Programmes for Animation. A Handbook for Animation Technicians

390 Pages·1978·23.41 MB·English

by  Brian Salt (Auth.)

PROGRAMMES
FOR ANIMATION
A Handbook for Animation Technicians
57 Programmes in Animation for a Programmable Calculator
By
BRIAN SALT
PERGAMON PRESS
OXFORD · NEW YORK · TORONTO · SYDNEY · PARIS · FRANKFURT
U.K. Pergamon Press Ltd., Headington Hill Hall,
Oxford OX3 0BW, England
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CANADA Pergamon of Canada Ltd., 75 The East Mall,
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FEDERAL REPUBLIC Pergamon Press GmbH, 6242 Kronberg-Taunus,
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Copyright © 1978 Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means: electronic, electro­
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permission in writing from the publishers.
First edition 1978
British Library Cataloguing in Publication Data
Salt, Brian George Daniel
Programmes for animation.
1. Animation (Cinematography) 2. Calculating-machines
I. Title
778.5,347,02854 TR897.5 78-40284
ISBN 0-08-023153-5
In order to make this volume available as economically and as rapidly as possible the
author's typescript has been reproduced in its original form. This method unfortu­
nately has its typographical limitations but it is hoped that they in no way distract
the reader.
Printed in Great Britain by William Clowes and Sons Ltd, Beccles, Suffolk
4
LIST OF PROGRAMMES
1 fj k and field widths/zoom counter readings - moving camera focus 7
2
2 Counter reading from field width - moving camera focus 29
3 Field width from counter reading - moving camera focus
30
4 fj k and field widths/zoom counter readings - moving lens focus 31
5 Counter reading from field width - moving lens focus 33
6 Field width from counter reading - moving lens focus 34
7 Lens and table off-sets for zoom shot 43
8 Linear movements with two fairings - moving camera focus 43
9 Linear movements with two fairings - moving lens focus 53
10 Linear zoom with two fairings - moving camera focus 60
11 Linear zoom with two fairings - moving lens focus 63
12 Exponential movements with two fairings - moving camera focus 70
13 Exponential movements with two fairings - moving lens focus 77
14 Exponential zoom with two fairings - moving camera focus 84
15 Exponential zoom with two fairings - moving lens focus 88
16 Linear movements with three fairings 95
17 Exponential movements with three fairings 103
18 Fairings and co-fairings 113
19 Centre and radius of circle 119
20 Circular pan with two fairings 125
21 Circular pan with three fairings 129
22 Linear zoom, pans and rotation with two fairings - moving camera focus 139
23 Linear zoom, pans and rotation with two fairings - moving lens focus 146
24 Exponential zoom and pans, linear rotation with two fairings - moving camera 154
focus
25 Exponential zoom and pans, linear rotation with two fairings - moving lens 163
focus
26 Linear zoom, circular pan and rotation with two fairings - moving camera focus 172
27 Linear zoom, circular pan and rotation with two fairings - moving lens focus 179
28 Circular pan and rotation with three fairings 187
29 Pan movement under constant acceleration - initial velocity known 201
30 Pan movement under constant acceleration - distance moved known 204
31 Zoom under constant acceleration - moving camera focus 208
32 Zoom under constant acceleration - moving lens focus 211
33 Object moving away under constant acceleration - moving camera focus 218
34 Object moving away under constant acceleration - moving lens focus 222
35 Number of frames to and from an intermediate position 228
36 Linear movements with two parabolic fairings - moving camera focus 230
37 Linear movements with two parabolic fairings - moving lens focus 235
38 Constant speed zoom on perspective artwork - moving camera focus 244
39 Constant speed zoom on perspective artwork - moving lens focus 249
40 Constant acceleration zoom on perspective artwork - moving camera focus 256
41 Constant acceleration zoom on perspective artwork - moving lens focus 259
42 Swing of pendulum 263
43 Movement of piston and crank 266
44 Exposures at different field widths 270
45 Linear zoom with several pieces of artwork - moving camera focus 274
46 Linear zoom with several pieces of artwork - moving lens focus 283
5
47 Exponential zoom with several pieces of artwork - moving camera focus 292
48 Exponential zoom with several pieces of artwork - moving lens focus 301
49 Fitting y = our3 + fix2 + yx + <5 to a given curve 315
50 Fitting several curves to a given curve 326
51 For plotting y = our3 + $x2 + yx + 6 333
52 Movement along y = cur3 + fix2 + yx + 6, linear with two fairings 337
53 Movement along several curves, linear with two fairings 347
54 £> k and h and zoom counters/lens compound positions for A.I. projection 364
Ί
55 Aerial image projection: linear movements with two fairings 370
56 Aerial image projection: exponential movements with two fairings 378
57 Random number generator 388
6
LIST OF SYMBOLS USED IN TEXT AND PROGRAMMES
a (1) Total distance travelled in a two-fairing movement
(2) A constant acceleration
(3) Distance between table top and lens 2 in aerial image projection
b Distance between aerial image 1 and lens 2 in aerial image projection
c (1) Total number of frames in a two-fairing movement
(2) Number of frames from A to B in a three-fairing movement
(3) Initial distance of background (programmes 31 and 32)
(4) Constant i n aerial image projection
c' Number of frames from B to C in a three-fairing movement
d Number of frames in an initial fairing
e (1) Number of frames in a final fairing
(2) Base of natural logarithms (equals approximately 2.71828)
F (1) Field width
(2) F = smallest field width in programme 44
S
(3) Width of camera field in aerial image projection
f (1) Focal length of lens
(2) f number = lens aperture
(3) f(x) = function of x
g Acceleration under gravity
j Rate of change of acceleration or "jerk"
k (1) Difference between u and z for moving camera focus, and between (u+v) and
z for moving lens focus
(2) Constant in aerial image projection
(3) Distance moved under a constant acceleration in feet (programme 30)
I E/W coordinate for lens off-set
I' N/S coordinate for lens off-set
rn Number of frames in a middle fairing
n Frame count
0 (1) Origin for rectangular coordinates
(2) Centre of field chart
P Force in lbs.
7
p (1) E/W movement of lens compound in aerial image projection
(2) Number of frames in move of constant acceleration (programme 30)
(3) Width of item in near distance (programmes 40 and 41)
p ' N/S movement of lens compound in aerial image projection
q Width of item in far distance (programmes 40 and 41)
R Distance moved in a final fairing
v (1) Distance moved in an initial fairing
(2) Radius vector in polar coordinates
(3) Radius of circle for circular pans
(4) Distance between near and far items (programmes 40 and 41)
SM "Steady Move": distance moved per frame between fairings in linear movements
or log of same in exponential movements. With subscripts SM^ SM. SM SM
3
indicates SM for field, E/W movements, N/S movements and turntable angle.
s (1) Distance moved in time t or up to frame n in parabolic fairings
(2) Distance of object to camera in live-action
(3) s equals near distance in programmes 40 and 41
(4) Distance along a curve or length of curve
T T register in HP-97 stack
t (1) E/W coordinate of table off-set
(2) Time taken to move a distance s
(3) Contents of T register in HP-97 stack
t1 N/S coordinate in table off-set
u (1) Distance between object and front node of lens
(2) Distance between projector gate and lens 1 in aerial image projection
(3) Initial velocity
(4) Gradient of curve at start of an exponential middle fairing
V (1) Distance between back node of lens and focal plane
(2) Distance between lens 1 and aerial image 1 in aerial image projection
(3) Final velocity
(4) Gradient of curve at end of an exponential middle fairing
W (1) Mass in lbs.
(2) νϊ = width of aerial image 1 and W„ = width of aerial image 2
η
w Width of camera gate, or projector gate in aerial image projection
8
X (1) E/W coordinate of centre of circle for circular pans
(2) E/W coordinate of zero point for exponential moves
(3) E/W coordinate of vanishing point
(4) X register in HP-97 stack
x (1) E/W position*
(2) Contents of X register in HP-97 stack
Y (1) N/S coordinate of centre of circle for circular pans
(2) N/S coordinate of zero point for exponential moves
(3) N/S coordinate of vanishing point
(4) Y register in HP-97 stack
y (1) N/S position*
(2) Contents of Y register in HP-97 stack
Z (1) Zero point in exponential moves
(2) Z register in HP-97 stack
z (1) Zoom counter reading for camera carriage
(2) Contents of Z register in HP-97 stack
a (1) Acceleration in parabolic fairings
(2) Coefficient of x3 in curve y = ax3 + &x2 + yx + 6 (Chapter XVI)
3 Coefficient of x2 in curve y = ax3 + fcc2 + yx + 6 (Chapter XVI)
γ Coefficient of x in curve y = our3 + $x2 + yx + 6 (Chapter XVI)
6 Coefficient or constant in curve y = our3 + 3x2 + yx + 6 (Chapter XVI)
ζ x coordinate of centre of curvature
η y coordinate of centre of curvature
Θ (1) Angular coordinate in polar coordinates
(2) Any angle
φ (1) Turntable angle
(2) Angle at centre of circle subtending a known arc (Chapter XVI)
(3) φ(χ) = function of x when fix) has already been used for another function
* When a rotation takes place x and y are used as the E/W and N/S positions before the
Λ
turntable has been rotated^ and x' and y' as the positions after rotation. xr and
y' are the positions that have to be set on the counters, but x and y have to be cal­
culated initially and used for conversion into polar coordinates.
9
π Ratio of circumference to diameter of circle (equals approximately 3*14159)
p Radius of curvature
Σ Denotes a summation process and is used in vector arithmetic and statistics
CAMERA GATE STANDARDS
35mm Full Gate 0*980 ins. nominal * 0*735 ± 0*002 ins.
+ 0*02
35mm Academy Gate 0*864 ins. minimum x 0*63
+ 0*004
16mm Standard Gate 0*404 ins. nominal x 0*295
- Λ0 *Λ0Λ0Λ3
11
INTRODUCTION
After the completion of the artwork of an animation scene, the time required to
shoot it is often very considerable, particularly if various camera movements are required
in the course of the scene. The operator may have to set several controls by hand for
each frame in addition to changing eels or other artwork modifications. For many years
there has been a tendency to automate these controls as far as is possible, both to save
shooting time and to eliminate one source of human error.
Auto-focus has been a standard device on animation stands for many years, this
saving the need to set the focus by hand every frame during a zoom shot. Since, when
large fields are being used, the focus control may be out of reach of the operator,
necessitating the use of a step-ladder, the saving of time by using this device may be
very considerable. Auto-fade and mix devices eliminate the need to set the shutter
control each frame during a fade or mix, and if a pre-determine counter is fitted, the
fade or mix will start automatically at some pre-determined frame. Auto-cycling equip­
ment combined with a capping shutter enables cycles of eels against a static background
to be shot one eel at a time, which usually not only saves time but eliminates wear on
the artwork peg-holes.
But it is when we come to zooms, pans, peg-bar movements and turntable rotations
that the problems of automation become difficult. These movements can be set by hand
to any required position using either analogue or digital devices. A vertical scale
can be mounted alongside the camera carriage, and a reading point on the carriage itself
can then indicate either field width and decimals thereof or the height of the carriage
above the table top. The pantograph can be used to set the E/W and N/S pan movements
to any required position. Sometimes scales are recessed into the table top alongside
the travelling peg-bars with a reading point in the peg-bars themselves, which enables
each bar to be set to a required position. All these are analogue devices. As an
alternative, and usually in addition, are digital devices in the form of four-figure
counters. In non-metric countries, the first figure of the zoom, pan and peg-bar
counters represents tens of inches, the second figure inches, the third tenths of an
inch and the fourth hundredths of an inch. In other words the decimal point can be
imagined after the second figure. In the case of the turntable, the first figure
represents hundreds of degrees, the second tens of degrees, the third degrees, and the
fourth tenths of a degree. In other words the decimal point can be imagined after the
third figure. Again in non-metric countries, one turn of the appropriate handwheel
will move the zoom, pans and peg-bars by one tenth of an inch, and one turn of the
turntable handwheel will turn the turntable by one degree. If therefore the drum of
each handwheel is divided into one hundred sectors and a fixed reading point is fitted
adjacent to the drum, turning a handwheel through one sector will move the zoom, pans
and peg-bars one-thousandth of an inch and the turntable through one-hundredth of a
degree. Such an accuracy of setting is obviously far beyond the limits of the analogue
devices.
Some animation stands have the camera lens fitted on a small and very accurate
compound, so that it can be off-set E/W or N/S or a combination of the two. If a
zoom is required which would normally involve E/W and N/S table movements in addition
to the zoom movement, by off-setting the lens E/W and N/S to calculated amounts, and
off-setting the table E/W and N/S to other calculated amounts, it is possible to
perform the movement using the zoom only. Of course in such cases the lens has to
be of a design that will cover an area considerably larger than the camera gate with­
out vignetting, as otherwise vignetting would occur as soon as the lens is off-set.
12
Given such a lens however, considerable time can be saved in shooting such a zoom
shot, since only one adjustment per frame will be required instead of three. The
use of a lens compound in this way is only applicable if the field being panned moves
in a straight line (though perhaps at varying speeds). If in addition to panning
and zooming, it is required to rotate the field and the turntable is fitted above the
compound (which is its usual position), the required E/W and N/S positions for each
frame will not lie on a straight line because they will be affected by the angle of
rotation. In such cases therefore four movements - zoom, E/W pan, N/S pan and rotat­
ion - will have to be made for every frame.
Now zooms, pans, peg-bar movements or rotations may be of many different kinds.
For example, they can be linear (constant speed) with one or two fairings, exponential
with one or two fairings, circular pans may be required, or pan movements may/be
affected by rotations. Sometimes when the speed of a pan movement is required to
change in the course of a shot, middle fairings have to be employed, and sometimes
pans are required along curves which are neither straight lines nor circles. To
achieve satisfactory results on such shots, the quantities to be set on each of the
counters for each frame have to be calculated in advance. This of course can be
done using ordinary, and usually fairly elementary, mathematics, and the figure work
can be shortened using tables and/or an electronic calculator. Even so, such cal­
culation generally takes a considerable time.
The advent of the programmable calculator has changed all this. A programme
can be written and stored permanently on a magnetic card for each type of movement
required. When a shot has to be calculated, the appropriate programme is loaded into
the calculator, the data for the actual scene is keyed in, and the calculator started.
It will then calculate the required quantities for each frame, and if it is a model
with print-out, will print them out without further attention.
A programmable calculator is in all essentials a mini computer. It differs from
a computer in degree rather than kind. While a computer is normally a far more complex
machine with greater possibilities, the current brand of programmable calculators is
more than adequate for almost all calculations likely to be required for animation.
There is one thing however which such a calculator will not do: it cannot directly
control the animation stand. The results of its calculations will still have to be
set by hand on each of the several counters on the animation stand.
From the user's point of view, the essential differences between a programmable
calculator and a computer boil down to (a) methods of inputting, which includes both
writing and loading a programme, and entering data for a particular shot, and (b)
methods of output, i.e. methods of displaying or recording calculations.
The keyboard of a calculator is what may be called a function keyboard. In
addition to the numerals 0 through 9, it will have keys labelled X2 3 1/ΧΛ SIN> LOGj
ex and so on. A programme consists basically of a list of keystrokes, in proper
sequence, required to solve a given problem, though there are also various devices
such as branches, loops, conditionals etc. which are used to shorten and simplify a
programme. This being so, anyone familiar with elementary mathematics can write a
programme for such a calculator, though a certain amount of practice is necessary to
avoid making mistakes and to write a programme in the most satisfactory way. On the
other hand, the keyboard of a computer usually resembles that of a typewriter. Pro­
grammes have to be written in one of the special computer languages such as FORTRAN,
which the computer can understand. Such languages are not particularly difficult to
learn, but it seems probable that few animation technicians will in fact take the trouble
to do so. If therefore a computer is being used for animation purposes, any programmes