Mathematics for 3D game programming and computer graphics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass.
Course Technology
2012
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 545 S. graph. Darst. |
| ISBN: | 9781435458864 1435458869 |
Internformat
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| 245 | 1 | 0 | |a Mathematics for 3D game programming and computer graphics |c Eric Lengyel |
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Datensatz im Suchindex
| _version_ | 1804148770660679680 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE XIII
WHAT S NEW IN THE THIRD EDITION XIII
CONTENTS OVERVIEW XIV
WEBSITE AND CODE LISTINGS XVII
NOTATIONAL CONVENTIONS XVII
CHAPTER 1 THE RENDERING PIPELINE 1
1.1 GRAPHICS PROCESSORS 1
1.2 VERTEX TRANSFORMATION 4
1.3 RASTERIZATION AND FRAGMENT OPERATIONS 6
CHAPTER 2 VECTORS 11
2.1 VECTOR PROPERTIES 11
2.2 THE DOT PRODUCT 15
2.3 THE CROSS PRODUCT 19
2.4 VECTOR SPACES 26
CHAPTER 2 SUMMARY ;29
EXERCISES FOR CHAPTER 2 ~. 30
CHAPTER 3 MATRICES 31
3.1 MATRIX PROPERTIES 31
3.2 LINEAR SYSTEMS 34
3.3 MATRIX INVERSES 40
3.4 DETERMINANTS 47
3.5 EIGENVALUES AND EIGENVECTORS 54
3.6 DIAGONALIZATION 58
III
IMAGE 2
IV
CONTENTS
CHAPTER 3 SUMMARY EXERCISES FOR CHAPTER 3
62 64
67 67 68 70
70 71 74 75
76 77 78 78
80 80 82 86
89 91
93 93 93 94
97 98 99 101 102 103 106 107 108 110 111 112 116
CHAPTER 4 TRANSFORMS 4.1 LINEAR TRANSFORMATIONS 4.1.1 ORTHOGONAL
MATRICES 4.1.2 HANDEDNESS
4.2 SCALING TRANSFORMS 4.3 ROTATION TRANSFORMS 4.3.1 ROTATION ABOUT AN
ARBITRARY AXIS 4.4 HOMOGENEOUS COORDINATES
4.4.1 FOUR-DIMENSIONAL TRANSFORMS 4.4.2 POINTS AND DIRECTIONS 4.4.3
GEOMETRICAL INTERPRETATION OF THE W COORDINATE 4.5 TRANSFORMING NORMAL
VECTORS 4.6 QUATEMIONS
4.6.1 QUATEMION MATHEMATICS 4.6.2 ROTATIONS WITH QUATEMIONS 4.6.3
SPHERICAL LINEAR INTERPOLATION CHAPTER 4 SUMMARY EXERCISES FOR CHAPTER 4
CHAPTER 5 GEOMETRY FOR 3D ENGINES 5.1 LINES IN 3D SPACE 5.1.1 DISTANCE
BETWEEN A POINT AND A LINE 5.1.2 DISTANCE BETWEEN TWO LINES
5.2 PLANES IN 3D SPACE 5.2.1 INTERSECTION OF A LINE AND A PLANE 5.2.2
INTERSECTION OF THREE PLANES 5.2.3 TRANSFORMING PLANES 5.3 THE VIEW
FRUSTUM
5.3.1 FIELD OF VIEW 5.3.2 FRUSTUM PLANES 5.4 PERSPECTIVE-CORRECT
INTERPOLATION 5.4.1 DEPTH INTERPOLATION
5.4.2 VERTEX ATTRIBUTE INTERPOLATION 5.5 PROJECTIONS 5.5.1 PERSPECTIVE
PROJECTIONS 5.5.2 ORTHOGRAPHIC PROJECTIONS
IMAGE 3
V
5.5.3 EXTRACTING FRUSTUM PLANES 5.6 REFLECTIONS AND OBLIQUE CLIPPING
CHAPTER 5 SUMMARY EXERCISES FOR CHAPTER 5
118 120 126 129
131 131 131
132 135 136 139 140 141 143 144 145 147 148 149 150 151 153 154
157 157 158
158 159 159 160 161 162 164 166 167 169 171
CHAPTER 6 RAY TRACING 6.1 ROOT FINDING 6.1.1 QUADRATIC POLYNOMIALS 6.1.2
CUBIC POLYNOMIALS
6.1.3 QUARTIC POLYNOMIALS 6.1.4 NEWTON S METHOD 6.1.5 REFINEMENT OF
RECIPROCALS AND SQUARE ROOTS 6.2 SURFACE INTERSECTIONS
6.2.1 INTERSECTION OF A RAY AND A TRIANGLE 6.2.2 INTERSECTION OF A RAY
AND A BOX 6.2.3 INTERSECTION OF A RAY AND A SPHERE 6.2.4 INTERSECTION OF
A RAY AND A CYLINDER 6.2.5 INTERSECTION OF A RAY AND A TORUS 6.3 NORMAL
VECTOR CALCULATION 6.4 REFLECTION AND REFRACTION VECTORS
6.4.1 REFLECTION VECTOR CALCULATION 6.4.2 REFRACTION VECTOR CALCULATION
CHAPTER 6 SUMMARY EXERCISES FOR CHAPTER 6
CHAPTER 7 LIGHTING AND SHADING 7.1 RGB COLOR 7.2 LIGHT SOURCES 7.2.1
AMBIENT LIGHT
7.2.2 DIRECTIONAL LIGHT SOURCES 7.2.3 POINT LIGHT SOURCES 7.2.4 SPOT
LIGHT SOURCES 7.3 DIFFUSE REFLECTION 7.4 SPECULAR REFLECTION 7.5 TEXTURE
MAPPING
7.5.1 STANDARD TEXTURE MAPS 7.5.2 PROJECTIVE TEXTURE MAPS 7.5.3 CUBE
TEXTURE MAPS 7.5.4 FILTERING AND MIPMAPS
IMAGE 4
VI
CONTENTS
7.6 EMISSION 7.7 SHADING MODELS 7.7.1 CALCULATING NORMAL VECTORS 7.7.2
GOURAUD SHADING
7.7.3 BLINN-PHONG SHADING 7.8 BUMP MAPPING 7.8.L BUMP MAP CONSTRUCTION
7.8.2 TANGENT SPACE
7.8.3 CALCULATING TANGENT VECTORS 7.8.4 IMPLEMENTATION 7.9 A PHYSICAL
REFLECTION MODEL 7.9.L BIDIRECTIONAL REFLECTANCE DISTRIBUTION FUNCTIONS
7.9.2 COOK-TORRANCE ILLUMINATION 7.9.3 THE FRESNEL FACTOR 7.9.4 THE
MICROFACET DISTRIBUTION FUNCTION 7.9.5 THE GEOMETRICAL ATTENUATION
FACTOR
7.9.6 IMPLEMENTATION CHAPTER 7 SUMMARY EXERCISES FOR CHAPTER 7
CHAPTER 8 VISIBILITY DETERMINATION 8.1 BOUNDING VOLUME CONSTRUCTION
8.1.1 PRINCIPAL COMPONENT ANALYSIS 8.1.2 BOUNDING BOX CONSTRUCTION
8.1.3 BOUNDING SPHERE CONSTRUCTION 8.1.4 BOUNDING ELLIPSOID CONSTRUCTION
8.1.5 BOUNDING CYLINDER CONSTRUCTION 8.2 BOUNDING VOLUME TESTS
8.2.1 BOUNDING SPHERE TEST 8.2.2 BOUNDING ELLIPSOID TEST 8.2.3 BOUNDING
CYLINDER TEST 8.2.4 BOUNDING BOX TEST 8.3 SPATIAL PARTITIONING
8.3.L OCTREES 8.3.2 BINARY SPACE PARTITIONING TREES 8.4 PORTAL SYSTEMS
8.4.1 PORTAL CLIPPING
8.4.2 REDUCED VIEW FRUSTUMS
174 175 175 176 177
178 178 180 180
185 187 187 191
192 195 198 200 205
209
211 211 212 215
217 218 220 221 221
222 226 228 230
230 232 235 236
238
IMAGE 5
VII
CHAPTER 8 SUMMARY EXERCISES FOR CHAPTER 8
240 244
CHAPTER 9
9.1
POLYGONAL TECHNIQUES
DEPTH VALUE OFFSET 9.1.1 PROJECTION MATRIX MODIFICATION 9.1.2 OFFSET
VALUE SELECTION 9.1.3 IMPLEMENTATION 9.2 DECAL APPLICATION
9.2.1 DECAL MESH CONSTRUCTION 9.2.2 POLYGON CLIPPING 9.3 BILLBOARDING
9.3.1 UNCONSTRAINED QUADS
9.3.2 CONSTRAINED QUADS 9.3.3 POLYBOARDS 9.4 POLYGON REDUCTION 9.5
T-JUNCTION ELIMINATION 9.6 TRIANGULATION CHAPTER 9 SUMMARY EXERCISES FOR
CHAPTER 9
245
245 246 247 248 249 250 252 254 254 257 258 260 264 267 274 277
CHAPTER 10 SHADOWS
10.1 SHADOW CASTING SET 10.2 SHADOW MAPPING 10.2.1 RENDERING THE SHADOW
MAP 10.2.2 RENDERING THE MAIN SCENE
10.2.3 SELF-SHADOWING 10.3 STENCIL SHADOWS 10.3.1 ALGORITHM OVERVIEW
10.3.2 INFINITE VIEW FRUSTUMS
10.3.3 SILHOUETTE DETERMINATION 10.3.4 SHADOW VOLUME CONSTRUCTION 10.3.5
DETERMINING CAP NECESSITY 10.3.6 RENDERING SHADOW VOLUMES
10.3.7 SCISSOR OPTIMIZATION CHAPTER 10 SUMMARY EXERCISES FOR CHAPTER 10
279
279 281 281 283 284 286 286 291 294 299 303 307
309 314 315
IMAGE 6
VIII
CONTENTS
CHAPTER 12
12.1
COLLISION DETECTION PLANE COLLISIONS 12.1.1 COLLISION OF A SPHERE AND A
PLANE 12.1.2 COLLISION OFA BOX AND A PLANE
12.1.3 SPATIAL PARTITIONING 12.2 GENERAL SPHERE COLLISIONS 12.3 SLIDING
12.4 COLLISION OF TWO SPHERES CHAPTER 12 SUMMARY
EXERCISES FOR CHAPTER 12
317
317 320 322 322
326 327 329 331
334 335 340 342
345 348 350 355
357
361 361 362 364
366 366 371 372
376 378
379 379 381 381
385 388 390 394
CHAPTER 11 CURVES AND SURFACES
11.1 CUBIC CURVES 11.2 HERMITE CURVES 11.3 BEZIER CURVES 11.3.1 CUBIC
BEZIER CURVES
11.3.2 BEZIER CURVE TRUNCATION 11.3.3 THE DE CASTELJAU ALGORITHM 11.4
CATMULL-ROM SPLINES 11.5 CUBIC SPLINES
11.6 B-SPLINES 11.6.1 UNIFORM B-SPLINES 11.6.2 B-SPLINE GLOBALIZATION
11.6.3 NONUNIFORM B-SPLINES
11.6.4 NURBS 11.7 BICUBIC SURFACES 11.8 CURVATURE AND TORSION CHAPTER 11
SUMMARY
EXERCISES FOR CHAPTER 11
CHAPTER 13 LINEAR PHYSICS 13.1 POSITION FUNCTIONS 13.2 SECOND-ORDER
DIFFERENTIAL EQUATIONS 13.2.1 HOMOGENEOUS EQUATIONS
13.2.2 NONHOMOGENEOUS EQUATIONS 13.2.3 INITIAL CONDITIONS 13.3
PROJECTILE MOTION 13.4 RESISTED MOTION
IMAGE 7
IX
13.5 FRICTION CHAPTER 13 SUMMARY EXERCISES FOR CHAPTER 13
CHAPTER 14 ROTATIONAL PHYSICS 14.1 ROTATING ENVIRONMENTS 14.1.1 ANGULAR
VELOCITY 14.1.2 THE CENTRIFUGAL FORCE
14.1.3 THE CORIOLIS FORCE 14.2 RIGID BODY MOTION 14.2.1 CENTER OF MASS
14.2.2 ANGULAR MOMENTUM AND TORQUE
14.2.3 THE INERTIA TENSOR 14.2.4 PRINCIPAL AXES OF INERTIA 14.2.5
TRANSFORMING THE INERTIA TENSOR 14.3 OSCILLATORY MOTION
14.3.1 SPRING MOTION 14.3.2 PENDULUM MOTION CHAPTER 14 SUMMARY EXERCISES
FOR CHAPTER 14
CHAPTER 15 FLUID AND CLOTH SIMULATION 15.1 FLUID SIMULATION 15.1.1 THE
WAVE EQUATION 15.1.2 APPROXIMATING DERIVATIVES
15.1.3 EVALUATING SURFACE DISPLACEMENT 15.1.4 IMPLEMENTATION 15.2 CLOTH
SIMULATION 15.2.1 THE SPRING SYSTEM
15.2.2 EXTERNAL FORCES 15.2.3 IMPLEMENTATION CHAPTER 15 SUMMARY
EXERCISES FOR CHAPTER 15
396 400 402
CHAPTER 16 NUMERICAL METHODS 16.1 TRIGONOMETRIC FUNCTIONS 16.2 LINEAR
SYSTEMS 16.2.1 TRIANGULAR SYSTEMS
16.2.2 GAUSSIAN ELIMINATION
405 405 405 407 408 410 410 413 414 422 426 430 430 434 436 438
443 443 443 447 450 453 457
457 459 459 461 462
463 463 465 465 467
IMAGE 8
X CONTENTS
16.2.3 LU DECOMPOSITION 16.2.4 ERROR REDUCTION 16.2.5 TRIDIAGONAL
SYSTEMS 16.3 EIGENVALUES AND EIGENVECTORS 16.4 ORDINARY DIFFERENTIAL
EQUATIONS
16.4.1 EULER S METHOD 16.4.2 TAYLOR SERIES METHOD 16.4.3 RUNGE-KUTTA
METHOD 16.4.4 HIGHER-ORDER DIFFERENTIAL EQUATIONS CHAPTER 16 SUMMARY
EXERCISES FOR CHAPTER 16
APPENDIX A COMPLEX NUMBERS A.1 DEFINITION A.2 ADDITION AND
MULTIPLICATION A.3 CONJUGATES AND INVERSES A.4 THE EULER FORMULA
470 477 479 483
490 490 492
493 495 496 498
499 499 499 500
501
APPENDIX B TRIGONOMETRY REFERENCE B.1 FUNCTION DEFINITIONS B.2 SYMMETRY
AND PHASE SHIFTS B.3 PYTHAGOREAN IDENTITIES
B.4 EXPONENTIAL IDENTITIES B.5 INVERSE FUNCTIONS B.6 LAWS OF SINES AND
COSINES
APPENDIX E ANSWERS TO EXERCISES CHAPTER 2
505 505 506 507 507 508 509
513 513 514 516 520
523 523 525 526
529 529
APPENDIX C COORDINATE SYSTEMS C.1 CARTESIAN COORDINATES C.2 CYLINDRICAL
COORDINATES C.3 SPHERICAL COORDINATES C.4 GENERALIZED COORDINATES
APPENDIX D TAYLOR SERIES D.1 DERIVATION D.2 POWER SERIES D.3 THE EULER
FORMULA
IMAGE 9
XI
CHAPTER 3 529
CHAPTER 4 530
CHAPTER 5 530
CHAPTER 6 530
CHAPTER 7 531
CHAPTER 8 531
CHAPTER 9 531
CHAPTER 10 531
CHAPTER 11 532
CHAPTER 12 532
CHAPTER 13 532
CHAPTER 14 533
CHAPTER 15 534
CHAPTER 16 534
INDEX 535
|
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| author_facet | Lengyel, Eric |
| author_role | aut |
| author_sort | Lengyel, Eric |
| author_variant | e l el |
| building | Verbundindex |
| bvnumber | BV039839468 |
| classification_rvk | ST 320 ST 324 |
| ctrlnum | (OCoLC)725520619 (DE-599)BSZ350207542 |
| dewey-full | 794.8/16693 |
| dewey-hundreds | 700 - The arts |
| dewey-ones | 794 - Indoor games of skill |
| dewey-raw | 794.8/16693 |
| dewey-search | 794.8/16693 |
| dewey-sort | 3794.8 516693 |
| dewey-tens | 790 - Recreational and performing arts |
| discipline | Sport Informatik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV039839468 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:12:25Z |
| institution | BVB |
| isbn | 9781435458864 1435458869 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024699391 |
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| owner_facet | DE-859 DE-523 DE-898 DE-BY-UBR DE-Aug4 DE-B768 DE-858 |
| physical | XVIII, 545 S. graph. Darst. |
| publishDate | 2012 |
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| publishDateSort | 2012 |
| publisher | Course Technology |
| record_format | marc |
| spelling | Lengyel, Eric Verfasser (DE-588)13723841X aut Mathematics for 3D game programming and computer graphics Eric Lengyel 3. ed. Boston, Mass. Course Technology 2012 XVIII, 545 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computerspiel (DE-588)4010457-6 gnd rswk-swf Computergrafik (DE-588)4010450-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Dreidimensionale Computergrafik (DE-588)4133691-4 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Dreidimensionale Computergrafik (DE-588)4133691-4 s Mathematik (DE-588)4037944-9 s Computerspiel (DE-588)4010457-6 s Programmierung (DE-588)4076370-5 s 1\p DE-604 Computergrafik (DE-588)4010450-3 s 2\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024699391&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lengyel, Eric Mathematics for 3D game programming and computer graphics Computerspiel (DE-588)4010457-6 gnd Computergrafik (DE-588)4010450-3 gnd Mathematik (DE-588)4037944-9 gnd Dreidimensionale Computergrafik (DE-588)4133691-4 gnd Programmierung (DE-588)4076370-5 gnd |
| subject_GND | (DE-588)4010457-6 (DE-588)4010450-3 (DE-588)4037944-9 (DE-588)4133691-4 (DE-588)4076370-5 |
| title | Mathematics for 3D game programming and computer graphics |
| title_auth | Mathematics for 3D game programming and computer graphics |
| title_exact_search | Mathematics for 3D game programming and computer graphics |
| title_full | Mathematics for 3D game programming and computer graphics Eric Lengyel |
| title_fullStr | Mathematics for 3D game programming and computer graphics Eric Lengyel |
| title_full_unstemmed | Mathematics for 3D game programming and computer graphics Eric Lengyel |
| title_short | Mathematics for 3D game programming and computer graphics |
| title_sort | mathematics for 3d game programming and computer graphics |
| topic | Computerspiel (DE-588)4010457-6 gnd Computergrafik (DE-588)4010450-3 gnd Mathematik (DE-588)4037944-9 gnd Dreidimensionale Computergrafik (DE-588)4133691-4 gnd Programmierung (DE-588)4076370-5 gnd |
| topic_facet | Computerspiel Computergrafik Mathematik Dreidimensionale Computergrafik Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024699391&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lengyeleric mathematicsfor3dgameprogrammingandcomputergraphics |