The geometry of computer graphics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove, Calif.
Wadsworth & Brooks/Cole Advanced Books & Software
1992
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| Series: | The Wadsworth & Brooks/Cole mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 451 S. Ill., graph. Darst. |
| ISBN: | 0534171001 |
Staff View
MARC
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| 245 | 1 | 0 | |a The geometry of computer graphics |c Walter F. Taylor |
| 264 | 1 | |a Pacific Grove, Calif. |b Wadsworth & Brooks/Cole Advanced Books & Software |c 1992 | |
| 300 | |a XVI, 451 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804120884620820480 |
|---|---|
| adam_text | Contents
1 Review of linear algebra 1
1.1 Vector spaces and linear maps 1
1.1.1 Definition of vector spaces 1
1.1.2 Subspaces, spanning and linear independence 3
1.1.3 Bases and dimension 7
1.1.4 Sums and direct sums of spaces 8
1.1.5 Homomorphisms (linear transformations) 10
1.2 Matrices 14
1.2.1 The matrix of a linear transformation 14
1.2.2 The product of two matrices 15
1.2.3 The identity matrix and inverse matrices 17
1.2.4 Column operations on matrices 19
1.2.5 The rows of a column reduced matrix 24
1.2.6 Calculating the inverse of a matrix 27
1.2.7 Row operations on matrices 30
1.2.8 Cosets 33
1.2.9 Systems of linear equations 34
1.3 Determinants 36
1.3.1 The defining properties of determinants 38
1.3.2 The uniqueness of Dn 39
1.3.3 The existence of a determinant function 40
1.3.4 Calculation of determinants 42
1.3.5 Determinants and column operations 45
1.3.6 Another formula for the determinant 47
1.3.7 Determinants, area and volume 49
xii Contents
1.4 Eigenvalues and eigenvectors 55
1.5 Inner products, transposes and symmetry 65
1.5.1 Inner products 66
1.5.2 Transposes 68
1.5.3 Orthogonal matrices 70
1.5.4 Symmetric matrices 71
2 Languages for geometry 77
2.1 Computer languages 80
2.1.1 A language for sample programs 82
2.1.2 A simple program to draw a curve 83
2.2 A device independent language for line drawings 88
2.3 Interpreting the device independent language 93
2.3.1 A translation program 95
2.4 A Logo like language 102
2.5 Painting regions of the plane 107
2.6 Recursion in geometry 111
2.7 Pixeled images 122
2.7.1 A program to output a PostScript raster file 127
2.7.2 A probabilistic filter 133
3 Topics in plane analytic geometry 135
3.1 Conic sections 137
3.1.1 The circle 137
3.1.2 The ellipse 140
3.1.3 The hyperbola 141
3.1.4 The focus directrix property; the parabola 144
3.1.5 A uniform parametrization of conic sections 154
3.1.6 Change of coordinates 157
3.1.7 The general quadratic equation in two variables 159
3.2 Cubic curves and splines 164
3.2.1 Algebraic geometry 165
3.2.2 Cubic Bezier curves 166
Contents xiii
3.2.3 Connecting two cubic Bezier curves 170
3.2.4 Connecting several cubic Bezier curves 172
3.2.5 Piecewise cubic interpolants 174
3.2.6 Bezier curves as a language for geometry 177
3.3 Some maps from I2 to M2 184
3.3.1 Translations 186
3.3.2 Rotations about the origin 187
3.3.3 Rotations about an arbitrary point 190
3.3.4 Reflections; the general rigid motion 190
3.3.5 Magnifications 196
3.3.6 Area preserving transformations 205
3.3.7 Connections with eigenvalues and eigenvectors 210
3.3.8 AfEne maps and cubic Bezier curves 213
3.3.9 Exercises on maps M2 —? R2 216
3.4 Some graphic topics in calculus 217
3.4.1 The family of lines tangent to a curve 218
3.4.2 Drawing the family of tangent lines 218
3.4.3 The enveloping curve of a family of lines 221
3.4.4 The cardioid 223
3.4.5 A differential equation 234
3.4.6 The evolute of a curve 236
3.4.7 The evolute and centers of curvature 238
3.4.8 Involutes of a curve 240
3.4.9 The drawing of involutes 244
3.4.10 Nested squares 248
3.4.11 Envelopes in general 249
3.4.12 Horizons and shadows 259
4 Plane projective geometry 263
4.1 Perspectivity and homogeneous coordinates 263
4.1.1 A simple perspective drawing 263
4.1.2 Ideal points and lines 267
4.1.3 Homogeneous coordinates 268
4.2 Analytic projective plane geometry 268
4.2.1 Projective planes 268
4.2.2 Coordinatizing a projective plane 269
4.2.3 The equation of a line in a plane 270
xiv Contents
4.2.4 Forming an ordinary plane by removing a line 270
4.3 Synthetic projective geometry 271
4.4 Projective transformations of P2 272
4.4.1 Collineations that fix four points 273
4.4.2 Denning arithmetic in a projective plane 274
4.4.3 Automorphisms of the field R of real numbers 280
4.4.4 The proof of Theorem 4.6 282
4.4.5 Every collineation of P2(M) is given by a linear
map 285
4.5 Representing plane motions as collineations 290
4.5.1 Collineations of P2(R) that map the ordinary plane to
itself 290
4.5.2 Translations 291
4.5.3 Linear maps 291
4.5.4 Rotations 292
4.5.5 Reflections 292
4.5.6 Rigid motions 292
4.5.7 Magnifications 293
4.5.8 Shears 293
4.5.9 A compressions 293
4.6 Representing perspectivities as collineations 293
4.7 Projection from a plane to a line 294
4.8 Fixed points and fixed lines 297
5 Projective geometry of space 299
5.1 Projective spaces 299
5.1.1 Definitions 299
5.1.2 Elementary incidence theorems 299
5.1.3 Homogeneous coordinates 300
5.1.4 The equations of lines and planes in P3(R) 300
5.1.5 Forming an ordinary 3 space by removing a
plane 301
5.2 Collineations of projective space 301
5.3 A catalog of collineations of P3(E) 302
5.3.1 The general collineation mapping R3 to itself 302
Contents xv
5.3.2 Translations 302
5.3.3 Reflections 302
5.3.4 Rotations about one of the coordinate axes 302
5.3.5 Rigid motions 303
5.3.6 Magnifications 303
5.3.7 Shears 305
5.3.8 Compressions 305
5.3.9 Projection from space to the plane x3 = 0 305
5.4 Applications to spherical trigonometry 306
5.5 Cubic Bezier curves and B splines revisited 310
5.6 Horizons revisited 312
6 Applications of projective maps 315
6.1 Projections of a globe 316
6.1.1 The database 316
6.1.2 Reading the database 319
6.1.3 A coordinate system for viewing the globe 322
6.1.4 Coordinates for points on a sphere 323
6.1.5 Rotating the globe 324
6.1.6 Translating the globe 327
6.1.7 Projecting the globe 328
6.1.8 The main matrix for the world viewing program 328
6.1.9 Summary of a plan for drawing the globe 328
6.1.10 The visibility of a point on the sphere from the
viewpoint 330
6.1.11 The while loop revisited 331
6.1.12 Drawing the horizon circle 332
6.1.13 Rescaling the picture 333
6.2 Projections of ideal points (stars) 334
6.2.1 Celestial coordinates 336
6.2.2 Time 338
6.2.3 Calculating sidereal time 339
6.2.4 Two more necessary parameters 342
6.2.5 The database 342
6.2.6 Rotating the globe and stars 346
6.2.7 The main matrix for the star gazing program 347
6.2.8 Pseudo ideal points 347
xvi Contents
6.2.9 Discriminating the visible stars 349
6.2.10 Projecting the stars 349
6.2.11 Reflecting the picture 350
6.2.12 Summary of a plan for drawing the stars 351
6.3 3 dimensional device independent files 352
6.3.1 The language itself 352
6.3.2 Implementations of the language 353
6.3.3 Graphing a curve in space 364
6.4 Graphing a function of two variables 374
6.4.1 Removing hidden parts 377
6.4.2 Refinements to our hidden line algorithm 385
6.4.3 A polygonal method 387
6.4.4 The use of polygonal surface elements 389
6.4.5 The shading of polygonal surface elements 395
6.5 Bezier curves and engineering design 402
6.5.1 A program to draw a chair 403
6.5.2 An algorithm for B splines 408
6.6 Binocular vision 409
6.7 4 dimensional space 413
6.7.1 Is there a physical meaning to 4 dimensional
space? 413
6.7.2 Can one perceive 4 dimensional space? 415
6.7.3 Some objects of P4(R) 417
6.8 Elementary ray tracing 418
6.8.1 The main calculation of intensity 421
6.8.2 The effect of affine transformations 427
6.8.3 Reflections 429
6.8.4 Convex polyhedra 433
Index 442
|
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| ctrlnum | (OCoLC)694870339 (DE-599)BVBBV006609140 |
| dewey-full | 006.6 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.6 |
| dewey-search | 006.6 |
| dewey-sort | 16.6 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV006609140 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:49:11Z |
| institution | BVB |
| isbn | 0534171001 |
| language | English |
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| physical | XVI, 451 S. Ill., graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Wadsworth & Brooks/Cole Advanced Books & Software |
| record_format | marc |
| series2 | The Wadsworth & Brooks/Cole mathematics series |
| spelling | Taylor, Walter F. 1946- Verfasser (DE-588)121050661 aut The geometry of computer graphics Walter F. Taylor Pacific Grove, Calif. Wadsworth & Brooks/Cole Advanced Books & Software 1992 XVI, 451 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Wadsworth & Brooks/Cole mathematics series Computer graphics Computergrafik (DE-588)4010450-3 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Computergrafik (DE-588)4010450-3 s Geometrie (DE-588)4020236-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004222352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, Walter F. 1946- The geometry of computer graphics Computer graphics Computergrafik (DE-588)4010450-3 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4010450-3 (DE-588)4020236-7 |
| title | The geometry of computer graphics |
| title_auth | The geometry of computer graphics |
| title_exact_search | The geometry of computer graphics |
| title_full | The geometry of computer graphics Walter F. Taylor |
| title_fullStr | The geometry of computer graphics Walter F. Taylor |
| title_full_unstemmed | The geometry of computer graphics Walter F. Taylor |
| title_short | The geometry of computer graphics |
| title_sort | the geometry of computer graphics |
| topic | Computer graphics Computergrafik (DE-588)4010450-3 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Computer graphics Computergrafik Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004222352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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