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Physics Based Animation

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Physics Based Animation Authors Kenny Erleben, Jon Sporring, Knud Henriksen, and Henrik Dohlmann. Physics-based animation is becoming increasingly popular due to its use in computer games, for producing special effects in movies, and as part of surgical simulation systems. Over the past decade the field has matured, and today there is a wealth of simulation methods solving many simulation problems. There is a vast amount of examples where physics-based animation is used

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You will also learn how to use morph and bones-based animation and how to add physics to your scene. What you will learn from this book Create standard ...

“book” — 2005/9/30 — 15:44 — page i — #1

✐

Physics-Based Animation

Kenny Erleben Jon Sporring Knud Henriksen

Henrik Dohlmann

“book” — 2005/9/30 — 15:44 — page ii — #2

✐

LIMITED WARRANTY AND DISCLAIMER OF LIABILITY

CHARLES RIVER MEDIA, INC. (“CRM”) AND/OR ANYONE WHO HAS BEEN INVOLVED IN

THE WRITING, CREATION OR PRODUCTION OF THE ACCOMPANYING CODE IN THE TEX-

TUAL MATERIAL IN THE BOOK, CANNOT AND DO NOT WARRANT THE PERFORMANCE

OR RESULTS THAT MAY BE OBTAINED BY USING THE CONTENTS OF THE BOOK. THE AU-

THOR AND PUBLISHER HAVE USED THEIR BE ST EFFORTS TO ENSURE THE ACCURACY

AND FUNCTIONALITY OF THE TEXTUAL MATERIAL AND PROGRAMS DESCRIBED HEREIN.

WE HOWEVER, MAKE NO WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, REGARDING

THE PERFORMANCE OF THESE PROGRAMS OR CONTENTS. THE BOOK IS SOLD “AS IS”

WITHOUT WARRANTY (EXCEPT FOR DEFECTIVE MATERIALS USED IN MANUFACTURING

THE BOOK OR DUE TO FAULTY WORKMANSHIP).

THE AUTHOR, THE PUBLISHER, AND ANYONE INVOLVED IN THE PRODUCTION AND MAN-

UFACTURING OF THIS WORK SHALL NOT BE LIABLE FOR DAMAGES OF ANY KIND ARIS-

ING OUT OF THE USE OF (OR THE INABILITY TO USE) THE PROGRAMS, SOURCE CODE,

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DAMAGES ARISING OUT OF THE USE OF THE PRODUCT.

THE SOLE RE MEDY IN THE EVENT OF A CL AIM OF ANY KIND IS EXPRESSLY LIMITED TO

REPLACEMENT OF THE BOOK, AND ONLY AT THE DISCRETION OF CRM.

THE USE OF “IMPLIED WARRANTY” AND CERTAIN “EXCLUSIONS” VARIES FROM STATE TO

STATE, AND MAY NOT APPLY TO THE PURCHASER OF THIS PRODUCT.

“book” — 2005/9/30 — 15:44 — page iii — #3

✐

Physics-Based Animation

Kenny Erleben, Jon Sporring, Knud Henriksen, and Henrik Dohlmann

CHARLES RIVER MEDIA, INC.

Hingham, Massachusetts

“book” — 2005/9/30 — 15:44 — page iv — #4

✐

No part of this publication may be reproduced in any way, stored in a retrieval system of any type, or

transmitted by any means or media, electronic or mechanical, including, but not limited to, photocopy,

recording, or scanning, without prior permission in writing from the publisher.

Publisher: Jenifer Niles

Cover Design: Tyler Creative

Cover Image: Kenn y Erleben

Graphical Consultant: André Tischer Poulsen

CH ARLES RIVER MEDIA, INC.

10 Downer Avenue

Hingham, Massachusetts 02043

781-740-0400

781-740-8816 (FAX)

info@charlesriver.com

www.charlesriver.com

This book is printed on acid-free paper.

Kenny Erleben, Jon Sporring, Knud Henriksen, and Henrik Dohlmann. Physics-Based Animation.

ISBN: 1-58450-380-7

All brand names and product names mentioned in this book are trademarks or service marks of their re-

spective companies. Any omission or misuse (of any kind) of service marks or trademarks should not be

regarded as intent to infringe on the property of others. The publisher recognizes and respects all marks

used by companies, manufacturers, and developers as a means to distinguish their products.

Library of Congress Cataloging-in-Publication Data

Physics-based animation / Kenny Erleben . . . [et al.]. — 1st ed.

p. cm.

Includes index.

ISBN 1-58450-380-7 (hardcover : alk. paper)

1. Computer animation. I. Erleben, Kenny, 1974-

TR897.7.P525 2005

006.6’96–dc22

2005017654

05 7 6 5 4 3 2 First Edition

CH ARLES RIVER MEDIA titles are available for site license or bulk purchase by institutions, user groups,

corporations, etc. For additional information, please contact the Special Sales Department at 781-740-

0400.

“book” — 2005/9/30 — 15:44 — page v — #5

✐

Contents

Preface xi

1 Introduction 1

1.1 The Computer Graphics Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 The Taxonomy of Physics-Based Animation Methods . . . . . . . . . . . . . . . . . . . 3

1.3 Scientiﬁc Computing versus Computer Graphics in Practice . . . . . . . . . . . . . . . . 5

1.4 Future Points of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Readers Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

I The Kinematics 11

2 Articulated Figures 15

2.1 Links and Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Paired Joint Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Denavit-Hartenberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 Forward and Inverse Kinematics 45

3.1 End Effector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Forward Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.3 Inverse Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 Motion Interpolation 71

4.1 Key-Framing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.2 Scripted Motion Using Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

II Multibody Animation 85

5 Penalty-Based Multibody Animation 89

5.1 The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2 The Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.3 Picking Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.4 Solving Harmonic Oscillators Numerically . . . . . . . . . . . . . . . . . . . . . . . . . 104

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