3D CAD: Principles and Applications

283 Pages·1993·7.56 MB·English

by  Dr. Hiroshi Toriya, Prof. Dr. Hiroaki Chiyokura (auth.), Dr. Hiroshi Toriya, Prof. Dr. Hiroaki Chiyokura (eds.)

Computer Science Workbench
Editor: Tosiyasu L. Kunii
H. Toriya H. Chiyokura (Eds.)
3 D C A D
Principles
and Applications
Translated from the Japanese by Hiromi Yaguchi
With 177 Figures, 8 Colour Plates and 9 Tables
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo
Hong Kong Barcelona
Budapest
Dr. Hiroshi Toriya
RICOH Company, Ltd., Software Division
Tomin-Nissei -Kasugacho-Bldg.
1-1-17, Koishikawa
Bunkyo-ku Tokyo, 117 , Japan
Prof. Dr. Hiroaki Chiyokura
Faculty of Environmental Infonnation, Keio University
5322,Endoh
Fujisawa-shi Kanagawa, 252, Japan
Originally published in Japanese as by
Kyoritsu Shuppan Co., Ltd., Tokyo, Japan
Copyright © 1991 by Hiroshi Toriya and Hiroaki Chiyokura
ISBN-13: 978-3-642-45731-9 e-ISBN-13: 978-3-642-45729-6
001: 10.1007/978-3-642-45729-6
Library of Congress Cataloging-in-Publication Data
3-jigen CAD no kiso to oyo. English: 3D CAD principles and applications 1 H. Toriya, H. Chiyolrura,
eds. ; translated from the Japanese by Hiromi Yaguchi. --(Computer science workbench) Translation
of: 3-jigen CAD no kiso oyo. Includes bibliographical references and indeX.lsBN-13: 978-3-642-45731-9
I. Computer graphics. 2. Designbase. 3. CADICAM systems. 4. Three-dimensional display systems.
I. Toriya, H. (Hiroshi), 1960- . II. Chiyokum, Hiroaki. III. Title. IV. Series.
T385.AI513 1993 620'.0042'0285--dc20
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad
casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this
publication or parts thereof is only permitted under the provisions of the German Copyright Law of
September9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations
fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1993
Softcover reprint of the hardcover 1st edition 1993
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of
a specific statement, that such names are exempt from the relevant protective laws and regulations and
therefore free for general use.
Typesetting: Camera ready by author
33/3140 -5 4 3 2 1 0 -Printed on acid-free paper
PREFACE
In recent years, 3-dimensional computer aided design (3D CAD) has been
recognized as one of the most important technologies for survival of enter
prises. Conventionally, products are designed and manufactured through 2-
dimensional data media, so-called drawing. At present, however, drawings are
giving way to the media based on 3-dimensional data processed in a com
puter. It is not too much to say that use of the 3-dimensional CAD systems
and their application techniques can be the key to winning the competition in
the development of new products. Since 1984, RICOH Software Division has
been independently researching and developing DESIGN BASE, a 3-dimensional
CAD system. At present, DEslGNBAsE is widely used as a practical system
in design and production centers. This book introduces the implementation
method of a 3-dimensional CAD system and its wide range of applications,
based on the development of DEslGNBAsE Version 3.
DEslGNBAsE originates with my thesis for the master's degree at Keio
University. When I was a student in the master's course of the graduate school,
I read a paper about curved surfaces by the British mathematician Gregory.
I still remember that the paper deeply impressed me at that time. I was also
convinced that the idea would greatly influence the future CAD systems. After
that, I went on to pursue a doctorate in precision machinery engineering at the
University of Tokyo. There I developed MODIF as an experimental system in
which the functions of the Gregory patch, my original surface, could be fully
used. The concept of this system would later be applied to DESIGN BASE.
The development of DESIGN BASE started in 1984 in RICOH Software
Division and Version 1 was completed in 1987. Version 1 was immature and
many problems regarding its practical use were pointed out by the users.
Later on, these problems were gradually solved and the system improved with
the development of Versions 2 and 3. Up till now DEslGNBAsE has been
offered to many users. In Versions 1 and 2, the Gregory patch was the only
surface supported in DESIGN BASE, whereas in Version 3, many other types
of surfaces, such as the quadric surface, and the rational Bezier surface, were
added. Nonetheless the Gregory patch is constantly playing the principal role
in DESIGN BASE.
The authors of this book are the developers of DEslGNBAsE Version 3 and
are listed below by chapters. All are staff members of RICOH except Takashi
Nagafuku and Fuminori Gotoh of KUBOTA Corporation.
VI PREFACE
Chapter 1 Hiroshi Toriya, Kenji Ueda
Chapter 2 Hiroshi Toriya
Chapter 3 Tsuyoshi Harada, Hiroshi Toriya
Chapter 4 Miki Satoh, Teiji Takamura
Chapter 5 Koichi Konno, Teiji Takamura
Chapter 6 Teiji Takamura, Satoshi Higuchiuchi
Chapter 7 Toshiaki Satoh, Hiroshi Toriya
Chapter 8 Toshiaki Satoh
Chapter 9 Tsuyoshi Harada, Hiroshi Toriya
Chapter 10 Kenji U eda, Takashi Hashimoto
Chapter 11 N obuko Fujisawa
Chapter 12 Hideki Tamura
Chapter 13 Hideki Tamura
Chapter 14 Takashi Nagafuku, Fuminori Gotoh (Kubota Cor
poration), Masanori Harada
Translation: Hiromi Yaguchi
Because of a limitation of pages, some explanations may not be sufficiently
thorough. For those parts, the bibliography is presented at the end of this
book, which can be referenced through superscripts in the text. Use these
references for deeper understandings.
At present, DESIGN BASE Version 4 is released from RICOH COMPANY,
LTD. In this current version, NURBS is introduced as one of the basic rep
resentation methods of surfaces. The integration of surface and solid models,
which is highly appreciated in the practical environment, is also realized. This
is not our goal, and we are planning to keep on enhancing the functions.
Finally, I would like to thank Dr. Hideko S. Kunii, a director of the Soft
ware Division, for a lot of advice for writing this book. I also sincerely thank
Nobuo Yamada of KUBOTA COMPUTER INC. and Tadao !toh of D-MEC
LTD. for their help.
My sincere appreciation goes to Motoyasu Sasaki and Makiko Sugawara
for setting up and operating the software environment to edit this book on
computer.
My thanks are also due to Yoshinobu Satake, Kazunari Kojima, Shinichiro
Tsukimura, Masaaki Kagawa, Tsukasa Matsuoka, Hung-tien Ting, Manabu
Tsumagari, Teruaki !toh, Masanori Makino, Kenji Kohri, Ikumi Inoguchi,
Ichiro Kamiyama, Jun Satoh, Akihiro Miyazawa, Rieko Sakamoto, Tohru
Fukuhara, Koji Aragaki, Koji Tanaka, Shusaku Furushima, Naoyuki Satoh,
Chikara Kagimoto, Katsumi Awaji, Masahiro Nagase, Chatman Wong, and
Kenji lino, for their assistance in developing DESIGN BASE Versions 3 and 4.
Tokyo, February, 1993
Hiroaki Chiyokura
Table of Contents
1 OUTLINE OF CAD/CAM/CAE 1
1.1 Introduction . 1
1.2 CAD System 1
1.3 CAM System 3
1.4 CAE System 5
1.5 3D CAD Systems . 6
2 3D CAD SYSTEMS AND SOLID MODELS 9
2.1 Introduction. . . . . . . . . . . 9
2.2 How to Represent Solids . . . . . . . . . 9
.....
2.3 Advantages of a Solid Modeler 12
2.4 Representation of Objects in a Solid Modeler 14
2.4.1 CSG and boundary representations . 14
2.4.2 Hybrid systems . . . . . . . . . . . . . 16
2.4.3 Other representation methods. . . . . 17
2.5 Comparison of CSG and Boundary Representations. 19
3 SOLID MODELER DESIGNBASE 23
3.1 Introduction. . . . . . . . . . . . 23
3.2 Features of DEslGNBAsE .... 23
3.3 Software Structure of DESIGN BASE 25
3.4 Data Structure of Boundary Representations 26
3.4.1 Solid models with boundary representations . 27
3.4.2 Data structures of boundary representations. 28
3.4.3 Data structure of topological elements in DESIGN BASE 33
3.4.4 Data structure of geometric elements in DESIGN BASE 35
3.5 Primitive Operations . . . . . . . . . . . . . . . 37
3.5.1 Topological elements and Euler formula 37
3.5.2 Euler operations ............ 38
3.5.3 Primitive operations in DESIGN BASE 40
3.6 An Example of Primitive Operations . . . . . 45
VIII Table of Contents
4 FREE-FORM CURVES 51
4.1 Introduction.... 51
4.2 Parametric Curves 51
4.2.1 Algebraic representation . 51
4.2.2 Parametric representation 52
4.3 Bezier Curves . . . . .. ... 53
4.3.1 How to represent Bezier curves 54
4.3.2 Division and connection of Bezier curves . 57
4.3.3 Degree elevation of Bezier curves . . . 58
4.4 Rational Bezier Curves. ... ... ... 59
4.4.1 How to represent rational Bezier curves 59
4.4.2 Weights and their effects. 60
4.4.3 Creation of conic sections . . . 60
4.5 B-Spline Curves. . . . . . . . . . . 62
4.5.1 How to represent B-spline curves 62
4.5.2 Knot vectors and curves . . . . 64
4.5.3 Connection and division of curves 65
4.6 NURBS . . . . . . . ... .. 66
4.6.1 How to represent NURBS .. 67
4.6.2 How to represent conic sections with NURBS 67
4.6.3 Connection of curves . . . . . . 68
4.7 Programs ... . .... . 69
4.7.1 Program to obtain coordinates on a curve . . 70
4.7.2 Program to obtain a derivative vector on a curve 74
4.7.3 Program to divide a curve. 77
5 FREE-FORM SURFACES 83
5.1 Introduction. . . . . 83
5.2 Quadric Surfaces 83
5.3 Parametric Patches . 84
5.4 Coons Surfaces . . 85
5.5 Bezier Surfaces . . 89
5.6 Rational Bezier Surfaces 91
5.7 NURBS . . . . .. .. 93
5.8 Gregory Patches . . 94
5.9 Rational Boundary Gregory Patches 96
5.10 Connection of Patches . . 98
5.10.1 Conditions on connectivity 99
5.10.2 Connection of Gregory patches 99
5.10.3 Connection of rational boundary Gregory patches. 102
5.11 Interpolation of Patches . . 104
5.11.1 Irregular meshes .. 104
5.11.2 Interpolation of curve meshes 105
5.11.3 Interpolation of triangular surfaces 107
Table of Contents IX
5.11.4 Interpolation of surfaces containing an odd number of
sides ............................. 108
5.11.5 Interpolation of surfaces containing an even number of
sides. . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.11.6 Interpolation of curve meshes containing T-nodes .... 111
5.12 Transformation of Patches . . . . . . . . . . . . . . . . . . . . . 112
5.12.1 Transformation between Bezier surface and Coons surface112
5.12.2 Transformation of rational boundary Gregory patch into
rational Bezier surface . . . . . . . . . . . . 113
5.13 Programs .............................. 115
5.13.1 Program to obtain coordinates on a surface ....... 116
5.13.2 Program to obtain a partial derivative vector of a surface 127
6 INTERSECTION CALCULATIONS 139
6.1 Introduction. . . . . . . . . . . 139
6.2 Intersection Calculations Between Curves 139
6.2.1 Algebraic calculation method ... 139
6.2.2 Geometric calculation method. . . 142
6.3 Intersection Calculations Between a Curve and a Surface . 147
6.3.1 Algebraic calculation method .... 148
6.3.2 Geometric calculation method. . . . . . . . . . . . 149
6.4 Intersection Calculations Between Surfaces ........ 150
6.4.1 Intersection calculations between quadratic surfaces 151
6.4.2 Intersection calculations between free-form surfaces . 156
6.4.3 Recursive subdivision method . . . 157
6.4.4 Marching method. . . . . . . . . . 159
6.5 Intersection Calculation in DESIGNBASE . 163
7 LOCAL OPERATIONS ............ . 165
7.1 Introduction ................ . 165
7.2 Creation and Modification of Solids with Surfaces. 165
7.2.1 Defining surfaces by skinning ....... . 165
7.2.2 Defining surfaces by translating control points 166
7.2.3 Defining surface by interpolation .... 167
7.2.4 Defining surfaces by Boolean operations . . 167
7.3 Primitive Solid Generation ............. . 167
7.3.1 Creation of a parallelepiped and a cylinder 168
7.3.2 Creation of a rotational model .. 169
7.3.3 Creation of a mirror-image model . 170
7.3.4 Creation of a skinning model 170
7.3.5 Creation of a sweep model. . . . . 171
7.4 Local Modification Operations ..... . 171
7.4.1 Creation and modification of edges 172
7.4.2 Lifting operation 174
7.4.3 Model cutting. 175
7.4.4 Model gluing . . 176
X Table of Contents
7.5 Programs of Local Operations. 177
8 BOOLEAN OPERATIONS . . . . . 183
8.1 Introduction........... 183
8.2 Boolean Operations of Solids with Free-Form Surfaces and
Their Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2.1 Intersection calculations . . . . . . . . . 183
8.2.2 How to deal with intersection curves . . . . . . . . . 184
8.3 Boolean Operation Algorithm in DEslGNBAsE . . . . . . . 187
8.3.1. Intersection calculations between edges and surfaces 188
8.3.2 Intersection calculations between surfaces 189
8.3.3 Creation of intersection vertices. . . . . . . . . . . . 191
8.3.4 Creation of intersection edges . . . . . . . . . . . . . 192
8.3.5 Classification of boundaries and deletion of unnecessary
parts ......... . 192
8.3.6 Gluing of two solids . 194
8.3.7 Examples of execution 194
9 ROUNDING OPERATION . . . . 197
9.1 Introduction.......... 197
9.2 Problems with the Rounding Operation 197
9.3 Rounding Operation in DESIGN BASE . 198
9.4 Example of Rounding Operation Execution 199
9.5 Algorithm of Rounding Operation ..... 201
9.6 How to Calculate Trajectories Drawn by Tangent Points 202
10 FUNCTIONS IN AIDING DESIGN 207
10.1 Introduction. . . . . . . . . 207
10.2 Parametric Design . . . . . 207
10.3 UNDO· REDO Operations 209
10.3.1 Interactive system . 209
10.3.2 UNDO· REDO operations in DESIGN BASE . 209
10.3.3 Representation of the solid creation process 211
10.3.4 UNDO· REDO with Boolean operations. 212
10.4 Creation of Similar Shapes. . . . . . . . . . . . . 213
10.4.1 Limits of the UNDO· REDO operations. 213
10.4.2 Reexecution function. . . . . . 213
10.4.3 Limits of reexecution function. 216
11 RENDERING 217
11.1 Introduction. . . . . . . . . . . . . . . 217
11.2 Color Components and Shading Model . 218
11.2.1 Color representation . 218
11.2.2 Ambient light . . . . . . 219
11.2.3 Diffuse reflection light . 219
11.2.4 Specular reflection light 220
Table of Contents XI
11.2.5 Transmission light 223
11.3 Z-Buffer Method . . . . . 224
11.4 Scan Line Method .... 224
11.4.1 Characteristics of scan line method. 224
11.4.2 Actual processing in the scan line method 225
11.4.3 Coherence in the scan line method 226
11.4.4 Antialiasing - A-buffer method .... 227
11.5 Ray Tracing Method. . . . . . . . . . . . . . . 228
11.5.1 Antialiasing in the ray tracing method. 230
11.6 Mapping Method. . . . . . . . 231
11.6.1 Significance of mapping 231
11.6.2 Texture mapping . . 231
11.6.3 Reflection mapping. 232
11.6.4 Refraction mapping 233
11.6.5 Bump mapping. 234
11.6.6 Solid texture 234
12 MASS PROPERTIES . . 235
12.1 Introduction. . . . . 235
12.2 How to Obtain Surface Area. 235
12.2.1 Monte Carlo method. 235
12.2.2 Element subdivision method 236
12.2.3 Polygonization . . . . . . . . 237
12.2.4 Numerical integration . . . . 237
12.3 How to Obtain Volume, Center of Gravity, and Moment of Inertia239
12.3.1 Monte Carlo method. . . . . . . . 239
12.3.2 Element subdivision method .... 240
12.3.3 Method using integration theorem . 241
12.4 Mass Property Calculation in DEslGNBAsE 242
13 3-DIMENSIONAL MODELING METHOD 245
13.1 Introduction .......... . 245
13.2 Resin Model Creation System. 245
13.2.1 Fundamental principles 245
13.2.2 UV curing resin. 246
13.2.3 Laser control . . 247
13.2.4 Data processing. 248
13.3 Link with Modeler . . . 250
13.3.1 Link with surface modeler. 251
13.3.2 Link with solid modeler . . 252
13.4 DESIGN BASE and Resin Model Creation System 253
14 SOLID MODELS AND STRUCTURE ANALYSIS 255
14.1 Introduction ................ . 255
14.2 History of Finite Element Method ... . 255
14.3 Finite Element Method and Solid Models 257