L, M, N) which is identical (except for magnitude) with the vector (l, m, n); the other is parallel but in the opposite direction. To identify the correct value of θ, the vector (L,M, N) is calculated with θ=θ₀. Using the relations (1), (2), or (3) the sign of k is checked. If k is positive, then θ=θ₀; if k is calculated to be negative, then θ=θ₀+π.

Method of calculating the rotation of limbs in LABAN: Rotations of the torso (bodyparts 1-10) were not allowed in this version of LABAN. Only the rotations for the arms and legs were calculated.

Each complex limb was considered to be composed of three simple bodyparts: upper, lower and extremity. If a limb was not bent the subroutines ARMS or LEGS were used to calculate the angle of rotation. These subroutines assigned rotations to certain directional angles and could calculate, using a basic formula, the angle of rotation for the other directional angles. If a limb was bent so that part of the limb lay in a different plane, subroutine CHCK was used to calculate the angle of rotation. CHCK was based on the theory outlined in the section above (i.e. equating two sets of normal coordinates).

Admissible ranges of rotation between the lower limb and the extremity were set up and checked, changing any previous value for θ if necessary to bring its value within an admissible range. Once the angle of rotation of each bodypart for a particular best-step was calculated and stored in arrays, the contraction modifications could be calculated for the facings of the limbs were then known, and the plane of movement of the contraction was known.

(v) Limb modification -- The basic problem involved when flexes or, folds modified a position was that the φ and ψ of the bodyparts involved in the flex or fold would change.

Contraction occur in the plane described by the normal of the limb. The normal is known because the angle of rotation is known (θ).

Owing to the Labanotation convention that flexes and folds modify two adjacent bodyparts, detailed calculation had to be done if the bodyparts were the upper and lower arms (or legs). Any movement of the upper or lower arm (or leg) would move the hand (or foot). If the extremity had the same φ and ψ as the lower limb (same direction and level), the modification of the lower limb would affect the extremity as well.

Theory used to calculate limb contractions: A line of intersection (all points satisfying two linear equations simultaneously) of two planes has as its directional vector the cross-product of each of the two normals to the planes.

In Figure 8, let AB and BC be two lines in a plane P₁ with the normal N₁. BC is also in the plane P₂, with normal N₂. Then the line of intersection of P₁, and P₂ is BC.

If AB and BC represent two adjacent simple limbs of a complex limb, ABC, their normals are known (θ for each limb has just, been calculated). The cross-product of these normals yields the directional cosine of the limb BC. Since the length of BC is known, the coordinates of B can be calculated.

Knowing that a limb can be described by two- angles φ, ψ and the length of a limb (L), the rectangular coordinates of the endpoint can be calculated, using the following formulae (see Figure 9).

x = L ⋅ cosψsinφ       (8)
y = L ⋅ cosψcosφ       (9)
z = L ⋅ sinψ           (10)

Inversely, once the coordinates of a point are known, the angles φ and ψ can be calculated, from (10),

   sinψ = -L/z,    giving a value for ψ
   
From (8) and (9), 
   sinφ = x/L ⋅ cosψ 
   cosφ = y/L-cosψ       giving a value for φ

This results in the directional angles φ and ψ for a limb BC after a modification. The angle of rotation will not have changed, for the contraction has occurred within the plane of the limb.

Method of flexion calculation in LABAN1: The initial position of the whole limb before contraction is represented by PR in Figure 10. The upper limb (called MODB in the program) and the lower limb (MODB1) are PQ and QR. respectively. Angle PQR is the angle of flexion derived from the degree of flexion specified in the initial labanotation command to flex. (The amount of contraction is called degrees of contraction in Labanotation)

Using the sine rule,

PR = (QR ⋅sin PQR)/sin QPR

and PS and SQ can be calculated:

PS = -PQ ⋅ cos QPR
SQ =  PQ ⋅ sin QPR

The directional cosines of PQ and QR (= -RQ) must be then of RQ and PQ, given the lengths PR, QR and the angle PRQ, in addition to the directional cosine of PR and the normal to the plane PRQ (the angle of rotation defines the normal). This subroutine took the cross- product of the normal to the plane PRQ and PR, yielding the directional cosine of SQ. Knowing the coordinates of S, the coordinates of Q were then calculated and the required directional cosines of PR and QR derived.

Once the directional cosines were known, the subroutine PHPSTA calculated the φ, ψ and θ for the limb, given the directional cosines of the normal to the limb.

Method of fold calculation in LABAN1: In a fold, the upper part of a limb remains stationary and the lower part of the limb moves. In Figure 11, PR represents the stationary part of the limb. (MODB in the program), RQ represents the moving limb (MODB1). Angle PRQ is the angle of folding derived from the degree of folding specified in the initial Labanotation movement command.

The fold modification is simpler to calculate than the flex modification, because the only directional cosine required is that of RQ (only one component part of a complex limb moves in a folding contraction).

 PS = PR - QR - cos PRQ        Directional cosine QR
 SQ = QR ⋅ sin PRQ
 

The subroutine DCS in LABAN1 calculated the directional cosine of RQ, by finding the directional cosine of SQ, the coordinates of S and deriving the coordinates of Q. Once the coordinates of Q and directional cosine of RQ were known, the subroutine PHPSTA was called. This routine calculated the φ, ψ and θ given the normals to. the planes of the limbs.

(vi) Transfer of data onto file to be used in next section of, LABAN -- The previously stored values for the modified bodyparts were then changed to.the newly calculated ones. Once all the modifications had been completed, the arrays storing the φ, ψ and θ values for each body-part at a particular beat-step were written onto a file to be used by the next section of LABAN.

(vii) Summary - LABAN1 (1) converted final direction and level commands into directional angles φ, ψ (2) stored information on supportive bodyparts; (3) converted complex limbs to simple component parts (4) calculated the angle of rotation for each sinple bodypart, before any contractions (flex or fold) had occurred; (5) changed the φ, ψ of each bodypart involved in a modification; (6) transferred the finalized φ, ψ and θ and durations of the movement of each simple bodypart at a particular beat-step onto file.

The six steps outlined above were repeated over again for every beat-step of the dance. When the signal for the end of the dance was reached, the program called the next section of LABAN (LABAN2) and proceeded with the new section.

3. Calculation of the Numerical Representations of Movements

(a) Introduction

Up to this point in the conversion program, LABAN, calculations have been based on final positions and the duration required to complete the movements. However, in order to have the necessary data to eventually produce a dynamic display of the realized movements, it is necessary to know the actual position of the limbs at specific points in time. This section of the program is concerned with calculating this type of information.

Outline of LABAN2 (Section two of LABAN)

This section of the program first read in the final φ, ψ and θ and the time left to complete the final position for each bodypart for a particular beat-step. By interpolation, it then computed the φ, ψ and θ values of each bodypart at the end of each frame.

A frame indicates a drawing of a figure at the end of a small interval of time (e.g. 1/l2th of a second). After photographing the frame with other frames in a series (using animation techniques) a conventional animated film would result.

The position at the end of each frame was called the current time, position, the directional angles have 'current time' values, as well. In this section of the program, the current time values for each bodypart's directional angles were calculated. Rectangular coordinates of each joint (extremity point of each limb, in this case) were calculated, and then stored ih arrays, later to be written onto files for use by the third section of LABAN.

(i) Calculation of current time φ, ψ and θ values - The information stored in the arrays passed on from LABAN1 represented the final position to be reached and the duration required to complete the movement. In order to know the exact position of the linb at any point in time (e.g. in a frame), the values of φ, ψ and θ at that moment, had to be known. These values φ, ψ and θ were named current time values for they represented the state of the limb at the desired time interval, not the ultimate position reached.

Theory of the current time values: The theory is based on the following assumptions. A movement occurs in a plane and each segment of the movement must remain in that plane. There exists an angle between the initial and final positions of the movement. At the end of a frame, there is an angle between the initial and current time positions, which is a fraction of the first angle. To calculate the current time position, the current time angle is first calculated using linear interpolation. Since the normal of the plane is known, the current time values of φ, ψ and θ can be calculated. The mathematics involved are very similar to that used in fold calculations on LABAN1. For each calculation of current time values of φ and ψ, a current time value of θ has to be calculated as well.

If a bodypart is either part of the torso or the proximal section of the limbs, the following procedure is used. The initial (previous current time) position of the bodypart is represented in Figure 12 by PR, PO represents the final position (PR = PQ = PO). Angle OPR is the total angle of movement between initial and final positions(= β). Angle RPQ represents the amount moved in one frame (current time angle). The normal to the plane PRQ is obtained by taking the cross-product of PR and PO). The lengths of PS and SQ can be obtained because angle RPQ is known. The directional cosines of PQ can be calculated and from there, the values of φ, ψ calculated for the position.

For lower sections of limbs, the following procedures are used to calculate the φ, ψ values.

PR is the current time position of the upper section of the limb (LMUP in the program). Angle PRQ is the interpolated value of the current time angle between the upper and lower sections. The normal to the plane is the normal to the current time position of the upper part of the limb, PR. The directional cosine of RQ can be calculated, and the current time φ and ψ values of the lower section of the limb worked out subsequently.

Method of calculating current time values in LABAN2: The initial angle and the final angle were calculated and the current time value for the limbs were calculated.through linear interpolation. The routine NEWDA calculated these interpolations in a similar manner to the fold calculation used in LABAN1.

If a limb moved through Place High or Place Low, the θ value would change by π radians, and a flip in the limb would be noticeable. To accommodate this and to allow for a smooth transition, equivalent values which did not give rise to a flip were given to the φ and ψ values of a limb, whenever the limb had a φ value of ±π/2 radians.

(ii) Rectangular coordinate generation -- Once the current time values of φ, ψ and θ were known for each bodypart for a particular frame, the rectangular coordinates of each joint were calculated. The computer program set the coordinates of the first joint in the hierarchy at (0, 0, 0) and looped through this section of LABAN2, calculating the coordinates relative to the first set of coordinates.

The program also determined if a support duration was stored for a particular joint. If there was a support duration stored, the z-coordinate of this joint was set to zero to represent the floor (whose z-coordinate is treated as being zero). Then all previously calculated coordinates were readjusted to accommodate this change. Since most cases calculated have the support on the feet, certain provisions had to be made to insure that a gesture of a leg would not bring the foot through the floor (i.e. have a z-coordinate which is a negative value).

(iii) Additional plotting points -- Additional points used for plotting purposes (right and left sides of the head, thumbs and palms of hands) were also calculated in LABAN2. The x-, y-, z- coordinates of each of the additional points were taken relative to the bound end of the limb in question (head or hand) and were part of the initial data read in by LABAN1 and passed on to LABAN2. By applying the transformation matrix A (same as in LABAN1) rotations through the angles φ, ψ and θ were obtained. Using the φ, ψ and θ values of the head or hand, the coordinates of the specific additional points were obtained (using subroutine TRDSP).

(iv) Transfer of data -- Once these coordinates were calculated, all the information needed to plot the particular frame was written onto a file for use by the next section of LABAN (LABANPL).

(v) Summary -- Section two of LABAN, LABAN2- (1) calculated the current time values of φ, ψ and θ values; (2) worked out rectangular coordinates of each joint for each frame of a beat-step; (3) calculated the coordinates of the additional points (used for plotting); and (4) stored the data of the previously calculated information as arrays, and wrote the current time values on file. Reiteration of LABAN2 continued for all the frames of any particular beat-step. Once the beat-step was completed, all the arrays concerned with the completed beat-step (φ, ψ and θ and the duration) were transferred to another set of arrays (called previous data arrays) and the program was looped through again until the end of the data from LABAN1 was reached.

4. Graphic Output

(a) Introduction

This section read in the rectangular coordinates of each joint for a particular frame, calculated the projection of the x-, y-, z- coordinates of each joint onto a plane Y =0, using previously supplied information so as to determine the height, distance and angle of the performer (stickfigure) from the camera (apparent viewpoint of viewers of the ultimate product -- an, animated film), and plotted out a stickfigure drawing which diagrammed this information.

(b) Outline of LABANPL (Section three of LABAN)

(1) General theory of projections -- Projection of a point (X_p,Y_p,Z_p) onto a plane Y_s= 0 from a point (X_c,Y_c,Z_c) is the point (X_s,Y_s,Z_s) where

  Xs = Xc + λ(Xp - Xc)     (1)
  Ys = Yc + λ(Yp - Yc)     (2)
  Zs = Zc + λ(Zp - Zc)     (3)

Because Ys=0.
  λ = -Yc/(Yp-Yc)     (4)
  
Then

Xs = Xc - Yc(Xp-Xc)/(Yp-Yc)    (5)

Zs = Zc - Yc(Zp-Zc)/(Yp-Yc)    (6)

However (X_p,Y_p,Z_p) might not always be in the same set of axes as (X_s,Y_s,Z_s). In this case (X_p,Y_p,Z_p) must be transformed.

Using Figure 14,

  Xp = -NP      (7)
  Yp = ON      (8)
  Zp = ZN      (9)

Using (7)

Xp = -QP-QN = -XN ⋅ cosφ -YN ⋅ sinφ   (10)

Using (8)

Yp =  OL-NL = -YN ⋅ cosφ -XN ⋅ sinφ   (11)

By substituting these values of X_p, Y_p and Z_p in equations (5) and (6), the projected point (X_S, Y_S, Z_S) can be found.

(ii) Method of calculating projections of coordinates in LABANPL

The point (X_p, Y_p, Z_p) represented a point on the stickfigure calculated in LABAN2. Point (X_c, Y_c, Z_c) represented the camera and had the coordinates (projected onto the plane v_s = O of the plotter) of. (0, r_c, h_c), where r_c represented the distance of the camera from the stickfigure and h_c represented the height of the camera above ground level. These were the names assigned to these parameters in the program LABANPL, and were initially entered into the program at the beginning of LABAN1 or at the start of LABANPL.

The subroutine PROJ calculated the projection of the points passed on from LABAN2, onto a plane Y = 0. The plotter's X-axis and the stickfigure's X-axis were in different directions, because when viewing the stickfigure from the front, its right became left and left became right.

A stage (five points on the plane Z = 0) was also drawn, in order to provide additional visual cues.

(iii) Other features of LABANPL -- If no plotting was desired, LABANPL skipped the plotting routines and only listed the rectangular coordinates of each joint, as passed on from LABAN2, and each joint's projected coordinates as calculated in LABANPL. If only specific frame information was wanted, this was done by supplying special data cards which were read at the start of LABANPL.

Evaluation Procedure

The computer program LABAN was used to interpret movement commands given in specially coded Labanotation commands. A Calcomp plotter, available at the Simon Fraser University Computer Centre, was used to produce the individual frames of a film. Each frame was numbered and drawn in black ink on 12 inch wide white paper, using a pen size of 0.5 mm. In order to photograph the frames, conventional animation techniques were used. Each frame had to be made into a separate 9" by 12" sheet. Instructions to the plotter allowed for this, and a line was drawn separating each frame from the next, at a distance of 10 inches. Appendix D gives samples of the plots.

Animation stands have specially constructed bars at the top of the photographic area, so special paper had to be attached to the top of each frame drawing. The stage remained stationary throughout the dance, so its corners were used as reference points in aligning each frame drawing with the next. The stand in the Simon Fraser Film Workshop produced the most aesthetic images using a size nine field. The camera used was a 16 mm Bolex reflex with single frame shutter capability using black and white film (TRI-X reversal, with an ASA of 160).

The conventional technique of photographing each frame twice was used, resulting in twelve image changes per second, with a cine rate of twenty-four per second. (More stable perceptual images arise in the case of doubling, and work on the part of the animator is substantially reduced.)

The same movements, coded in Labanotation, were danced by a dancer and these were also photographed on 16 mm film. Specific coordinates (duplicating those points of the computer derived stickfigure drawings) were obtained from each frame of the dancer film using a Vanguard Motion Analyzer. The coordinates were punched on cards and a plotting program was written to have the Motion Analyzer stickfigure drawings plotted on the Calcomp plotter. This was done to produce two sets of similar looking figures. The same animation techniques were used to produce a 16 mm black and white film of the Motion Analyzer derived films, using the same camera and film type.

Both films were made into film loops to allow viewing of the movements several times in quick succession. The two loops were shown to forty assessors. All but three had had at least one course in beginning dance at Simon Fraser University. The other three were professional dancers. A questionnaire was distributed before the showing of each loop. It asked assessors to rate the animation, timing of the movements, clarity, drawing and movements of the figure, using a five-point scale.

Questions requiring written answers were also included in the questionnaire. It was felt that these types of answers would provide valuable information on the acceptability of the films, even though they were not amenable to rigourous statistical analysis. Each film, being only eight seconds long, was shown fifteen times in rapid succession providing the assessors a chance to fully examine the contents of each film.

Analysis of Data

A sign test was applied to every assessor's responses. The direction of the differences, not the quantitative difference, was considered. The ratings of the Motion Analyzer derived film were compared with the computer derived film. If the rating of the former was higher, a positive sign was given; if the rating was lower, a negative sign was given. If both were rated equal, a zero score was assigned and the total number of pairs reduced when doing the statistical analysis for that question. [Seigel, 1956].

Table II shows the results of the questions for the Motion Analyzer film and the computer derived film, giving totals for each rating for each question.

2. TOTALS FOR COMPUTER DERIVED FILM ASSESSMENTS AND MOTION ANALYSER FILM ASSESSMENTS FOR EACH RATING

Computer derived film ratings are on the left hand side of each column; the Motion Analyser film ratings on the right side of each column.

See Appendix C for the text of the questionnaires.

Table III shows the total of positive and negative signs and the probability at the 5% level of significance. Table IV shows the results of the assessments as to how mechanical looking the movements appeared to each assessor. The results of the sign tests, as well as a sample of the questionnaire are listed in Appendix C.

TABLE III: DATA FROM THE SIGN TEST (5% LEVEL OF SIGNIFICANCE)

TABLE IV: ASSESSMENT OF QUESTION NINE OF THE QUESTIONNAIRE

The assessors were asked if they found the movement mechanical looking

V. CONCLUSIONS

Discussion of Results

There were several assumptions made when initially writing the LABAN interpreter program which were not anatomically or mechanically correct when describing human movement, but would perhaps be acceptable when looking at movement in animated films. In general, the assumptions made were simplifications; simplifying the stickfigure drawings to what might be the most basic acceptable form, and simplifying the velocity calculations for each movement.

1. Stickfigure Drawing

In order to produce as close an approximation to a human form as possible, curved, filled-in forms would be needed. Such drawings would: (a) be very costly to draw from the standpoint of computer time, (b) involve some type of solution of the hidden line problem.

It was decided to choose the simplest possible drawing which could show some three-dimensional characteristics. A stickfigure drawing with a torso, palms and head shapes, and straight lines for arms and legs was chosen. This figure could be drawn relatively simply using a series of vectors (each vector having eight points within it which were specified). The waist of the figure was a single point, obviously artificial. The head was a diamond shape, only a rough approximatjon of a general rounded shape (See figure 6.

2. Joint Articulation

To have anatomically and mechanically correct information would require knowledge of mass and volume of each bodypart. It was decided to eliminate all kinetic descriptions of movements and to use only kinematic descriptions. This allowed the limbs to be treated as straight rods having no mass. Therefore the only mathematics required were those which defined the positions of the limbs in space.

Limits to the range of movement of the elbow, knee, wrist and ankle were programmed and set at 165°. This was chosen from a purely visual point of view. These limitations were necessary in order to make the movements of the figure agree somewhat with what we would normally see when observing a person move. The articulations of the shoulders and hips were not limited in any way; it was felt. that the Labanotation commands used would never provide visually impossible movements at these two sets of joints. In addition, movements of the arms and legs did not produce accompanying movements of the torso.

3. Timing of Movements

Human movement is not always accomplished with a constant velocity. Typically, there.will be phases of acceleration, constant velocity and deceleration during a movement. However in LABAN, this was not observed. Each complete movement was divided up into equal time intervals and the following general formula was used in calculating the interval.

                Initial      (Final Position - Current Position)
Movement Per  = Starting  +  -----------------------------------
 Frame          Position     (Total Amount of Frames Needed to
                                 COMPLETE the Movement)

Animators do not always follow this general formula [Dunn, 1973]. They sometimes use geometric, rather than arithmetic progressions to split up the total time, giving a much clearer acceleration and deceleration. For purposes of this research, it was felt that the arithmetic progressions used might be sufficient to give information about the realized movements.

The assumptions outlined above could potentially contribute to a loss of information concerning the movements demonstrated in the animated films. To what extent this would occur, was unknown. The questionnaires given to evaluate the films examined the drawing and timing of the movements separately, as well as the clarity of the animation and tried to get an overall impression of the assessors' feelings towards the usefulness of such types of films.

4. The Questionnaire

There were four sections to the questionnaire: animation techniques, timing of the movements, stickfigure drawing and general appreciations.

(a) Animation Techniques

In answering how well an experienced dancer might reproduce the movements shown in the film strip, twenty-five assessors gave the same response for both sets of films, and fifteen assessors gave different answers. The differences are not significant at the 5% level and judging from the total number of people who rated the films, equally, this might indicate that the films may be sufficiently coherent to be used in learning a movement phrase.

There was a significant difference in the apparent smoothness of the two films. Most assessors found the Motion Analyzer derived film to be smoother. However, since both films were made using the same technique, the same camera, film and photographic techniques, the smoothness of the films might have been influenced by the contents of the films themselves. In general, however, judging from the results, most people viewing the films seemed to be able to accept animation as a method of portrayal of movement.

(b) Timing of the Movements

There was a significant difference in the ratings of impulses and accents as shown in both films. The Motion Analyzer derived film showed impulses and accents better than did the other film. But when asked how well an experienced dancer might be able to understand the timing, only fourteen assessors differed from their original answers and this difference was not significant. In the fourth section of the questionnaire, however, general written conments did concern themselves with the fact that the computer derived film showed mechanical looking movements, which might have partially influenced how assessors would understand the timing and rhythm of the movements of the film.

Because the LABAN program did have a simplified method of calculating velocity of the movements, the fact that people would find the movements somewhat mechanical was reasonable. Some comments mentioned that the computer derived film seemed to be very fast at the start. The lack of a more definite acceleration and deceleration would make the movements appear faster than they would normally appear if the acceleration and deceleration calculations had been closer to the manner in which human bodies are expected to move [Dunn, 1973].

Stickfigure Drawings

Significant differences were found in the ratings of the torso size, arm shape and arm connection to the torso, as well as how clearly the leg movements could be observed. The torso in the computer derived film had broader shoulders and was squarer looking (to use the words of one assessor).

The arms were straight lines and assessors felt that they could have been formed. The arm connection to the torso was also an area which had been simplified for programing ease. Assessors felt that the arm connections in the Motion Analyzer film did make a significant contribution to the naturalness of the image on the screen. The lack of associated shoulder girdle movement which should have accomplished some of the arm movements (particularly those which brought the arms overhead) was a shortcoming in the computer derived film.

There was a significant difference, in clarity of arm movements between both films. The arm movements appeared to be more visible and comprehensible in the Motion Analyzer film.

(d) General Appreciations

This section of the questionnaire tried to gain information about how useful the films might be as a cursory method of viewing movement. Subjective responses to questions were encouraged. When asked if they found the movements mechanical looking, nine assessors answered affirmatively for both types of films. Several mentioned the angularity of the stickfigure as being a reason for the mechanical looking movements. Eight assessors felt that only the computer derived movements appeared mechanical, two found only the Motion Analyzer derived movements mechanical.

Since both films were approximately the same shape and proportions, factors other than the angularity of the stickfigure may have affected the assessments. One assessor noted that the stillness of the non-moving bodyparts in the computer derived film was very artificial. Unfortunately the LABAN program has no method of producing associated shoulder or hip movements when the arms or legs moved. Another assessor stated that the timing was mushy. Impulses, often given at the start of movements in dance as an unconscious accent, were not programmed into LABAN, instead, the velocity was equal throughout a movement, a manner of moving not normally observed in dance. The differences between the ratings of the timing element of the films in the second section of the questionnaire were significant, and the method of velocity calculation in the program might have been a reason for this.

The dancer in the original film added embellishments to the movements that were part of her performing style and the film of her probably showed movements which were more complex than those produced by the computer. Rather than being more mechanical, the latter film could be thought of as being less complex, when compared to the Motion Analyzer derived film.

Thirty-one of the thirty five assessors who conmented on- the useability of these films as cursory methods of visualizing dance, felt that the films were extremely clear and an excellent method of showing the essentials of the movements.

Conclusions

There are three elements which could contribute to the loss of information in this research. The first is the use of film as a viewing medium which can destroy much of the dynamic qualities of movements. However, in this research, the use of film is completely unavoidable.

The second element lies in the use of stickfigure drawings. The figure might be too simple to be of use. The results of the questionnaires given showed that stickfigure drawings are comprehensive and coherent. The assessors realized and accepted the abstract human form represented by the stickfigure drawing, for the drawings had enough detail to be easily identified as a human form. Reference was made to the mechanical man feature of straight line drawings, suggesting that the body should be more rounded; however, it was also noted that the figure was still coherent.

Perhaps the element which contributed most to the loss of information was the method of velocity calculation in the LABAN program. The method used in the program may not have mirrored the usual movements of human bodies closely enough, giving rise to artificial looking movements in the computer derived stickfigure drawings. Animator's rule of thumb of geometric progressions for interpolation of time intervals are more acceptable to observers than the arithmetic progression used to split up the time required to go from position to position, as in the program.

In analyzing the direction and level commands the program did provide adequate interpretations of the Labanotation symbols, for the assessors felt that they could recreate the movements seen on both films equally well. In general, no one element proved to be detrimental to the overall comprehension of the movements of the figures in the films. Both types of films were judged as satisfactory by the majority of assessors.

In conclusion, it has been demonstrated that it is possible to write a program to interpret selected Labanotation commands and produce stickfigure drawings, which when viewed as an animated film, adequately represent the movements notated.

The development of a computer system which could interpret movement notation (specifically Labanotation) is feasible. Further work on the use of Labanotation symbols, rather than codes, as the method of entering commands into the system should be done. The way notation is handled in labanotation is by symbols, and their use would make an interpreter computer system more inviting. Undoubtedly, the bulk of any further work would have to be done in the incorporation of a larger set of Labanotation commands. In order for the system to be useable, additional movement description possibilities are necessary. To provide a general mathematical analysis of notion description, however, would require much work, for in this type of description, the direction of movement, rather than the specific position, is stated. Real-time displays of the interpreted movements should also be part of a fully developed system. Some sort of cathode ray tube device would be required.

Making the reconstruction of notated movement scores simpler might encourage their use by dancers, choreographers and directors. Familiarity with Labanotation might encourage these same people to develop literacy, thus providing dance with a reliable, uniform notation system it still requires.

BIBLIOGRAPHY

American Academy of Orthopaedic Surgeons (1965). Joint Motion - Method of Measuring and Recording. Chicago, Ill, American Academy of Orthopaedic Surgeons.

Causley, Marguerite (1967). An Introduction to Benesh Movement Notation. London: Max Parrish.

Cunningham, Merce (1973). Personal communication.

Dance Notation Bureau (1973). Catalogue New York: Dance Notation Bureau.

Dunn, John (1973). Personal-communication.

Eshkol, Noa and Abraham Wachmann (1958). Movement Notation. London: Weidenfeld and Nicolson.

Eshkol, Noa; Peter Melvin; Jean Michl; Heinz Von Foerster and Abraham Wachmann (1970). Notation of Movement. University of Illinois, Dept Electrical Engineering, Biological Computer Laboratory, Report BCL 10.0.

Fulkerton, Louis (no data, circa 1967). A Dance Notation Computer Program. Unpublished proposal submitted to the Dance Notation Bureau.

Hackney, Peggy; Sally Hanno, and Muriel Topaz (1970). Correspondence Course in Labanotation. New York: Dance Notation Bureau.

Hackney, Peggy (1972). Personal communication.

Hutchinson, Ann (1967). Choreography and, Computers: A Reply, , Dance Magazine. 41, (1), 45-46 and 81-82.

Hutchinson, Ann (1970). Labanotation: The System of Analyzing and Recording Movement. second edition , New York: Theatre Arts Books.

Hutchinson, Ann (1972). Personal communication.

Jay, Leticia (1957). A Stickman Notation, Dance Observer. (1), 7-8.

Kallis, S.. (1969). Motion Picture Animation by Computer, Computer and Automation, 18, (12), 30-34.

Laban, Rudolph (1956) Principles of Dance and Movement Notation. London: Macdonald and Evans.

McCrea,, William (1953). Analytical Geometry of Three Dimensions. Edinburgh: Oliver and Boyd.

McGraw, Charles (1964). Scoreography. Ann Arbor, Mich: Edward Brothers (Lithographers) .

Morris, Margaret (l928). The Notation of Movement. London: Kegan Paul, Trench Truber and Co.

Nikolais, Alwin (1948). A New Approach to Dance Notation, Theatre Arts. 32, (2), 63-66.

Preston-Dunlop, Valerie (1969). A Notation System for Recording Observable Motion, International Journal of Man-Machine Studies. 1 361-386.

Seigel, S. (1956). Nonparametric Statistics for the Behavioral Sciences. London: McGraw-Hill.

Shapiro, Marla (1972). Personal communication.

Stepanov, V.I .. (1892). Alphabet of Movement of the Human Body. Translated by. Raymond Lister from the French Edition, Brooklyn: Dance Horizons, 1969.

Tetley, Glen (1948). 116-117. Choroscript, Dance Observer. 15, (9), 116-117.

Turnbaugh, Douglas B. (1970). Dance Notation: Potential and Problems, Dance Scope. Spring 1970, 39-47.

APPENDIX A - PROGRAM LISTING OF LABAN

The FORTRAN code below was not completely readable in the listing and there may be some errors in the text below. Some minor changes have been made. The major one is to remove some unused statement labels where a 3-way IF had been replaced by a logical IF statement that no longer needed the label.

C  LABANOTATION RECOSTRUCTION
C THIS PROGRAMME READS AND INTERPRETS SPECIALLY CODED LABANOTATION AND PRODUCES
C THE STICKFIGURE REPRESENTATION OF THE COMMANDS
C
C DIMENSION STATEMENTS
      DIMENSION JPHIA(35),JPSIA(35),JDURA(35),JTTA(35),JMOV(35)
      DIMENSION LPRS1(35),LPRS2(35),LNTHL(35),JTDIS(35),JTPRX(35)
C     (DIMENSIONED BY NUMBER OF LIMBS: NLMS)
      DIMENSION JPRS1(35),JPRS2(35),LIMBJ(23),ISDUR(23),JSDUR(23)
      DIMENSION IX(3,35),IEXCO(3,6),IEXTL(3)
C     (DIMENSIONED BY NUMBER OF JOINTS: NJTS)
      DIMENSION LIMND(13),ISBAS(13),JBND(13)
C     (DIMENSIONED BY NUMBER OF COMPLEX LIMBS: NPRIS - NSIMP)
      DIMENSION IDNAM(9),IDANG(9),ILNAM(3),ILANG(3)
C     (DIMENSIONED BY NUMBER OF DIRECTIONS,LEVELS)
      DIMENSION IS(8),IXD(3),ISIMP(40),ICAM(9)
      DIMENSION IDR(6),ILVL(6)
      DIMENSION MOD1(10),MOD2(10),MODJBT(10),XI(3,3)
      DATA IBLANK/'    '/
C     (WORKING STORAGE)
C
C -----------------------------INCNT------------------------------------ 
C INIT BEAT AND FRAME COUNTERSALIZE
C2345678901234567890123456789012345678901234567890123456789012345678901234567890
      API=3.14159
      JB=0
      JMOD=0
      FRAME=1.0
C
C READ IN PREDEFINED DATA
C NUMBER OF LIMBS:SIMPLE COMPONENTS OF LIMBS; JOINTS; REPRESENTED BY
C NLMS,NSIMP, NJTS; MAXIMUM DRAWING ERROR (MXERR), AND BOUND END OF
C TORSO (JTBND)
      READ(5,10)NSIMP,NLMS,NJTS,MXERR,JTBND
  10  FORMAT(12I5)
C
C READ IN LIMB CONSTANTS: PRESIGNS FOR LIMBS(LPRS1,LPRS2),LENGTH OF LIMB
C (LNTHL), DISTAL AND PROXIMAL JOINTS FOR LIMB (JTDIS,JTPRX),
C NUMBER OF COMPONENT PARTS (LN), LISTING OF COMPONENT PARTS(IS) ---
C ONLY FOR COMPLEX LIMBS.  FOR SIMPLE LIMBS, IS(1), IS(2), IS(3) ARE
C USED TO CONTAIN ASSUMED INITIAL DEFAULT VALUES OF PHI, PSI, THETA
C JTB IS THE NEW BOUND JOINT IN THE TORSO IF THIS IS CHANGED
  19  IBAS=0
      DO 45 LL=1,NLMS
      JDURA(LL)=0
      JMOV(LL)=0
      READ(5,20)L,LPRS1(L),LPRS2(L),LNTHL(L),JTDIS(L),JTPRX(L),LN,IS,JTB
      WRITE(5,20)L,LPRS1(L),LPRS2(L),LNTHL(L),JTDIS(L),JTPRX(L),LN,IS,JT
     *B
C
  20  FORMAT(I5,2X,A2,A1,13I5)
      IF(LN-1)40,40,25
  25  MM=L-NSIMP
      LIMND(MM)=LN
      DO 30 LS=1,LN
  30  ISIMP(IBAS+LS)=IS(LS)
      ISBAS(MM)=IBAS
      IBAS=IBAS+LN
      IF(JTB)35,33,35
  33  JTB=JTBND
  35  JBND(MM)=JTB
      GOTO 45
  40  JPHIA(L)=IS(1)
      JPSIA(L)=IS(2)
      JTTA(L)=IS(3)
  45  CONTINUE
      READ(5,50)IEXCO,IEXTL
  50  FORMAT(18I4,3I2)
C
C READ IN RELATED LIMB CONSTANTS FOR USE WITH ROTATIONS
C READ IN JOINT CONSTANTS: PRESIGNS FOR JOINTS(JPRS1,JPRS2),CORRESPONDING
C LIMB REFERRED TO BY PRESIGN(LIMBJ), DIRECTIONAL ANGLE(PHI) CHANGES
C DIRECTEDN(L/N)=IDANG,IDNAM,  DIRECTIONAL ANGLE (PSI) CHANCES LEVEL
C (L/N)-- ILANG,ILNAM
      DO 51 JJ=1,NJTS
      JSDUR(JJ)=0
      READ(5,20)J,JPRS1(J),JPRS2(J),LIMBJ(J)
      WRITE(6,20)J,JPRS1(J),JPRS2(J),LIMBJ(J)
  51  CONTINUE
      READ(5,60)IDNAM,ILNAM,IDANG,ILANG
      WRITE(3)NSIMP,NLMS,NJTS,JTBND,MXERR,
     *  (LNTHL(L),JTDIS(L),JTPRX(L),L=1,NSIMP) ,IEXCO,IEXTL
  60  FORMAT(9(3X,A2),3(4X,A1)/12I5)
C
C READ IN DANCE CONSTANTS AND CAMERA POSITIONS
C BEATSTOPS/BEAT (IBSBT), TIME SIGNATURE (KYTIM), FRAMES/SEC(ICINE),
C IPLOT IS THE NUMBER OF BEATS IN THE DANCE
C BEATSTEPS/SEC(BSPSC), FRAMES/SEATSTEP(FRATO) ARE COMPUTED
      READ(5,10)IBSBT,KYTIM,ICINE,IPLOT
      READ(5,10) ICAM
      BSPSC=FLOAT(IBSBT-KYTIM)/60.
      FRATO=FLOAT(ICINE)/BSPSC
      BSPBT=IBSBT
      WRITE(3) IBSBT,KYTIM,ICINE,IPLOT,ICAM
C
C--------------------------INJ-----------------------------------
C READING IN THE COMMANDS
C NT IS KEY FOR SUPPORT OF GESTURE, AND IS 0 FOR END OF DATA
C IBEAT, BTFR ARE BEAT NUMBER AND PART OF BEAT; IBTS, DURFR ARE DURATION
C IN BEATS AND PART OF A BEAT
C IST IS THE STARTING BEATSTEP, IDUR IS THE DURATION IN BEATSTEPS
C IEND=1 SIGNALS END OF INPUT DATA
  100 READ(5,111)NT,IBEAT,BTFR,IPRS1,IPRS2,IBTS,DURFR, MODIF ,
     *(IDR(I),ILVL(I),I=1,6)
  111 FORMAT(I2,I3,F3.2,1X,A2,A1,I3,F3.2, I4,6(1X,A2,A1))
      BE=FLOAT(IBEAT)+BTFR
      DE=FLOAT(IBTS)+DURFR
      IST=BE*BSPBT+0.001
      IDUR=DE*BSPBT+0.001
  124 IF(IST-JS)199,125,200
  125 WRITE(6,112)BE,IPRS1,IPRS2,DE,(IDR(I),ILVL(I),I=1,6),NT,MODIF
  112 FORMAT(F6.2,1X,A2,A1,F6.2,6(1X,A2,A1), 2I4)
      IF(NT)130,131,131
  130 JB=-1
      WRITE(3)(JB,J=1,113)
      REWIND 3
      WRITE(6,129)
  129 FORMAT(' LEAVING STAGE ONE')
      STOP
C 
C ==============================CNVPS==========================
C CONVERT PRESIGN INTO NUMBER OF BODYPART JBPT, WITH JTP=0 FOR A JOINT
C AND JTP=1 FOR A LIMB
  131 JTP=0
      DO 135 JBPT=1,NJTS
      IF(IPRS1.NE.JPRS1(JBPT))GO TO 135
      IF(IPRS2.EQ.JPRS2(JBPT))GOTO 150
  135 CONTINUE
      JTP=1
      DO 145 JBPT=1,NLMS
      IF(IPRS1.NE.LPRS1(JBPT))GOTO 145
      IF(IPRS2.EQ.LPRS2(JBPT))GOTO 150
  145 CONTINUE
C ERROR: INVALI PRESIGN
      IER=1
      WRITE(6,147)IER,IPRS1,IPRS2
  147 FORMAT(I5,1X,A2,A1)
      STOP
C =========================END OF CNVPS=========================
C
  150 IF(NT)199,180,155
C
C IF THE NT INDICATES A GESTURE
  155 IF(JTP)161,160,161
  160 JBPT=LIMBJ(JBPT)
  161 IF(NT-2)170,162,162
C STORAGE OF MODIFICATIONS
C  NT:    CODE FOR MODIFICATIONS STORED IN ARRAY, MOD1
C MODIF:  DEGREES OF MODIFICATIONS STORED IN ARRAY MOD2
C MODJBT: ARRAY OF BODYPARTS BEING MODIFIED
C JMOD IS THE COUNTER TO INDICATE THE NUMBER OF MODIFICATIONS IN EACH
C BEATSTEP
  162 JMOD=JMOD+1
      MOD1(JMOD)=NT
      MOD2(JMOD)=MODIF
C STORAGE OF BODYPART, DEPENDING ON WHETHER IT'S A  LIMB OR JOINT
      IF(JTP)163,163,164
C JOINT AS INPUT
  163 MODJBT(JMOD)=JBPT
      GOTO 170
  164 IF(JBPT-NSIMP)167,167,165
C (LIMB IS A COMPLEX ONE)
  165 IBAS=ISBAS(JBPT-NSIMP)
      JJC=ISIMP(IBAS+1)
      MODJBT(JMOD)=JJC
      GOTO 170
C ERROR:
  167 WRITE(6,168)
  168 FORMAT(' CONTRACTION OF SIMPLE LIMB')
      STOP
C
C ============================CNVOL==============================
C CONVERT DIRECTION LEVEL INTO DIRECTIONAL LEVELS AND
C DETERMINATION OF INTERMEDIATE DIRECTIONS
C INTERMEDIATE DIRECTIONS ARE GIVEN BY A SERIES OF COMPONENTS OF THE
C DESIRED POSITION. TO FIND THE DESIRED POSITION, THE AVERAGE OF THE
C  COMPONENT DIRECTIONS IS TAKEN
C IF THERE IS MORE THAN ONE DIRECTION/LEVEL COMMAND INTERMEDIATE
C DIRECTIONS HAVE BEEN GIVEN
C
C
  170 JPHD=360
      JPSD=0
      DO 179 J=1,6
C  THERE WILL NOT BE MORE THAN SIX INTERMEDIATE COMPONENT DIRECTIONS
C THIS COULD REPRESENT THE ABILITY TO SPECIFY UP TO 7 DEGREES CHANGE
      IDRJ=IDR(J)
      IF(IDRJ.EQ.IBLANK) GOTO 1736
C THE END OF THE COMPONENT DIRECTION COMMANDS HAS BEEN REACHED
C     NOT BLANK
      DO 171 K=1,9
      IF(IDRJ .EQ.IDNAM(K)) GOTO 173
  171 CONTINUE
C ERROR STATEMENT INVALID DIRECTION
      IER=2
      WRITE(6,172)IER,IDR
  172 FORMAT(I5,1X,A2)
      STOP
C TAKE AVGE OF DIRECTIONS READ SO FAR. NOTE THAT PLACE DOES NOT
C AVERAGE -- OTHER DIRECTION REMAINS
  173 IF(K-9)1731,1735,1731
 1731 IF(JPHD-360)1733,1732,1733
 1732 JPHD=IDANG(K)
      GOTO 1735
 1733 JPHD=JPHD+IFIX(FLOAT(IDANG(K)-JPHD)/FLOAT(J))
 1735 DO 174 N=1,3
      IF(ILVL(J).EQ.ILNAM(N)) GOTO 175
      IF(ILVL(J) -ILNA1(N))174,175,174
  174 CONTINUE
C ERROR STATEMENT: INVALID LEVEL
      IER=3
      WRITE(6,172)IER,ILVL
      STOP
  175 IA=ILANG(N)
      IF(K-9)178,177,178
  177 IA=IA+IA
C PLACE PSI IS DOUBLED
  178 JPSD=JPSD+IFIX(FLOAT(IA-JPSD)/FLOAT(J))
  179 CONTINUE
 1736 IF(J-2)1740,1737,1737
C ============================END OF CNVOL====================
C
 1737 JMOV(JBPT)=1
 1738 JPHIA(JBPT)=JPSD
      JPSIA(JBPT)=JPSD
 1739 JDURA(JBPT)=IDUR
      GOTO 100
C NO DIRECTION LEVEL COMMANDS GIVEN AT  TIME OF MODIFICATION
C THE J WILL BE EQUAL TO ONE
 1740 IF(JBPT-NSIMP)1739,1739,1741
 1741 JPHD=JPHIA(JJC)
      JPSD=JPSIA(JJC)
      GOTO 1738
C
C IF THE NT INDICATES A SUPPORT
  180 IF(JTP)184,182,184
C SUPPORT IS A JOINT(JTP=0)
  182 JSDUR(JBPT)=IDUR
      GOTO 100
C SUPPORT IS A LIMB(JTP=1)
  184 JSDUR(JTPRX(JBPT))=IDUR
      JSDUR(JTDIS(JBPT))=IDUR
      GOTO 100
C ERROR:TIME SEQUENCE CHECK
  199 WRITE(6,197)
  197 FORMAT(25X,'STOP1000')
      STOP
C
C---------------------COXSIM-------------------
C CHANGES THE COMPLEX LINES TO SIMPLE BODYPARTS FOR BEATSTEO J
C
  200 LL=NSIMP+1
      DO 240 M=LL,NLMS
      JP=JDURA(M)
      IF(JP)215,240,215
  215 MM=M-NSIMP
      JTBND=JBMC(MM)
      NP=LIMND(MM)
      IBAS=ISBAS(MM)
      JPH=JPHIA(1)
      JPS=JPSIA(1)
      DO 230 N=L,NP
      JSMPL=JSIMP(N+IBAS)
      JS=JDURA(JSMPL)
      IF(JS) 230,220,230
  220 JDURA(JSMPL)=NP
      JMOV(JSMPL)=1
      JPHIA(JSMPL)=JPH
      JPSIA(JSMPL)=JPS
  230 CONTINUE
  240 CONTINUE
C
C---------------------SET UP DEFAULT VALUES FOR INITIAL POSITION
C
  249 IF(JB) 280,250,280
  250 DO 270 KL=1,NSIMP
      IF(JDURA(KL))270,260,270
  260 JDURA(KL)=1
  270 CONTINUE
C
C-----------AMOUNT OF  ROTATION ALONG AXIS OF LIMB WORKED OUT HERE ------
C----------
C---TORSO---
C-----------
C NO TORSO ROTATIONS ALLOWED FOR YET
  280 DO 287 K=1,10
      IF(JMOV(K))285,287,285
  285 JTTA(K)=0
  287 CONTINUE
C
C***LIMBS***
C***********
      DO 400 K=11,20,3
      JMOVS=JMCV(K)+JMOV(K+1)+JMOV(K+2)
C IF NO MOVEMENT KEEP OLD THETAS, ELSE CALCULATE THEM IN 'ROTAT'
      IF(JMOVS)290,400,290
  290 CALL ROTAT(JPHIA,JPSIA,JTTA,K)
  400 CONTINUE
C -----------------CONTRACTIONS----------------
      IF(JMOD)338,338,500
  500 DO 599 JM=1,JMOD
      MODFN=MGO1(JM)
      IF(MODFN-3)501,501,600
  501 MODB=KBDJB(JM)
C AB IS LENGTH OF FIRST LIMB
C B IS DISTAL END OF FIRST LIMB, A IS PROXIMAL END OF THIS LIMB
      AB=LNTHL(MODB)  
      IB=JTBIS(MODB)
      IS=JTPRX(MODB)
C MODB1 IS THE ADJACENT LIMB DOWNWARDS. BC IS ITS LENGTH, C, ITS DISTAL END
      MODB1=MODB+1
      BC=LNTHL(MODB1)
      IC=JTBIS(MODB1)
C CHECK TO SEE THAT DISTAL OF FIRST IS EQUAL TO PROXIMAL OF SECOND LIMB
      IF(JTPRX(MODB1)-IB)620,510,620
  510 JDURA(MODB1)=JDURA(MODB)
C MODB2 IS 'AUXILLARY LIMB' EG. LIKE HAND AND FOOT
      MODB2=MODB+2
      IF(JTPRX(MODB2)-IC)535,520,535
C THE AUXILLARY LIMB IS ATTACHED TO THE SECOND LIMB
  520 IF(JFHIA(MODB1)-JPHIA(MODB2))530,525,530
  525 IF(JPSIA(MODB1)-JPSIA(MODB2))530,527,530
  530 IF(JDURA(MODB2))535,527,535
  527  JDURA(MODB2)=JDURA(MODB)
C
C JMODT=1 REPRESENTS AN AUXILLARY LIMB THAT MUST BE CHANGED AFTER MODIFICATION.
C JMODT=0 MEANS THAT THERE IS NO CHANGE TO THE AUX LIMB AFTER MODIFICATION
C OR THAT WE ARE DEALING WITH CONTRACTION AT ANKLE OR WRIST.
C CD IS LENGTH OF AUXILLARY (BRD) LIMB IF IT IS INVOLVED IN CONTRACTION
      JMODT=1
      CD=LNTHL(MODB2)
      GOTO 540
  535 JMODT=0
      CD=0.0
C
C CALCULATION OF DEGREES OF MODIFICATION
C THE DEGREES ARE GIVEN AS INTEGERS WHICH DEFINE THE ANGLE OF CONTRACTION BETA
  540 DEG=MOD2(JM)
      IF(DEG-6.0)560,550,560
  550 PIX=DEG*API*23./24.
      GOTO 565
  560 PIX=DEG*API
  565 BETA=API-PIX/2.
      CALL COSIN (BETA,CSBTA,SNBTA)
C
C CALC DIRECTION COSINES OF UNCONTRACTED LIMB, AND OF NORMAL TO LIMB,
C AND SIGN OF NORMAL (-FOR CONTRACTION AT KNEE, ELSE +)
      CALL VECNML(JPHIA(MODB),JPSIA(MODB),JTTA(MODB),DCLX,DCLY,DCLZ,
     * DCNX,DCNY,DCNZ)
      FNML=SNML(MODB)
      IF(MODFN-2)600,2570,3007
C CALC DIPN COSINES DCRQ OF FOLDED LIMB MODB1
 2570 PR=AB
      QR=BC
      PS=PR-QR*CSBTA
      SQ=QR*SNBTA
      CALL DCS(PR,QR,0.0,PS,SQ,DCLX,DCLY,DCLZ, PNML,  DCNX,DCNY,DCNZ,
     *  DCRQX,DCRQY,DCRQZ, DCPQX,DCPQY,DCPQZ)
C  GET PHI, PSI,THETA OF MODB1 AND POSSIBLY MODB2 FROM D.C.'S DCPO
      CALL PHRSIA(DCRQX,DCRQY,DCRQZ,DCNX,DCNY,DCNZ,
     *                     JPNIA,JPSIA,JTTA,MODB1,JMODT)
      GOTO 599
C*****************FLEXION******************
C CHECKING FOR SUPPORT TO LIMB
 3007 IF(JSDUR(IB))3030,3030,3550
 3030 IF(JSDUR(IC))3570,3570,3560

C IA IS THE PROX JT. OF MODB, IB IS THE PROX. JT. OF MODB1, IC THE PRX, JT. OF
C MODB2  THEY ARE SET AROUND STATEMENT 501 IN MAIN PROGRAMME
 3560 JMODT=0
      CD=0.0
C IF IC IS A SUPPORT, THE AUXILLARY LIMB CANNOT BE INVOLVED IN CONTRACTION
      GOTO 3570
C ERROR
 3550 WRITE(6,3551)
 3551 FORMAT(' CANNOT FLEX LIMB AT A SUPPORTED JOINT')
      STOP
 3570 QR=BC+0.5*CD
      PQ=AB
      XT=(API-BETA)/2.
      TANNE=(PQ-QR)-TAN(XT)/(PQ+QR)
      YT=ATAN(TANNE)
      P=XT-YT
      R=XT+YT
      CALL COSIN(P,CSP,SNP)
      PR=QR-SNBTA/SNP
      PS=PQ-CSP
      SQ=PQ-SNP
C CALC DIRN COSINES DCPQ OF  1ST LIMB MODB,
C AND NEGATIVES DCRD OF DIRN COSINES OF SECOND LIMB MODB1
      CALL DCS(PR,QR,PQ,PS,SQ,DCLX,DCLY,DCLZ, -FNML,DCNX,DCNY,DCNZ,
     *DCRQX,DCRQY,DCRQZ, DCPQX,DCPQY,DCPQZ)
      CALL PHRSTA(DCPQX,DCPQY,DCPQZ, DCNX,DCNY,DCNZ, JPHIA,JPSIA,JTTA,
     *MODB,0)

C GET PHI,PSI,THETA OF MODE FROM D.C.'S DCPO
      CALL PHRSTA(-DCRQX,DCRQY,DCRQZ, DCNX,DCNY,DCNZ, JPHIA, JPSIA,
     *  JTTA,MODB1,0)
C
  599 CONTINUE
      JNCD=0
      GOTO 338
C ERRORS
  600 WRITE(6,610)MODFN
  610 FORMAT('INVALID NT ASSIGNMENT',I4)
      STOP
C ERROR
  620 WRITE(6,621) IB
  621 FORMAT(' CONTRACTION AT JOINT',I4,' IMPOSSIBLE')
      STOP
  338 WRITE(3)JB,(JPHIA(L),JPSIA(L),JTTA(L),JOURA(L),L=1,NSIMP),JSDUR,
     *JTBND
      WRITE(6,339)JS,(JPHIA(L),L=1,NSIMP),(JPSIA(L),L=1,NSIMP),
     *      (JTTA(L),L=1,NSIMP),(JDURA(L),L=1,NSIMP)
  339 FORMAT(I5,'  PHI ',22I5/5X,'  PSI ',22I5/5X,'THETA  ', 22I5/
     *5x,'  DUR   ',22I5//)
      JB=JB+1
C ********************************************************************
C ZERO ALL COMPLEX LIMBS
      DO 920 J=1,NLMS
      JMOV(J)=0
      IF(J-NSIMP) 905,905,903
  903 JDURA(J)=0
      GOTO 920
  905 JDM=JDURA(J)-1
      IF(JDM) 920,910,910
  910 JDURA(J)=JDM
  920 CONTINUE
      DO 940 J=1,NJTS
      JDM=JSDUR(J)-1
      IF(JDM) 940,930,930
  930  JSDUR(J)=JDM
  940 CONTINUE
      GOTO 124
      END
C
C-----SUBROUTINE ARMS(IPHI,IPSI,K,ITA)--------
      SUBROUTINE ARMS(IPHI,IPSI,K,ITA)
      IF(IPHI)20,35,20
  20  IF(IPHI-130)30,35,30
  30  IF(IPHI-36)40,35,40
C FRONT, BACK AND PLACE HAVE THETA=90
  35  ITA=90
      GOTO 60
  40  ITA=IPSI+90
C COMPLEX LIMBS
  60  IF(K-28)70,90,100
  70  IF(K-27)80,90,90
  80  IF(K-14) 90,100,100
C RIGHT SIDE OF THE BODY HAS DIFFERENT THETA
  90  ITA=360-ITA
 100  RETURN
      END
C------LEGS----
      SUBROUTINE LEGS(IPHI,K,ITA)
      IF(IPHI-90)10,20,20
  10  ITA=0
      GOTO 50
  20  IF(IPHI-270)40,10,10
  40  ITA=540-2*IPHI
  50  RETURN
      END   
C-----ROTAT------
      SUBROUTINE ROTAT(JPHI,JPSI,JTT,K)
      DIMENSION JPHI(22),JPSI(22),JTT(22)
      KPH=JPHI(K)
      KPPH=JPHI(K+1)
      KPPPH=JPHI(K+2)
      KPS=JPSI(K+1)
      KPPPS=JPSI(K+2)
C CHECK TO SEE IF FIRST PAIR SAME PHI,PSI
      IF(KPH-KPPH)295,292,295
 292  IF(KPS-KPPS)295,370,295
C DIFFERENT UPPER,LOWER DIRECTIONS
 295  PNML=SNKL(K)
C ARMS -- NORMAL POSITIVE X-DIRN FOR UPPER LOWER LIMB PAIR
C LEGS -- NORMAL NEGATIVE X-DIRN FOR UPPER,LOWER LIMB PAIR
C CALCULATE THETA FOR UPPER LOWER
C305  CALL CHCK(KPH,KPS,KPPH,KPPS,PNML,ITA,ITAP)
      CALL CHCK(KPH,KPS,KPPH,KPPS,PNML,ITA,ITAP)

      JTT(K)=ITA
      JTT(K+1)=ITAP
C ARE LOWER,EXTREMITY SAME PHI,PSI?
      IF(KPPH-KPPPH)315,310,315
 310  IF(KPPS-KPPPS)315,325,315
 315  CALL CHCK(KPPH,KPPS,KPPPH,KPPPS,+1.0,ITAP,ITAPP)
      JTT(K+1)=ITAP
 320  JTT(K+2)=ITAPP
      GOTO 330
C SAME LOWER,EXTREMITY (DIFFERENT UPPER,LOWER)
 325  ITAPP=ITAP
      GOTO 320
C CHECK IF ARMS
 330  IF(K-16)335,335,399
C YES, ARMS, MUST CHECK ADMISSIBLE TANGE OF LOWER ARM THETA
 335  IF(K-13)340,340,345
C RIGHT SIDE
 340  LOW=ITA-180
      GOTO 350
C LEFT SIDE
 345  LOW=ITA
 350  IDELTA=ITAP-LOW
C     (OK ITAP LT 360; -180 LT LOW LT 360; SO -360 LT IDELTA LT 540)
      IF(IDELTA.GE.360)IDELTA=IDELTA-360
      IF(IDELTA.LT.0)IDELTA=IDELTA+360
C     (0 LT IDELTA LT 360)
C CHECK RANGE
      IF(IDELTA.LE.180) GOTO 399
C OUT OF RANGE, SUBTRACT 180 TO GET A POSSIBLE SOLUTION
C365  IF(ITAP.LT.180)ITAP=ITAP+360
      IF(ITAP.LT.180)ITAP=ITAP+360

      JTT(K+1)=ITAP-180
      IF(ITAPP.LT.150)ITAPP=ITA+360
      JTT(K+2)=ITAPP-150
      GOTO 399
C
C THE UPPER,LOWER ARE SAME,TRY LOWER EXTREMITY
 370  IF(KPPH-KPPPH)375,372,375
 372  IF(KPPS-KPPPS) 375,380,375
C DIFFERENT LOWER,EXTREMITY (SAME UPPER,LOWER)
 375  CALL CHCK(KPPH,KPPS,KPPPH,KPPPS,+1.0,ITAP,ITAPP)
      JTT(K)=ITAP
      JTT(K+1)=ITAP
      JTT(K+2)=ITAPP
      GOTO 399
C
C ALL THREE SAME PHIS,PSIS
C CHECK IF LEGS OR ARMS
 380  IF(K-17)390,385,385
C LEGS
 385  CALL LEGS(KPH,K,ITA)
      GOTO 395
C ARMS
 390  CALL ARMS(KPH,KPS,K,ITA)
 395  JTT(K)=ITA
      JTT(K+1)=ITA
      JTT(K+2)=ITA
 399  RETURN
      END
C--------------CHCK----------------
      SUBROUTINE CHCK (IPHI,IPSI,IPHIPR,IPSIPR,FNML,ITA,ITAP)
C FINDS NORMAL TO FL,FM,FN TO LIMB PAIR (PHO,PSI), AND (PHITPR,PSIPR)(EITH SIGN
C FNML) AND HENCE OBTAINS CORRESPONDING THETA ANSD THETAPR FROM ;CHECK' SUBROUTIN
C
      APHPR=RAD(IPHIPR)
      APSPR=RAD(IPSIPR)
      APH=RAD(IPHI)
      APS=RAD(IPSI)
      CALL COSIN(APHPR,CSPHP,SNPHP)
      CALL COSIN(APSPR,CSPSP,SNPSP)
      CALL COSIN(APH,CSPH,SNPH)
      CALL COSIN(APS,CSPS,SNPS)
C              *
      VECX=CSPS*SNPH
      VECY=CSPS*CSPH
      VECZ=-SNPS
      VECPX=CSPSP*SNPHP*FNML
      VECPY=CSPSP*CSPHP*FNML
      VECPZ=-SNPSP*FNML
      CALL CROSP(VECX,VECY,VECZ, VECPX,VECPY,VECPZ, DCNX,DCNY,DCNZ)
      ITA=ITHETA(DCNX,DCNY,DCNZ,CSPH,CSPS,SNPH,SNPS)
      ITAP=ITHETA(DCNX,DCNY,DCNZ,CSPHP,CSPSP,SNPHP,SNPSP)
C (RESULTS ARE POSITIVE)
      RETURN
      END
C
      FUNCTION ITHETA (FL,FM,FN,CSPH,CSPS,SNPH,SNPS)
C THIS ROUTINE WAS ORIGINALLY SAME AS CHECK. THIS ROUTINE FINDS THE THETA WHICH
C WHEN COMBINED WITH THE PHI, PSI YIELDS THE  GIVEN NORMAL (FL,FM,FN)
      API=3.14159
      U=CSPH*SNPS
      V=SNPH*SNPS
C
C WORK OUT FIRST SET OF RATIOS
      P1=(FM-CSPS)+FN-U
      P2=FN*SNPH
      IF(ABS(P1)+ABS(P2)-0.001) 15,15,10
  10  PONE=P1
      PTWO=P2
      GOTO 35
C
C IF THE FIRST RATIO ZERO, WORK OUT SECOND
C
  15  P3=FL*CSPS-FN*V
      P4=-FN*CSPH
      IF(ABS(P3)+ABS(P4)-0.001) 25,25,20
  20  PONE=P3
      PTWO=P4
      GOTO 35
C
C IF SECOND RATIO ZERO, WORK OUT THIRD
  25  P5=SNPS*(FN*SNPH-FL*CSPH)
      P6= FM*CSPH+FL*SNPH
C ??????????? was 33
      IF(ABS(P5)+ABS(6)-0.001) 35,35,30
  30  PONE=P5
      PTWO=P6
C PONE=0,PTWO NOT 0
  35  IF(PONE)120,110,120
 110  IF(PTWO)115,199,115
 115  TTAZO=API/2.
      GOTO 135
C
C FIRST = TO POSITIVE, PTWO=0
 120  IF(PTWO)130,125,130
 125  TTAZO=0.
      GOTO 135
C
C BOTH NOT ZERO
 130  TANTH=PTWO/PONE
      TTAZO=ATAN(TANTH)
C THETA LIES BETWEEN -90 AND 90)
      IF(TTAZO)133,135,135
 133  TTAZO=TTAZO+API
C
C USE NAN TO FIND TTAZO
 135  CALL COSIN(TTAZO,CSTA,SNTA)
      IF(ABS(FN)-0.001) 160,160,140
 140  CHCKN=-FN*CSPS*SNTA
      IF(ABS(CHCKN)-0.001)160,160,142
 142  IF(CHCKN)150,160,145
 145  THETA=TTAZO
      GOTO 195
 150  THETA=TTAZO+API
      GOTO 195
C
C USE M*M
 160  IF(ABS(FL)-0.001)180,180,170
 170  CHCKM=-(FM*SNPH*CSTA)-(FM*U*SNTA)
      IF(ABS(CHCKM)-0.001)180,180,172
 172  IF(CHCKM) 150,180,145
C USE L*L
 180  IF(ABS(FL)-0.001)199,199,190
 190  CHCKL=FL*CSPH*CSTA-(FL*V*SNTA)
      IF(ABS(CHCKL)-0.001)199,199,192
 192  IF(CHCKL)150,199,145
 195  ITHETA=IRND(THETA/0.17453)
      RETURN
C ERRORS
 199  WRITE(6,200)
 200  FORMAT('ALL NUMBERS  ARE ZERO')
      STOP
      END
C------------PHPSTA
      SUBROUTINE PHPSTA(DCX,DCY,DCZ, DCNX,DCNY,DCNZ,JPHIA,JPSIA,JTTA,
     * LIMB,JMOOT)
      DIMENSION JPHIA(35),JPSIA(35),JTTA(35)
      SNPS=DCZ
C     (-VE SIGN  FOR PSI BECAUSE THAT CORRESPONS To +VE Z)
      CSPS=SQRT(1.0-SNPS*SNPS)
      APSJ=ARCSN(SNPS)
C     (-PI/2 LT APSJ LT PI/2
      IF(CSPS-0.001)30,30,10
  10  SNPH=DCX/CSPS
      CSPH=DCY/CSPS
      APHJ=ARCTN(SNPH,CSPH)
C   (0 LT APHJ LT 2*PI)
      ITA=ITHETA(DCNX,DCNY,DCNZ,CSPH,CSPS,SNPH,SNPS)
      LAST=LIMB*JMOOT
      DO 20 LIM=LIMB,LAST
      JPHIA(LIM)=IRND(APHJ/0.17453)
      JPSIA(LIM)=IRND(APSJ/0.17453)
      JTTA(LIM)=ITA
  20  CONTINUE
      RETURN
  30  WRITE(6,31)
  31  FORMAT(' ATTEMPT TO FIND PHI IN PHPSTA WITH PSI +90 OR -90')
      STOP
      END
C
      FUNCTION ARCSN(Y)
      X=Y
      IF(ABS(X).LE.1.0)GOTO 20
      WRITE(6,11)X
  11  FORMAT(' ARCSIN OF',F8.4)
      IF(X .GT. 1.0) X=1.0
      IF(X.LT.-1.0)X=-1.0
  20  ARCSN=ARSIN(X)
      RETURN
      END
C
      FUNCTION ARCTAN(X,Y)
      ARCTAN=ATAN2(X,Y)
      IF(ARCTAN)30,40,40
  30  ARCTN=ARCTN+6.26318
  40  RETURN
      END
C
      SUBROUTINE COSIN(A,CS,SN)
      CS=COS(A)
      SN=SIN(A)
      RETURN
      END
C
      FUNCTION IRND(X)
      RND=X+0.5
      IF(RND)10,20,20
  10  RND=RND-1
  20  IRND=RND
      RETURN
      END
C
      FUNCTION RAD(I)
      IF(I-360) 10,20,10
  10  RAD=FLOAT(I)*0.017453
      RETURN
  20  RAD=0.0
      RETURN
      END
C
      FUNCTION SNML(MODB)
      IF(MODB-17)20,30,10
  10  IF(MODB-20)20,30,20
  20  SNML=1.00
      RETURN
  30  SNML=-1.00
      RETURN
      END
C-------------CROSP----------
      SUBROUTINE CROSP(X1,X2,X3,Y1,Y2,Y3,CROSS1,CROSS2,CROSS3)
C FINDS UNIT VECTOR NORMAL TO TWO GIVEN VECTORS
      CROS1=X2*Y3-X3*Y2
      CROS2=X3*Y1-X1*Y3
      CROS3=X1*Y2-X2*Y1
      SNTH=SORT(CROS1*CROS1 + CROS2*CROS2 + CROS3*CROS3)
      CROSS1=CROSS1/SNTH
      CROSS2=CROSS2/SNTH
      CROSS3=CROSS3/SNTH
      RETURN
      END
C------------------DCS
      SUBROUTINE DCS(PR,QR,PQ,PS,SQ,DCPRX,DCPRY,DCPRZ,FNMULT,DCNX,DCNY,
     * DCNZ,DCRQX,DCRQY,DCRQZ,DCPQX,DCPQY,DCPQZ)
C AS INPUT TO THIS ROUTINE, PR,PS,SQ REQUIRED. IF QR>0.0 REQUIRE DCIS OF VECTOR
C RQ. IF PQ>0.0, REQUIRE DC'S OF PQ ((LDC IS DIRECTIONAL COSINE)).
      DCNNX=DCNX*FNMULT
      DCNNY=DCNY*FNMULT
      DCNNZ=DCNZ*FNMULT
      CALL CROSP(DCNNX,DCNNY,DCNNZ,DCPRX,DCPRY,DCPRZ,DCSQX,DCSQY,DCSQZ)
      PQ1=PQ
      IF(PQ1)10,10,20
  10  PQ1=1.0
  20  DCPQX=(PS*DCPRX+SQ*DCSQX)/PQ1
      DCPQY=(PS*DCPRY+SQ*DCSQY)/PQ1
      DCPQZ=(PS*DCPRZ+SQ*DCSQZ)/PQ1
      IF(QR)40,40,30
  30  DCRQX=(PQ1*DCPQX-PR*DCPRX)/QR
      DCRQY=(PQ1*DCPQY-PR*DCPRY)/QR
      DCRQZ=(PQ1*DCPQZ-PR*DCPRZ)/QR
  40  RETURN
      END
C-----------------VECNML------------
      SUBROUTINE VECNML(IPH,IPS,ITA,DCVX,DCVY,DCVZ,DCNX,DCNY,DCNZ)
C THIS ROUTINE(VECNML CAKCULATES THE NORMAL FROM PHI,PSI,THETA
C IT FINDS THE DIRECTIONAL COSINES OF A LIMB AND OF THE NORMAL TO THE LIMB GIVEN
C THE THREE ANGLES, PHI,PSI,THETA.
      CALL COSIN(RAD(IPS),CSPS,SNPS)
      CALL COSIN(RAD(ITA),CSTA,SNTA)
      CALL COSIN(RAD(IPH),CSPH,SNPH)
      DCVX=CSPS*SNPH
      DCVY=CSPS*CSPH
      DCVZ=-SNPS
      SS=SNPS*SNTA
      DCNX=CSPH*CSTA-SNPH*SS
      DCNY=-SNPH*CSTA-CSPH*SS
      DCNZ=-CSPS*SNTA
      RETURN
      END

C  LABAN2
C------------------------------------------------------------------
      DIMENSION IPHIA(22),IPSIA(22),IDURA(22),ITTA(22)
      DIMENSION JPHIA(22),JPSIA(22),JDURA(22),JTTA(22)
      DIMENSION JPHKT(22),JPSKT(22),JTTKT(22)
      DIMENSION                     LNTHL(22),JTDIS(22),JTPRX(22)
      DIMENSION                              ISDUR(23),JSDUR(23),IC(23)

      DIMENSION XD(3),   IXD(3)
      DIMENSION IX(3,35), IEXCO(3,6), IEXTL(3)
      DIMENSION ICAM(9)
      DATA DASH/'----'/
      WRITE(6,10)
  10  FORMAT(' ENTERING STAGE TWO')
      READ(3)NSIMP,NLMS,NJTS,JTBND,MXERR,
     *  (LNTHL(L),JTDIS(L),JTPRX(L),L=1,NSIMP) ,IEXCO,IEXTL
      WRITE(6,1984)
     *        NSIMP,NLMS,NJTS,JTBND,MXERR,
     *  (LNTHL(L),JTDIS(L),JTPRX(L),L=1,NSIMP) ,IEXCO,IEXTL
 1984 FORMAT(5I5/(3I5))
      READ(3) IBSBT,KYTIM,ICINE,IPLOT,ICAM
      WRITE(6,1985)IBSBT,KYTIM,ICINE,IPLOT,ICAM
 1985 FORMAT(13I5)
      BSPSC=FLOAT(IBSBT*KYTIM)/60.
      FRATO=(FLOAT(ICINE))/BSPSC
      BSPBT=IBSBT
      FRAME=1.0
      WRITE(4) IBSBT,KYTIM,ICINE,IPLOT,ICAM
 100  READ(3)JB,(JPHIA(L),JPSIA(L),JTTA(L),JDURA(L),L=1,NSIMP),JSDUR,J
     *TBND
      WRITE(6,101)JB,JPHIA,JPSIA,JTTA
 101  FORMAT(I5, '  PHI',22I5/5X,'  PSI '  , 22I5/5X,'THETA  '  ,22I5//)
      IF(JB)130,280,280
 130  KFR=-1
      JBEAT=JB/IBSBT
      WRITE(4)KFR,JB,JBEAT,IX
      REWIND 4
      WRITE(6,140)
 140  FORMAT(' LEAVING STAGE TWO')
      STOP
 280  FJBF=FLOAT(JB)*FRATO
 290  TMFRN=FRAME-1.0-FJBF
C
C
C-----------------------------FRMKT-----------------------------------
C
C  FRMKT FINDS THE CURRENT TIME DIRECTIONAL ANGLE FOR EACH FRAME AT EACH BEAT
C
 400  DO 499 IBPRT=1,NSIMP
      JDAB=JDURA(IBPRT)
      DJFR=FLOAT(JDAB)*FRATO
      IF(TMFRN) 410,450,450
C FRAME OVERLAPS TWO BEATS
 410  IDAB=IDURA(IBPRT)
      IF(IDAB+JDAB) 420,499,420
 420  IF(IDAB) 430,493,430
C SOMETHING IN SECOND
 430  IF(IDAB-1) 460,440,460
 440  DURIF=DJFR/(1.0+TMFRN)
      IF(IDAB) 470,480,470
C NO OVERLAP
 450  IF(JDAB) 460,499,460
C SOMETHING IN SECOND AND NO OVERLAP, OR SOMETHING CONTINUING IN BOTH
 460  DURIF=DJFR-TMFRN
      IF(JB) 480,475,480
C OVERLAPS WITH SOMETHING IN BOTH WHICH IS NOT CONTINUOUS
 470  IPH=IPHIA(IBPRT)
      IPS=IPSIA(IBPRT)
      ITA=JTTA(IBPRT)
      GOTO 490
C BEATSTEP 0
 475  IPH=JPHIA(IBPRT)
      IPS=JPSIA(IBPRT)
      ITA=JTTKT(IBPRT)
C SOMETHING IN SECOND AND NO OVERLAP (NOT FRAME 1) OR CONTINUATION WITH
C OVERLP
 480  IPH=JPHKT(IBPRT)
      IPS=JPSKT(IBPRT)
      ITA=JTTKT(IBPRT)
 490  CALL NEWDA(IBPRT,IPH,IPS,ITA,JPHIA(IBPRT),JPSIA(IBPRT),
     *   JTTA(IBPRT),DURIF,JPHKT,JPSKT,JTTKT,LNTHL)
      GOTO 499
C OVERLAP BUT NOTHING IN SECOND
 493  JPHKT(IBPRT)=IPHIA(IBPRT)
      JPSKT(IBPRT)=IPSIA(IBPRT)
      JTTKT(IBPRT)= ITTA(IBPRT)
 499  CONTINUE
C
C------------------------COORDINATES-------------------
C CALCULATES THE COORDINATES OF EACH JOINT AT EACH FRAME
C
 600  DO 610 J=1,NJTS
 610  IC(J)=0
      IF(JSDUR(JTBND)) 620,620,630
C ARRANGEMENT OF TORSO HIERARCHY
 620  DO 625 K=1,3
 625  IX(K,JTBND)=0
 630  IC(JTBND)= 1
      DO 780 L=1,NSIMP
      IF(L-4) 640,640,680
 640  IF(JTBND-3) 680,650,670
 650  IF(L-2) 660,660,680
 660  LL=3-L
      GOTO 690
 670  LL=5-L
      GOTO 690
 680  LL=L
 690  JBD=JTDIS(LL)
      JFR=JTPRX(LL)
      IF(IC(JBD))710,700,710
 700  JT=JBD
      JFR=JT
C CALCULATION OF DISPLACEMENT IN ABSOLUTE TERMS OF THE PLOTTER
 710  CALL DISP(JPHKT(LL),JPSKT(LL),LNTHL(LL), X1,X2,X3)
      XD(1)=X1
      XD(2)=X2
      XD(3)=X3
      ISP=JSDUR(JFR)
      DO 760 K=1,3
      IXDF=IRND(XD(K))
      NEWX=IX(K,JBD)+IXDF
      IF(ISP) 7,750,7
C SUPPORT ENCOUNTERD: MODIFY PREVIOUSLY CALCULATED RELATIVE COORDS TO
C REAL COORDINATES USING KNOWN REAL COORDS OF SUPPORT
C ON BEATSTEP ZERO, ASSUME SUPPORTING JOINTS ARE LOCATED ON FLOOR: Z=0)
 7    IF(JB)720,716,720
 716  IF(K-3)750,718,750 
 718  IX(K,JFR)=0
 720  IXM=IX(K,JFR)-NEWX
      IF(IABS(IXM)-MXERR) 760,760,730
 730  DO 745 J=1,NJTS
      IF(IC(J))740,745,740
 740  IX(K,j)=IX(K,J)+IXM
 745  CONTINUE
      GOTO 760
 750  IX(K,JFR)=NEWX
 760  CONTINUE
 770  IC(JFR)=1
 780  CONTINUE
C------------------------------------------
c CHANGE COORDINATES OF THE FOOT, IF IT GOES THRU THE FLOOR.
      DO 2001 IBPRT=19,22,3
      J=JTDIS(IBPRT)
      IF(IX(3,j))2005,2001,2001
C NEGATIVE Z COORD
 2005 IF(JPHKT(IBPRT)-90)2020,2010,2020
C PLACE LOW
 2010 ANG=RAD(JTTKT(IBPRT)+JPHKT(IBPRT))
      GOTO 2030
C NON-PLACE LOW
 2020 ANG=RAD(JPHKT(IBPRT))
 2030 CALL COSIN(ANG,CSANG,SNANG)
      AT=LNTHL(IBPRT)
      ATX=AT-SNANG
      ATY=AT+CSANG
      JBT=J-2
      WRITE(6,2000) IX(I,J),IX(2,J),IX(3,J)
 2000 FORMAT(' THE COORDINATES OF THE FOOT ARE',3I5)
      IX(1,J)=IFIX(ATX+FLOAT(IX(1,JBT)))
      IX(2,J)=IFIX(ATY+FLOAT(IX(2,JBT)))  
      IX(3,J)=0
 2001 CONTINUE
C---------------------------------------------------
      DO 795 IEXTR=1,3
      IEXLM=IEXTL(IEXTR)
      IEXTJ=JTPPX(IEXLM)
C CALCULATE THREE_DIMENSIONAL COORDS OF HANDS AND HEAD
C (IEXTL(1) IS THE HEAD, (2) IS THE RIGHT HAND, (3) IS THE LEFT HAND
C ORIGINAL JOINT OR EACH IS WRIST OR NECK
      ITA=JTTKT(IEXLM)
      IPH=JPHKT(IEXLM)
      IPS=JPSKT(IEXLM)
      DO 792 ISIDE=1,2
      ISUB=2*IEXTR+ISIDE-2
C ISUB=1 RIGHT SIDE OF HEAD
C ISUB=2 LEFT SIDE OF HEAD
C ISUB=3 RIGHT FINGERS
C ISUB=4 RIGHT THUMB
C ISUB=5 LEFT FINGERS
C ISUB=6 LEFT THUMB
      CALL TRDSP(ITA,IPH,IPS,IEXCO,ISUB,IXD)
      IEXJT=23*ISUB
      DO  790 K=1,3
      IX(K,IEXJT)=IX(K,IEXTJ)+IXD(K)
 790  CONTINUE
 792  CONTINUE
 795  CONTINUE
      KFR=FRAME
      JBEAT=FLOAT(JB)/BSPBT
      WRITE(4)KFR,JB,JBEAT,IX
      WRITE(6,310) KFR,JB,JBEAT
 310  FORMAT(' FRAME',I3,'; BEATSTEP',I3,'; BEAT',I3)
      WRITE(6,311) ((IX(K,J),J=6,29),K=1,3)
 311  FORMAT(24I5)
      WRITE(6,501)FRAME,JPHKT,JPSKT,JTTKT,(DASH,I=1,30)
 501  FORMAT(F5.0,' PHI',22I5/5X,' PSI',22I5/5X,'THETA',22I5/30A4//)
C -------------------FRAME AND BEATSTEP LOOP CONTROL ----------
 800  FRAME=FRAME+1.0
      IF(FRAME-FJBF-FRATO)290,290,830
C    (DO NEXT FRAME IF IT TERMINATES WITHIN CURRENT BEAT)
 830  JB=JB+1
C-------------------------MOVJ1-------------------
C TRANSFER DATA STORED IN AREA J INTO AREA I
 900  DO 920 J=1,NSIMP
      IPHIA(J)=JPHIA(J)
      IPSIA(J)=JPSIA(J)
      ITTA(J)=JTTA(J)
 920  CONTINUE
      DO 940 J=1,NJTS
      ISDUR(J)=JSDUR(J)
 940  CONTINUE
      GOTO 100
      END
C----------NONEG-----------
      SUBROUTINE NONEG(I)
C NONEG ALWAYS RETURNS A POSITIVE VALUE FOR ANGLE, WHERE 0  LT  X  LT  360
      IF(I)10,15,20
  10  I=I+360
  15  RETURN
  20  IF(I-360)15,15,25
  25  I=I-360
      GOTO 15
      END
C--------------NEWDA--------------
      SUBROUTINE NEWDA(IB,INIPH,INIPS,ITA,LASPH,LASPS,LTA,DURI,
     * JPHKT,JPSKT,JTTKT,LNTHL)
      DIMENSION JPHKT(22),JPSKT(22),JTTKT(22),LNTHL(22)
      API=3.149
      IF(DURI-1.0)14,14,10
  10  IF(INIPH-LASPH)20,12,20
  12  IF(INIPS-LASPS)20,13,20
C THERE IS NO INTERPOLATION NECESSARY FOR PHI AND PSI, BUT FOR THETA, THERE IS
  13  KPH=LASPH
      KPS=LASPS
      GOTO 200
  14  KTA=LTA
      KPH=LASPH
      KPS=LASPS
      GOTO 400
  20  IF(IB-10)30,30,25
  25  IREM=MOD(IB,3)
      IF(IREM-2)140,30,140
C 
C CALCULATE PHI,PSI FOR UPPER LIMBS AND TORSO
C--------------------------
  30  CALL DISP(INIPH,INIPS,1,PX,PY,PZ)
      CALL DISP(LASPH,LASPS,1,OX,OY,OZ)
      LSTLM=18
C     (CALC DIRN. COSINES OF INITIAL AND FINAL LIMB POSITIONS)
      CBTA=PX*OX+PY*OY+PS*OZ
      IF(CBTA+0.99)130,130,40
C ERROR IF COS BETA = -1.,IE BETA=1801
  40  BTA=ARCOS(CBTA)
      P=BTA/DURI
C (P IS ANGLE OF ROTATION THIS FRAME)
      CALL CROSSP(PX,PY,PZ,OX,OY,OZ,FLP,FMP,FNP)
      PR=LNTHL(IB)
      PQ=PR
      CALL COSIN(P,CSP,SNP)
      PS=CSP*PQ
      SQ=SNP*PQ
      CALL DCS(PR,0.0,PQ,PS,SO,PX,PY,PZ,1.0,FLP,FMP,FNP,
     * DCROX,DCROY,DCROZ, DCPQX,DCPQY,DCPQZ)
C   (USING FOLD ROUTINE, CALC. D.C.'S OF CURRENT POSITION OF LIMB IB)
      CALL PHPS(DCPOX,DCPOY,DCPOZ,KPH,KPS,Q120)
      GOTO 200
 120  KPH=LASPH
C (IF CURRENT PSI IS +90 OR -90, SET CURRENT PHI = DESTINATION PHI)
      GOTO 200
 130  WRITE(6,131)IB
 131  FORMAT(' ROTATION OF LIMB',I4,' THROUGH 180 DEGREES: ILLEGAL')
      STOP
C CALCULATE PHI,PSI FOR LOWER LIMBS
C------------------
 140  LMUP=IB-1
C    (PREVIOUS, IE ADJACENT UPPER, LIMB)
      CALL VECNML(JPHKT(LMUP),JPSKTL(LMUP),JTTKT(LMUP),
     * DCLUPX,DCLUPY,DCLUPZ, DCNUPX,DCNUPY,DCNUPZ)
C GET D.C.'S OF UPPER LIMB AND OF NORMAL TO UPPER LIMB)
      FNML=SNML(LMUP)
      IF(LMUP-LSTLM)150,160,150
C THE D.C.'S OF THE PREVIOUS (UPPER) LIMB WEREN'T CALCULATED IN
C THE PREVIOUS CALL TO NEWDA, SO THEY ARE EQUAL TO THE CURRENT D.C.'S
C OF LMUP, I.E. TO DCLUPX,Y,Z
 150  PX=DCLUPX
      PY=DCLUPY
      PZ=DCLUPZ
      DX=PX
      DY=PY
      DZ=PZ
 160  CALL DISP(INIPH,INIPS,1,PPX,PPY,PPZ)
C  (D.C.'S OF INITIAL POSITION OF LIMB (B)
      CALL DISP(LASPH,LASPS,1,DQX,DQY,DQZ)
C  (D.C.'S OF FINAL POSITION OF LINE IB)
      CBTAIN=-(PX-PPX + PY-PPY + PZ-PPZ)
      CBTALS=(DX+DQX + DY+DQY + DZ-DQZ)
C  (COSINES OF INITIAL AND FINAL ANGLES BETWEEN UPPER LIMB LMUO
C  AND THIS LINE IB  == MINUS SIGN TO GET INCLUDED ANGLE)
      BTAIN=ARCOS(CBTAIN)
      BTALS=ARCOS(CBTALS) 
      BTAKT=BTAIN + (BTALS-BTAIN) / DURI
C    (INTERPOLATE LINEARLY FOR CURRENT ANGLE BETWEEN LIMBS)
      IF(BTAKT-API+0.01)170,180,180
 170  PR=LNTHL(LMUP)
      QR=LNTHL(IB)
      CALL COSIN(BTAKT,CSBTAK,SNBTAK)
      PS=PR - QR*CSBTAK
      SQ=QR+SNBTAK
      CALL CCS(PR,OR,0.0,PS,SQ,   DCLUPX,DCLUPY,DCLUPZ,  FNML,
     *  DCNUPX,DCNUPY,DCNUPZ, DCRQX,DCRQY,DCRQZ, DCPQX,DCPQY,DCPQZ)
C    (USING FOLD ROUTINE, CALC D.C.'S OF FOLDED LIMB IB)
      CALL PHPS(DCRQX,DCRQY,DCRQZ,KPH,KPS,Q175)
      GOTO 190
 175  KPH=LASPH
C     (IF CURRENT PSI IS +90 OR -90, SET CURRENT PHI = DEST PHI)
C     (USING D.C.'S OF LIMP IB, CALC PHI AND PSI)
      GOTO 190
 180  KPH=JPHKT(LMUP)
      KPS=JPSKT(LMUP)
C    (IF ANGLE BETN LIMBS IS 180, PHI AND PSI OF LOWER LIMB ARE SAME
C     AS THOSE OF UPPER LIMB)
 190  IF(IREM)200,195,200
 195  PX=PPX
      PY=PPY
      PZ=PPZ
      DX=DQX
      DY=DQY
      DZ=DQZ
      LSTLM=IB
C     (SAVE INITIAL AND FINAL D.C.'S OF LOWER LIMB FOR USE WHEN CALCULATING
C     EXTREMITY)
C
C CALCULATE THETAS
C--------------------
 200  IF(IB-10)210,210,220
C NO ROTATIONS OF TORSO ALLOWED
 210  KTA=0
      GOTO 400
C ROTATIONS OF LIMBS
C MODIFY INITIAL THETA IF INIT PSI=+90 OR -() TO DEST PHI
 220  ITAM=ITA
      IF(INIPH-360)270,232,270
 232  IF(INIPS+90)240,250,240
 240  IF(INIPS-90)270,260,270
C PLACE HIGH INITIALLY
 250  ITAM=ITA+LASPH
      GOTO 265
C PLACE LOW INITIALLY
 260  ITAM=ITA-LASPH
C IF INIT PSI=+90 OR -90, NO CHANGE TO DEST THETA REQUIRED
 265  LTAM=LTA
      GOTO 340
C IF INITIAL PSI NOT +90 OR -90,
C MODIFY DESTINATION THETA IF DEST PSI IS +90 OR -90
 270  LTAM=LTA
      IF(LASPH-360)310,272,310
 272  IF(LASPS+90)280,290,280
 280  IF(LASPS-90)310,300,310
C PLACE HIGH FINALLY
 290  LTAM=LTA+INIPH
      GOTO 340
C PLACE LOW FINALLY
 300  LTAM=LTA-INIPH
      GOTO 340
 310  IF(IABS(INIPH-LASPH)-180)340,320,340
 320  CALL MODDT(INIPH,LASPH,KPH,ITAM,LTAM)
C   (MODIFY THETA IF MOVE GOES THROUGH PLACE LOW OR PLACE HIGH FROM
C    FRONT TO BACK OR VICE VERSA)
 340  CALL NEWDT(IB,ITAM,LTAM,DURI,KPH,KTA)
 400  JPHKT(IB)=KPH
      JPSKT(IB)=KPS
C     JTTKT(IB)=KTA
      RETURN
      END
C-------------NEWDT---------
      SUBROUTINE NEWDT(IB,ITAM,LTAM,DURI,KPH,KTA)
C INTERPOLATES THETAS
      DIMENSION IMPOSS (2,4)
      DATA IMPOSS/30,30,330,330,180,0,180,0/
C IMPOSS ORDER: RAF RAB LAF LAB RLF RLB LLF LLB
      KFRONT=1
      IF( (KPH.LT.270) .AND. (KPH.GT.90) ) KFRONT=2
C KFRONT ID 1 IF CURRENT LIMB POSITION IS IN FRONT OF BODY
C KFRONT ID 2 IF CURRENT LIMB POSITION IS IN  BACK OF BODY
      LIMND=(IB-2)/3-2
C 1= P ARM, 2 = L ARM, 3=P LEG, 4 = L LEG
      ITA=ITAM
      LTA=LTAM
      CALL NONEG(ITA)
      CALL NONEG(LTA)
      IMPOS=IMPOSS(KFRONT,LIMND) 
       IF((LTA-IMPOS)*(IMPOS-LTA))40,50,10
C A FORMULA WHICH FINDS IF A NUMBER LIES BETWEEN TWO NUMBERS IF THE DIFFERENCE
C IN THE FIRST AND NUMBER IN QUESTION AND THE DIFFERENCE BETWEEN THE SECOND AND
C NUMBER IN QUESTION, MULTIPLIED BY EACH OTHER YIELDS A POSITIVE ANSWER
C IMPOSSIBLE SITUATION (+VE)
C IT IS IMPOSSIBLE TO GO DIRECTLY TO LAST POSITION
 10   IF(ITA-LTA) 20,40,30
 20   LTA=LTA+360
C (INCREASE THE SMALLER BY 360)
      GOTO 40
  30  LTA=LTA+360
  40  INCR=FLOAT(LTA-ITA)/DURI+0.5    
      KTA=LTA+INCR
      CALL NONEG(KTA)
      RETURN
  50  WRITE(6,51) ITA,LTA,LIMND,KFRONT
  51  FORMAT(' INIT OR FINAL THETA',2I5,' FOR LIMB',I4,'IN FONT/BACK',
     * I3,' IS AN IMPOSSIBLE VALUE')
      STOP
      END
C
      SUBROUTINE COSIN(A,CS,SN)
      CS=COS(A)
      SN=SIN(A)
      RETURN
      END

C
      FUNCTION SNML(IB)
C     SIGN O N*L: +1 EXCEPT FOR THIGHS
      IF(IB-17)5,10,2
   2  IF(IB-20)5,10,5
   5  SNML=1.00
      RETURN
  10  SNML=-1.00
      RETURN
      END
C
      FUNCTION ARCTN(X,Y)
      ARCTN=ATAN2(X,Y)
      IF(ARCTN)30,40,40
  30  ARCTN=ARCTN+6.26318
  40  RETURN
      END
C
      FUNCTION ARCSN(Y)
      X=Y
      IF(ABS(X).LE.1.0)GOTO 20
      IF(X .GT. 1.0) X=1.0
      IF(X.LT.-1.0)X=-1.0
  20  ARCSN=ARSIN(X)
      RETURN
      END
C -----------DISP------
      SUBROUTINE DISP(IPH,IPS,LNT,X1,X2,X3)
      APH=RAD(IPH)
      APS=RAD(IPS)
      CALL COSIN(APH,CSPH,SNPH)
      CALL COSIN(APS,CSPS,SNPS)
      X1=CSPS+SNPH*LNT
      X2=CSPS+CSPH*LNT
      X3=SNPS*LNT
      RETURN
      END

C
      FUNCTION RAD(I)
  10  RAD=FLOAT(I)*0.017453
      RETURN
      END
C
      FUNCTION IRND(X)
      RND=X+0.5
      IF(RND)10,20,20
  10  RND=RND-1
  20  IRND=RND
      RETURN
      END
C
C------------MODDT----------
      SUBROUTINE MODDT(IN,LA,KP,ITS,LTS)
C     CHECKS IF LIMB MOVES IN FRONT TO PACK OR V.V.
  12  IF((IN.LT.270).AND.(IN.GT.90)) GOTO 30
C INITIAL IN FRONT-CHECK FINAL PHI
  14  IF((LA.GE.270).OR.(LA.LE.90)) GOTO 40
C (INITIAL AND FINAL PHI BOTH FRONT, RETURN SAME THETA)
  18  IF((KP.LT.270).AND.(KP.GT.90)) GOTO 24
C FROM LINE 18 - INIT F: CURRENT F:FINAL B
C FROM LINE 32 - INIT 3; CURRENT 8 FINAL F
  20  LIS=LTS+180
      IF(LTS-360)40,21,21
  21  LTS=LTS-360
      GOTO 40
C INIT B CHECK FINAL
  30  IF((LA.LT.270).AND.(LA.GT.90)) GOTO 40
C INITIAL B, FINAL F
  32  IF((KP.LT.270).AND.(KP.GT.90)) GOTO 20
C FROM LINE 18 INIT F, CURRENT B, FINAL B
C FROM LINE 32 INIT B, CURRENT F, FINAL F
  24  LIS=LIS+180
      IF(LIS-360)40,25,25
  25  ITS=ITS-360
  40  RETURN
      END
C
C----------PHPS
      SUBROUTINE PHPS(DCX,DCY,DCZ,KPH,KPS,*)
C PHPS CALCULATES THE PHI,PSI, GIVEN DIRECTION COSINES OF A VECTOR)
      SNPS=-DCZ
C   (-VE SIGN FOR PSI BECAUSE THAT CORRESPONDS TO +VE Z)
      CSPS=SQRT(1.0-SNPS*SNPS)
      APSJ=ARCSN(SNPS)
C   (-PI/2  LT  APSJ  LT  PI/2)
      KPS=IRND(APSJ/0.017453)
      IF(CSPS-0.001)20,20,10
  10  SNPH=DCX/CSPS
      CSPH=DCY/CSPS
      APHJ=ARCTN(SNPH,CSPH)
C    (0  LT  APHJ  LT  2PI)
      KPH=IRND(APHJ/0.017453)
      RETURN
  20  RETURN
C   (IF PSI IS +90 UP -90, TAKE SPECIAL RETURN WITHOUT CALCULATING PHI)
      END
C-------------------TRDSP------------
      SUBROUTINE TRDSP(ITA,IPHI,IPSI,IEXCD,ISUB,IXD)
      DIMENSION IEXCD(3,6),IXD(3)
      DIMENSION DXX(3),DXXD(3),A(3,3)
      DO 10 K=1,3
      DXXD(K)=IEXCD(K,ISUB)
  10  CONTINUE
      THETA=RAD(ITA)
      PHI=RAD(IPHI)
      PSI=RAD(IPSI)
      CALL COSIN(THETA,CTA,STA)
      CALL COSIN(PHI,CPH,SPH)
      CALL COSIN(PSI,CPS,SPS)
      SS=SPS-STA
      A(1,1)=CPH*CTA-SPH*SS
      A(2,1)=-SPH*CTA-CPH*SS
      A(3,1)=CPS*STA
      A(1,2)=SPH*CPS
      A(2,2)=CPH*CPS
      A(3,2)=-SPS
      SC=SPS*CTA
      A(1,3)=CPH*STA+SPH*SC
      A(2,3)=SPH*STA+CPH*SC
      A(3,3)=CPS*CTA
      DO 100 I=1,3
      DXX(I)=0.
      DO 90 J=1,3
      DXX(I)=DXX(I)+ A(I,J)*DXXD(J)
  90  CONTINUE
 100  CONTINUE
      DO 110 K=1,3
      IXD(K)=IRND(DXX(K))
 110  CONTINUE
      RETURN
      END
C
C-------------CROSP----------
      SUBROUTINE CROSP(X1,X2,X3,Y1,Y2,Y3,CROSS1,CROSS2,CROSS3)
C FINDS UNIT VECTOR NORMAL TO TWO GIVEN VECTORS
      CROS1=X2*Y3-X3*Y2
      CROS2=X3*Y1-X1*Y3
      CROS3=X1*Y2-X2*Y1
      SNTH=SORT(CROS1*CROS1 + CROS2*CROS2 + CROS3*CROS3)
      CROSS1=CROSS1/SNTH
      CROSS2=CROSS2/SNTH
      CROSS3=CROSS3/SNTH
      RETURN
      END
C------------------DCS
      SUBROUTINE DCS(PR,QR,PQ,PS,SQ,DCPRX,DCPRY,DCPRZ,FNMULT,DCNX,DCNY,
     * DCNZ,DCRQX,DCRQY,DCRQZ,DCPQX,DCPQY,DCPQZ)
C AS INPUT TO THIS ROUTINE, PR,PS,SQ REQUIRED. IF QR>0.0 REQUIRE DCIS OF VECTOR
C RQ. IF PQ>0.0, REQUIRE DC'S OF PQ ((LDC IS DIRECTIONAL COSINE)).
      DCNNX=DCNX*FNMULT
      DCNNY=DCNY*FNMULT
      DCNNZ=DCNZ*FNMULT
      CALL CROSP(DCNNX,DCNNY,DCNNZ,DCPRX,DCPRY,DCPRZ,DCSQX,DCSQY,DCSQZ)
      PQ1=PQ
      IF(PQ1)10,10,20
  10  PQ1=1.0
  20  DCPQX=(PS*DCPRX+SQ*DCSQX)/PQ1
      DCPQY=(PS*DCPRY+SQ*DCSQY)/PQ1
      DCPQZ=(PS*DCPRZ+SQ*DCSQZ)/PQ1
      IF(QR)40,40,30
  30  DCRQX=(PQ1*DCPQX-PR*DCPRX)/QR
      DCRQY=(PQ1*DCPQY-PR*DCPRY)/QR
      DCRQZ=(PQ1*DCPQZ-PR*DCPRZ)/QR
  40  RETURN
      END
C-----------------VECNML------------
      SUBROUTINE VECNML(IPH,IPS,ITA,DCVX,DCVY,DCVZ,DCNX,DCNY,DCNZ)
C THIS ROUTINE(VECNML CAKCULATES THE NORMAL FROM PHI,PSI,THETA
C IT FINDS THE DIRECTIONAL COSINES OF A LIMB AND OF THE NORMAL TO THE LIMB GIVEN
C THE THREE ANGLES, PHI,PSI,THETA.
      CALL COSIN(RAD(IPS),CSPS,SNPS)
      CALL COSIN(RAD(ITA),CSTA,SNTA)
      CALL COSIN(RAD(IPH),CSPH,SNPH)
      DCVX=CSPS*SNPH
      DCVY=CSPS*CSPH
      DCVZ=-SNPS
      SS=SNPS*SNTA
      DCNX=CSPH*CSTA-SNPH*SS
      DCNY=-SNPH*CSTA-CSPH*SS
      DCNZ=-CSPS*SNTA
      RETURN
      END

C ----------------LABDPLOT-----------------------
C------------------------------------------------------------------
      DIMENSION IX(3,35), ICAM(9), IPX(2,35,3), IDATA(9),
     *  ISTGR(3,3),ISTGL(3,3)
      READ(4) IBSBT,KYTIM,ICINE,IPLOT,ICAM
      INIFR=1
      MAXFR=999999
      INCFR=1
   1  READ(5,2,END=40)KODE,IDATA
   2  FORMAT(10I5)
      GOTO(10,20,30),KODE
C KODE=1: STAGE DIMENSIONS:RIGHT WIDTH, LEFT WIDTH, FORWARD DEPTH,
C BACKWARD DEPTH, SCALING FACTOR, REQUIRED OUTPUT
  10  ISTGR(1,1)=IDATA(1)
      ISTGR(1,2)=IDATA(1)
      ISTGR(1,3)=0
      ISTGL(1,1)=0
      ISTGL(1,2)=-IDATA(2)
      ISTGL(1,3)=-IDATA(2)
      ISTGR(2,1)=-IDATA(4)
      ISTGL(2,2)=IDATA(3)
      ISTGR(2,3)=IDATA(3)
      ISTGL(2,1)=IDATA(3)
      ISTGL(2,2)=IDATA(3)
      ISTGL(2,3)=-IDATA(4)
      SCALER=IDATA(5)
      DO 15 L=1,3
      ISTGR(3,L)=0
      ISTGL(3,L)=0
  15  CONTINUE
      GOTO 1
C KODE=2: INITIAL AND LAST FRAMES. OPTIONAL INPUT.
  20  INIFR=IDATA(1)
      MAXFR=IDATA(2)
      INCFR=IDATA(3)
      IF(INCFR.LE.0) INCFR=1
      GOTO 1
C KODE=3   CAMERA DATA OVERRIDING THAT SUPPLIED IN STAGE 1. OPTIONAL.
  30  DO 35 L=1,3
      ICAM(L)=IDATA(L)
  35  CONTINUE
      GOTO 1
  40  WRITE(6,41)INIFR,MAXFR
  41  FORMAT(' DATA REQUESTED FOR FRAMES',I6, ' THRU',I6)
      FRMBT=FLOAT(ICINE*60)/FLOAT(KYTIM)
      NFRBT=FRMBT
      IF(INIFR.GE.NFRBT) GOTO 45
      WRITE(6,42)NFRBT
  42  FORMAT(' FIRST',I3,' FRAMES ARE IDENTICAL')
      INIFR=NFRBT
  45  INIFRM=INIFR-1
      IF(INIFRM.LE.0) GOTO 80
C    BYPASS UNWANTED FRAMES
      DO 50 I=1,INIFRM
      READ(4)
  50  CONTINUE
  80  IF(IPLOT.EQ.0)GOTO 100
C INITIALIZE PLOTTER
      IF(MAXFR.EQ.999999)MAXFR=FLOAT(IPLOT)*FRMBT
      XMAX=10*(MAXFR-INIFRM)+ 2
C     (NO OF INCHES OF PLOT THAT WILL BE PRODUCED = 10 X NO. OF FRAMES
      CALL PRFRM(IX,IBSBT,ICAM,XMAX,ISTGR,ISTGL,SCALER)
 100  DO 400 I=INIFR,MAXFR
      READ(4) KFR,JB,JBEAT,IX
      IF(KFR.LT.0)GOTO 500
C(END OF JOB)
      WRITE(6,310) KFR,JB,JBEAT
 310  FORMAT(' FRAME',I3,'; BEATSTEP',I3,'; BEAT',I3)
      IF(MOD((1-INIFR),INCFR))400,101,400
C    (PRINT AND PLOT ONLY EVERY INCFR'TH FRAME)
 101  IF(IPLOT)118,300,118
 118  FRAME=KFR
 119  CALL PRFRM(JB,FRAME)
      GOTO 400
 300  WRITE(6,311)(J,(IX(K,J),K=1,3),J=1,30)
 311  FORMAT(I5,5X,3I6)
 400  CONTINUE
C END OF DANCE
 500  WRITE(6,510)
 510  FORMAT(' END OF JOB')
      STOP
      END
C---------------PRFRM1--------------
      SUBROUTINE PRFRM1(IX,IBSBT,ICAM,XMAX,ISTGR,ISTGL,SCALER)
      DIMENSION IX(3,35),ICAM(9),IPX(2,35,3),LIST(8,5),XARRAY(10)
      DIMENSION ZARRAY(10),ISTGR(3,3),ISTGL(3,3),XSTG(5),ZSTG(5)
      EQUIVALENCE (XSTG,XARRAY(8)),(ZSTG,ZARRAY(6))
      DATA LIST/12,10, 8,6,1,2,6,1,2,14,16,18,20,26,18,27,14,5,22,23,24,
     *22,25,23,5,15,17,19,21,28,19,29,15,2,7,1,7,9,11,13/
      XARRAY(9)=0.0
      ZARRAY(9)=0.0
      XARRAY(10)=SCALER
      ZARRAY(10)=SCALER
      CALL PLOTS(IBSET,IBSBT)
      WRITE(6,1001)ICAM
 1001 FORMAT(T11,'DISTANCE FROM',T32,'CAMERA LOCATIONS',T58,'ANGLE TO
     *RIGHT'                            /T13,'PERFORMER',T30,'ELEVATION
     * ABOVE STAGE',T57,'OF STAGE FORWARD'
     *          /(T8,I10,T33,I10,T55,I10))
      NCAM=0
      DO 1003 I=1,3
      II=3*I-2
      IF(ICAM(II).EQ.0) GOTO 1005
      NCAM=NCAM+1
 1003 CONTINUE
 1005 XMAX=XMAX*FLOAT(NCAM)
      CALL XLIMIT(XMAX)
      RETURN
      ENTRY PRFRM(JB,FRAME)
      BEAT=JB/IBSBT
      PHIP=0.0
C     (ANGLE OF PERFORMER FORWARD FROM STAGE FORWARD)
      DO 1040 KAMERA=1,NCAM
      CAMERA=KAMERA
      KAMBAS=3*KAMERA
      RC=ICAM(KAMBAS-2)
C     DISTANCE FROM PERFORMER TO CAMERA
      HC=ICAN(KAMBAS-1)
C     (HEIGHT OF CAMERA ABOVE PERFORMER GROUND LEVEL)
      PHIC=RAD(ICAM(KAMBAS))
C     ANGLE OF CAMERA FROM STAGE  FORWARD)
      CALL NUMBER(0.0,1.0,0.14,FRAME,270.0,-1)
      CALL PLOT(0.0,0.0,-3)
C   (ORIGIN FOR DRAWING FIGURE)
      CALL PLOT(0.0,8.4,2)
C  (DRAWS A DIVIDING LINE BETWEEN FRAMES.)
      DO 1010 J=1,3
      CALL PROJ(RC,HC,PHIC,ISTGR,J,0.0,XSTG(J),ZSTG(J),3,SCALER)
 1010 CONTINUE
      CALL LINE(XSIG,ZSTG,3,1,0,2)
C    (DRAW STAGE)
      DO 1020 I=1,5
      DO 1030 J=1,8
      L=LIST(J,I)
      CALL PROJ(RC,HC,PHIC,IX,L,PHIP,X,Z,30,SCALER)
      XARRAY(J)=X
      XARRAY(J)=2
      IPX(1,L,KAMERA)=X
      IPX(2,L,KAMERA)=Z
 1030 CONTINUE
      CALL LINE(XARRAY,ZARRAY,8,1,0,1)
 1020 CONTINUE
      DO 1035 J=1,3
      CALL PROJ(RC,HC,PHIC,ISTGL,J,0.0,XSTG(J),ZSTG(J),3,SCALER)
 1035 CONTINUE
      CALL LINE(XSTG,ZSTG,3,1,0.2)
C     (DRAW STAGE)
      CALL PLOT(10.0,0.0,999)
C     (PLOT STICK FIGURE. THEN SHIFT ORIGIN READY FOR NEXT FRAME OR
 1040 CONTINUE
      DO 1050 J=1,29
C THE THIRD AND FOURTH POINTS COORDINATES ARE NOT CALCULATED FOR PLOTTING
      IF((J.EQ.3).OR.(J.EQ.4)) GOTO 1050
      WRITE(6,1031)J,(IX(K,J),K=1,3),((IPX(K,J,L),K=1,2),L=1,NCAM)
 1031 FORMAT(I5,5X,3I6,5X,2I6,5X,2I6,5x,2I6)
 1050 CONTINUE
      RETURN
      END
C-----------------PROJ-----------------
      SUBROUTINE PROJ(RC,ZC,PHIC,   IX,L,PHIP,X,Z,NSUB,SCALER)
      DIMENSION IX(3,NSUB)
C THE SCALER IS REALLY THE NUMBER USED BY THE PLOTTER TO REDUCE THE SIZE
C IN THE PROJ ROUTINE, THE SCALER IS THE NUMBER NECESSARY TO MOVE THE
C    STAGE AND DRAWINGS OVER TO THE CORRECT PLACE ON THE PAPER.
      XP=IX(1,L)
      YP=IX(2,L)
      ZP=IX(3,L)
      PHID=PHIP-PHIC
      XTP=XP*COS(PHID) + YP*SIN(PHID)
      YTP=YP*COS(PHID) - XP*SIN(PHID)
C     (PERFORMER COORDS TRANSFORMED TO SCREEN COORDS)
C     (SCREEN IS PERPENDICULAR TO LINE OF CAMERA TO PLACE)
      T= -RC / (YTP-RC)
      XQ=-T*XTP
      ZQ=T*(ZP-ZC)+ZC
      X=ZQ+2.6*SCALER
C THE 2.6 IS THE AMOUNT TO THE RIGHT OF THE PLOT ORIGIN FROM WHICH TO DRAW
C THE PLOTS FOR ANIMATION
      Z=4.95*SCALER-XQ
C 4.95 IS THE NUMBER WHICH CONVERTS THE PLOTTER COORDINATES FROM THE
C MOTION ANALYSER COORDINATES, BECAUSE THERE IS AN INVERSION TAKING PLACE
C THE X OF PLOTTER IS Y OF MOTION ANALYSERS AND Y OF PLOTTER IS X OF ANALYSER
C " CHANGE THE POINTS TO SUIT THE ANIMATION NECESSITIES. NORMAL XQ AND ZQ WILL 
C  BE THE X AND Z COORDS PAST AND WILL BE SUFFICIENT FOR THE CORRECT FIGURES
      RETURN
      END
C
      FUNCTION RAD(I)
      IF(I-360)10,20,10
  10  RAD=FLOAT(I)*0.017453
      RETURN
  20  RAD=0.0
      RETURN
      END

APPENDIX B - FLOWCHART OF LABAN

APPENDIX C - EVALUATION QUESTIONNAIRE AND SIGN TEST

I. ANIMATION

The following questions will ask you to evaluate the animation of the film.

(1) Animation techniques sometimes produce jumpy or flickering images. Please rate the animation as to:

(a) how smooth, or unflickering, the film appears to you.

(b) how clearly you could see the details in the film.

(2) How well do you think that an experienced dancer could reproduce the movements just shown in the filmstrip?

II. TIMING AND RHYTHM

Much of learning dances involves understanding rhythm and timing. The following questions will try to assess how clearly timing and rhythm are shown in the film.

(3) How well do you feel that accents or impulses were shown?

(4) How close an approximation to human timing of similar movements is the film, in your opinion?

(5) Please evaluate how well an experienced dancer might understand the timing of the movements shown.

III. THE DRAWING

The stickfigure drawing shown was chosen because it was felt to be the simplest possible drawing to show motion. Please evaluate the following as to the satisfactoriness (or otherwise, if need be) from the point of view of a dancer using these types of films to recreate movements.

(6) Use the five point scale to evaluate each question below:

(a) the use of stickfigure drawings in general.

(b) this particular stickfigure.

(c) the shape of the figure (e.g. fi1led-in areas).

(d) tbe body proportions in general.

(e) the head size in relation to the rest of the body.

(f) the head shape.

(g) the torso size.

(h) the torso shape.

(i) the leg length.

(j) the arm length.

(k) the arm shape.

(l) the hands and thumb as to size.

(m) the hands and thumb as to shape.

(n) the arm connection to the torso

(o) the leg connection to the torso

In looking at the arm movements:

(a) how wwell do the arm movements actually resemble human arm movements?

(b) how naturally does the torso respond to the arm movements?

(c) how clear are the directions of the arm movements?

(8) How clearly can you see what the legs are doing?

IV. GENERAL APPRECIATIONS

(9) Did you find the movements mechanical looking?

If YES. could you write some suggestions as to how you feel this could be avoided.

(10) Do you find that the film does not tell you enough about the movement for any specific thing, or for any reason. Please comment on your answer, if possible.

(11) Please comment on this type of film's useability as a cursory method of visualizing dance.

Sign Text Scores

Assessor                                Question
         1 1 2 3 4 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 8
         a b     a b a b c d e f g h i j k l m n o a b c

   1     + + 0 0 0 0 0 0 - 0 0 0 0 0 0 0 + 0 0 0 0 0 0 + 0
   2     + 0 + + + 0 0 0 0 + 0 0 0 + 0 + 0 0 0 0 0 0 0 0 +
   3     + 0 0 + + + 0 0 0 - 0 0 0 0 + + + - - 0 0 + 0 0 +
   4     + + 0 + 0 0 - 0 + + + 0 0 - 0 - 0 0 + + + + + + +
   5     0 + + 0 - 0 0 0 0 0 0 0 0 - 0 0 0 0 0 0 0 0 0 0 +
   6     0 0 0 0 0 0 0 0 0 0 - 0 0 0 0 0 0 0 0 0 0 0 0 + 0
   7     + 0 + + + + 0 + + + + + + + + + + + + + + + + + +
   8     + + + + + + + + + + + + + + + + + + + + + + + + +
   9     - 0 0 0 - - 0 - - 0 + - 0 - 0 - - - - 0 0 - - 0 0
  10     0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 0
  11     0 - 0 0 0 0 - 0 + - - - - - - 0 0 - - 0 0 0 + 0 0
  12     0 + 0 0 + 0 - 0 - 0 0 0 0 0 0 0 0 - - 0 0 - - - 0
  13     0 + + + 0 + - - - - - - - - - - - - - - - - - - -
  14     0 + + 0 0 0 + 0 + 0 0 0 0 0 0 + 0 - 0 0 0 0 0 0 0
  15     0 - 0 0 0 0 0 + + 0 0 0 + 0 0 0 0 0 0 0 0 - - 0 0
  16     0 + - 0 - - 0 0 0 0 + - - 0 + + + 0 0 + + + + + +
  17     + 0 0 + + + 0 0 0 + 0 0 + + 0 0 0 0 0 0 0 0 0 0 0
  18     0 + 0 - 0 - 0 0 - - - - - - - - - - - 0 - - - 0 -
  19     0 0 0 + + 0 0 0 0 0 + + + + 0 0 0 0 0 0 0 0 - 0 -
  20     0 - 0 0 - 0 0 - 0 + + + + 0 0 0 0 0 - 0 0 0 0 0 -
  21     + + - - 0 0 0 + 0 + + 0 0 0 + + + 0 0 0 0 + + + +
  22     0 0 0 0 0 0 0 + 0 0 + + 0 0 0 0 0 0 + + + 0 0 + +
  23     0 0 0 0 0 - - - - 0 + - 0 0 0 0 0 - 0 0 0 0 0 0 0
  24     - - 0 + 0 + 0 0 0 + - + + + 0 - 0 - - 0 0 - 0 0 0
  25     + + + + + + + + + 0 0 + 0 0 0 0 0 0 + + - - + + +
  26     0 0 + + 0 + 0 0 0 0 0 0 0 - 0 0 0 0 + 0 0 0 - + -
  27     + + + + + 0 0 + 0 0 0 - 0 - 0 0 0 0 + 0 0 + 0 + 0
  28     0 0 0 0 0 0 0 0 + + 0 0 + + 0 0 0 0 0 0 + 0 0 0 +
  29     + + 0 - + 0 0 + 0 + + + + 0 + + + + + + - + + 0 0
  30     + + - 0 - 0 0 0 + + 0 + 0 + 0 0 + 0 + + + 0 - - -
  31     + 0 - + 0 0 0 0 0 0 0 0 + + 0 0 0 - 0 0 0 - 0 - +
  32     0 0 0 0 + 0 + 0 0 0 0 0 + + + + 0 0 0 0 0 0 + 0 0
  33     0 0 0 0 - 0 0 0 0 0 + + + 0 - - + 0 0 + + 0 0 - 0
  34     + 0 0 + + 0 + - - 0 0 0 0 0 0 0 0 + + - - + + 0 0
  35     0 + 0 0 + - 0 0 + 0 + 0 0 0 0 0 0 0 - + + - 0 0 0
  36     0 - 0 0 0 0 0 0 0 0 0 + + 0 0 0 0 0 0 0 0 0 0 + 0
  37     0 + + + 0 0 + + 0 0 0 0 0 0 0 0 0 0 0 0 0 + + + 0
  38     + 0 0 + + + 0 + 0 + 0 + + 0 0 0 + + + 0 - + 0 + +
  39     + + 0 0 0 0 0 + 0 - 0 0 0 0 0 0 0 0 0 0 0 + 0 0 +
  40     + 0 0 + 0 0 + - 0 - - - 0 0 + + + + + + + + + + +

APPENDIX D - SAMPLE DRAWINGS FROM THE PLOTTER

APPENDIX E - LABANOTATION PHRASE USED AS INPUT TO PROGRAMME