Physically-Based Modeling for Computer Graphics: A Structured Approach Book

	Foreword	xi
	Preface	xiii
	Index of Figures	xv
	Notation	xxiii
Part I.	Introduction	1
1	Overview	2
1.1	What Kind of Modeling?	3
1.2	What Kinds of Structure?	4
1.3	Why "Structured Modeling"?	5
1.4	Goals for Structured Modeling	6
1.5	Mathematical Modeling Premise	7
1.6	Theme: A Goal-Oriented Approach	8
1.7	Wherein Computer Graphics?	9
1.8	Reader's Guide	10
2	Overview of Physically-Based Modeling	14
2.1	Background: Traditional Computer Graphics Modeling	15
2.2	Striving for Realism	16
2.3	Physically-Based Modeling	17
2.4	Goals for Modeling	17
2.5	Control of Physically-Based Models	19
2.6	Applications of Physically-Based Modeling	20
2.7	Notes on Physically-Based Computer Models	22
2.8	Where Does Structured Modeling Fit In?	23
2.9	Summary	23
Part II.	Structured Modeling	25
3	A Structured Analysis of Modeling	26
3.1	Canonical "ARI" Structure of a Model	27
3.2	Discussion of the ARI Structure	30
3.3	Progressive Decomposition of a Model	31
3.4	Relating ARI and Progressive Decomposition	35
3.5	Design Methodologies for Models	35
3.6	Communicating a Model to Other People	40
3.7	The Role of Computers in Modeling	41
3.8	Summary	47
4	Structured Physically-Based Modeling	50
4.1	Overview	51
4.2	Background: Applied Mathematical Modeling	52
4.3	Canonical "CMP" Structure of a Physically-Based Model	54
4.4	Discussion of the CMP Structure	57
4.5	Modularity and Hierarchy	63
4.6	Designing a Model	65
4.7	Communicating Models to Other People	70
4.8	Summary	72
5	Structured Mathematical Modeling	74
5.1	Overview	75
5.2	Motivation for Structured Mathematical Modeling	76
5.3	Aesthetics and Design Decisions	79
5.4	Borrowing from Programming	79
5.5	Distinctions from Programming	83
5.6	Naming Strategies	86
5.7	Abstract Spaces	91
5.8	Identifiers (IDs) and Indexes	97
5.9	State Spaces	102
5.10	Segmented Functions	111
5.11	Designing a Model	116
5.12	Summary	119
6	Computer Programming for Structured Modeling	122
6.1	Overview	123
6.2	Framework for Program Structure	124
6.3	How to Implement a CMP Model	130
6.4	Procedural Outlook	131
6.5	Why Have a Math Section?	132
6.6	Representational Outlook	132
6.7	Decoupling Model State from Program State	134
6.8	Efficiency	136
6.9	Debugging	137
6.10	Summary	138
Part III.	Prototype Physically-Based Model Library	139
7	Overview of Model Library	140
7.1	Goals for the Prototype Library	141
7.2	Features of the Library	142
7.3	Outline of the Library	143
7.4	Common Mathematical Idioms	143
7.5	Presentation of Each Module	145
8	Coordinate Frames Model	146
8.1	Background	147
8.2	Goals	148
8.3	Conceptual Model	149
8.4	Mathematical Model	152
8.5	Posed Problems	167
8.6	Implementation Notes	168
8.7	Derivations	170
9	Kinematic Rigid-Bodies Model	172
9.1	Goals	173
9.2	Conceptual Model	173
9.3	Mathematical Model	175
9.4	Posed Problems	180
9.5	Implementation Notes	181
10	Dynamic Rigid-Bodies Model	184
10.1	Goals	185
10.2	Conceptual Model	186
10.3	Mathematical Model	190
10.4	Posed Problems	205
10.5	Implementation Notes	208
11	"Fancy Forces" Model	212
11.1	Goals	213
11.2	Conceptual Model	214
11.3	Mathematical Model	217
11.4	Posed Problems	238
11.5	Implementation Notes	240
11.6	Derivations	244
12	Swinging Chain Model	248
12.1	Goals	249
12.2	Conceptual Model	250
12.3	Mathematical Model	251
13	"Tennis Ball Cannon"	254
13.1	Goals	255
13.2	Conceptual Model	255
13.3	Mathematical Model	257
13.4	Posed Problems	262
13.5	Implementation Notes	262
14	Extensions to the Prototype Library	266
14.1	Rigid-Body Collision	267
14.2	Rigid-Body Contact	268
14.3	Finite-State Control	269
14.4	Mixed Dynamic and Kinematic Motion	270
14.5	Flexible Bodies	272
14.6	Summary	273
Part IV.	Conclusion and Appendices	275
15	Concluding Remarks	276
15.1	Notes on the Design Strategy	277
15.2	Did We Meet Our Goals?	279
15.3	Have We Made Modeling Easy?	280
15.4	Computer-Assisted Mathematical Modeling	281
15.5	Future Directions	282
	Appendices
A	Miscellaneous Mathematical Constructs	284
A.1	Trees	285
A.2	Arrays	286
A.3	Implementation Notes	287
B	Prototype Implementation	288
B.1	Overview of the Presentation Style	289
B.2	The Conceptual Section	290
B.3	The Math Section	291
B.4	The Numerics Section	296
C	Solving Piecewise-Continuous ODEs	304
C.1	Formalism for Piecewise-Continuous ODEs (PODEs)	305
C.2	Solving a PODE	310
C.3	Computational Costs	315
	References	316
	Index	324