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Millington - Game physics engine development: how to build a robust commercial-grade physics engine for your game

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Game Physics Engine Development How to Build a Robust Commercial-Grade Physics - photo 1
Game Physics Engine Development

How to Build a Robust Commercial-Grade Physics Engine for your Game

Second Edition

Ian Millington

Morgan Kaufmann Publishers is an imprint of Elsevier 30 Corporate Drive Suite - photo 2

Morgan Kaufmann Publishers is an imprint of Elsevier.

30 Corporate Drive, Suite 400, Burlington, MA 01803, USA

This book is printed on acid-free paper.

Copyright 2010 Elsevier Inc. All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publishers permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

Library of Congress Cataloging-in-Publication Data

Millington, Ian.

Game physics engine development : how to build a robust commercial-grade physics engine for your game / Ian Millington. 2nd ed.

p. cm.

Includes index.

ISBN 978-0-12-381976-5 (pbk. : alk. paper)

1. Computer gamesProgramming. 2. PhysicsData processing. I. Title.

QA76.76.C672M55 2010

794.81526dc22
2010014533

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

ISBN: 978-0-12-381976-5

For information on all Morgan Kaufmann publications visit our Website at www.mkp.com or www.elsevierdirect.com

Typeset by: diacriTech, India

Printed in the United States of America

10 11 12 13 5 4 3 2 1

For Richard List of Figures 11 Trigonometry and coordinate geometry 9 - photo 3

For Richard

List of Figures
1.1Trigonometry and coordinate geometry9
2.13D coordinates19
2.2Left- and right-handed axes22
2.3A vector as a movement in space23
2.4The geometry of scalar-vector multiplication26
2.5The geometry of vector addition27
2.6Geometric interpretation of the scalar product33
2.7Geometric interpretation of the vector product36
2.8Same average velocity, different instantaneous velocity39
4.1Screenshot of the ballistic demo63
4.2Screenshot of the bigballistic demo65
4.3Screenshot of the fireworks demo66
6.1The games camera attached to a spring92
6.2A rope bridge held up by springs95
6.3A buoyant block submerged and partially submerged98
6.4A non-stiff spring over time102
6.5A stiff spring over time103
6.6The rest length and the equilibrium position108
7.1Contact normal is different from the vector between objects in contact117
7.2Interpenetrating objects122
7.3Interpenetration and reality124
7.4Vibration on resting contact127
7.5Resolving one contact may resolve another automatically131
8.1Screenshot of the bridge demo151
8.2Screenshot of the platform demo152
9.1Angle that an object is facing158
9.2The circle of orientation vectors160
9.3The relative position of a car component161
9.4The car is rotated162
9.5Aircraft rotation axes166
9.6A matrix basis is changed198
10.1A force generating no torque212
10.2The moment of inertia is local to an object217
11.1Screenshot of the flightsim demo241
11.2Different centers of buoyancy243
11.3Screenshot of the sailboat demo247
12.1The collision detection pipeline255
12.2A three-stage collision detection pipeline256
12.3A spherical bounding volume257
12.4A spherical bounding volume hierarchy260
12.5Bottom-up hierarchy building in action267
12.6Top-down hierarchy building in action268
12.7Insertion hierarchy building in action269
12.8Working out a parent bounding sphere272
12.9Removing an object from a hierarchy273
12.10A subobject bounding volume hierarchy275
12.11A BSP for level geometry280
12.12Identifying an objects location in a quad-tree282
12.13A quad-tree forms a grid284
12.14An object may occupy up to four same-sized grid cells287
13.1An object approximated by an assembly of primitives293
13.2Collision detection and contact generation295
13.33D cases of contact296
13.4Ignoring a vertexvertex contact297
13.5The relationship among the collision point, collision normal, and penetration depth299
13.6The vertexface contact data
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