Computer graphics through key mathematics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 343 S. Ill., graph. Darst. |
| ISBN: | 1852334223 |
Staff View
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Record in the Search Index
| _version_ | 1804128411138916352 |
|---|---|
| adam_text | HUW JONES COMPUTER GRAPHICS THROUGH KEY MATHEMATICS SPRINGER CONTENTS
PREFACE V 1 THE PROCESSES OF COMPUTER GRAPHICS 1 INTRODUCTION 1 OBJECT
MODEL BUILDING 1 DEPICTION OF MODELS 3 CONCLUSION 6 2 NUMBERS, COUNTING
AND MEASURING 7 INTRODUCTION 7 NATURAL NUMBERS 7 INTEGERS 12 RATIONAL
NUMBERS 14 REAL NUMBERS 17 COMPLEX NUMBERS 20 REPRESENTATIONS OF NUMBER
25 THE COMPUTER REPRESENTATION OF NUMBER 28 BOOLEAN ALGEBRA 32 SUMMARY
35 3 COORDINATES AND DIMENSION: REPRESENTATIONS OF SPACE AND COLOUR 37
INTRODUCTION 37 CARTESIAN COORDINATES 37 DEFINING SPACE BY EQUATIONS AND
INEQUALITIES 41 ANGLES 44 TRIGONOMETRY AND POLAR COORDINATES 46
DIMENSION 56 COORDINATE SYSTEMS IN THREE DIMENSIONS 61 COLOUR AND ITS
REPRESENTATION 66 SUMMARY 71 4 FUNCTIONS AND TRANSFORMATIONS: WAYS OF
MANIPULATING SPACE 73 INTRODUCTION 73 FUNCTIONS AS MAPPINGS 73 GRAPHS OF
FUNCTIONS 76 TRANSFORMATIONS IN2D 79 TRANSFORMATIONS IN 3D 86 COMBINING
AFFINE TRANSFORMATIONS 89 INVERSION OF AFFINE TRANSFORMATIONS 94
INVERSION OF FUNCTIONS 95 SHAPE TRANSFORMATION BY FUNCTION CHANGE 100
CONCLUSIONS 103 XII COMPUTER GRAPHICS THROUGH KEY MATHEMATICS 5 FORM
FROM FUNCTION: ANALYSIS OF SHAPES 105 INTRODUCTION 105 THE STRAIGHT LINE
105 DRAWING GENERAL FUNCTION GRAPHS 107 GRAPHS OF POLYNOMIALS 107
CALCULUS: DIFFERENTIATION 114 CALCULUS: INTEGRATION 124 SERIES
EXPANSIONS 129 CALCULUS AND ANIMATION 134 THE EXPONENTIAL FUNCTION 136
THE CONIC SECTIONS 136 SOME STANDARD 3D FORMS AND THEIR EQUATIONS 141
SUMMARY 245 6 MATRICES: TOOLS FOR MANIPULATING SPACE 147 MATRICES IN
COMPUTER GRAPHICS 147 DEFINITION AND NOTATION 147 FORMS OF MATRICES 148
OPERATIONS ON MATRICES: ADDITION 149 OPERATIONS ON MATRICES:
MULTIPLICATION 150 THE IDENTITY MATRIX 152 MATRICES AND EQUATIONS 154
THE INVERSE OF A SQUARE MATRIX 159 MATRICES, TRANSFORMATIONS AND
HOMOGENEOUS COORDINATES: TWO DIMENSIONS 160 MATRICES, TRANSFORMATIONS
AND HOMOGENEOUS COORDINATES: THREE DIMENSIONS 166 INVERSE OF A
TRANSFORMATION MATRIX 170 PERSPECTIVE PROJECTION 172 COMPUTER
IMPLEMENTATION OF MATRIX METHODS 176 SUMMARY 183 7 VECTORS: DESCRIPTIONS
OF SPATIAL RELATIONSHIPS 185 INTRODUCTION 185 DEFINITION OF A VECTOR 185
NOTATION 186 ADDITION OF VECTORS: THE PARALLELOGRAM AND TRIANGLE LAWS
186 MULTIPLICATION OF A VECTOR BY A SCALAR 188 EXAMPLES OF VECTOR
QUANTITIES 189 VECTORS IN 2D CARTESIAN SPACES 189 VECTORS IN 3D
CARTESIAN SPACES 191 MULTIPLICATION OF VECTORS: THE SCALAR OR DOT
PRODUCT 193 MULTIPLICATION OF VECTORS: THE VECTOR OR CROSS PRODUCT 194
REPRESENTATION OF LINES USING VECTORS 196 CLASSIFICATION OF POINTS
AGAINST PLANES USING VECTORS 197 REPRESENTATION OF PLANES IN STANDARD
FORM 198 INTERSECTION OF A LINE WITH A PLANE 200 INCLUSION OF A POINT IN
A TRIANGLE 203 REFLECTED AND REFRACTED RAYS 205 XU1 7 VECTORS:
DESCRIPTIONS OF SPATIAL RELATIONSHIPS CONTINUED DISTANCE BETWEEN TWO
SKEW LINES 208 INTERSECTION OF TWO PLANES 211 SUMMARY 213 8 GEOMETRIC
MODELLING AND FRACTALS: BUILDING DESCRIPTIONS OF OBJECTS. ..215
INTRODUCTION 215 DATA STRUCTURES 215 GEOMETRIC MODELLING SYSTEMS 218
VOXEL MODELLING METHODS 219 CONSTRUCTIVE SOLID GEOMETRY (CSG) 222
BOUNDARY REPRESENTATION (B-REP) 227 ISOSURFACE MODELLING 231 FRACTALS
234 FRACTAL DIMENSION 240 FRACTALS BASED IN THE COMPLEX PLANE: JULIA AND
MANDELBROT SETS 243 FRACTALS IN SIMULATION OF NATURAL PHENOMENA 249
SUMMARY 258 9 SPLINES: GENERATION OF CURVES AND SURFACES 259
INTRODUCTION 259 REASONS FOR SPLINES 259 INTERPOLATION 260 BEZIER
SPLINES FOR CURVE DRAWING 262 ANIMATION CONTROL USING CUBIC BEZIER
CURVES 268 DRAWING BEZIER CURVES 269 INTERPOLATING SPLINES FOR CURVE
GENERATION 271 ANIMATION CONTROL USING INTERPOLATING SPLINES 274
B-SPLINES 275 NON-UNIFORM RATIONAL B-SPLINES: NURBS 282 CIRCLES AND
OTHER CONIC SECTIONS 285 SURFACE CONSTRUCTION USING BEZIER PATCHES 286
SURFACE GENERATION BASED ON OTHER FORMS OF CURVE 292 DEPICTION OF
SURFACE PATCHES 293 SUMMARY 294 10 DRAWING AND RENDERING: HOW TO CREATE
PICTURES 295 WHAT IS A 3D DRAWING? 295 METHODS FOR RENDERING 298 HIDDEN
SURFACE REMOVAL 304 FLAT OR LAMBERT SHADING 306 SCAN LINE METHODS 308
GOURAUD SHADING 310 PHONG SHADING 313 EXACT OBJECT RENDERING 314 SHADOWS
315 SPECULAR HIGHLIGHTS 317 XIV COMPUTER GRAPHICS THROUGH KEY
MATHEMATICS 10 DRAWING AND RENDERING: HOW TO CREATE PICTURES CONTINUED
TEXTURES 319 RAY TRACING 320 RADIOSITY 321 ANTI-ALIASING 324 SUMMARY 326
SUGGESTIONS FOR FURTHER READING 327 MATHEMATICAL AND SCIENTIFIC MINDS
327 UNDERSTANDING OF MATHEMATICS 328 COMPUTER GRAPHICS IN GENERAL 329
GEOMETRIC MODELLING 329 FRACTALS AND RELATED ISSUES 330 JOURNALS 331
INDEX 333 NAMES 333 SUBJECT INDEX 335
|
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| dewey-full | 006.6 |
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| dewey-ones | 006 - Special computer methods |
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| dewey-search | 006.6 |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:48:49Z |
| institution | BVB |
| isbn | 1852334223 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009293857 |
| oclc_num | 247917796 |
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| physical | XIV, 343 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
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| spelling | Jones, Huw 1944- Verfasser (DE-588)122601564 aut Computer graphics through key mathematics Huw Jones London [u.a.] Springer 2001 XIV, 343 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Infographie Mathématiques Mathematik Computer graphics Mathematics Computergrafik (DE-588)4010450-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Computergrafik (DE-588)4010450-3 s Mathematik (DE-588)4037944-9 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009293857&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jones, Huw 1944- Computer graphics through key mathematics Infographie Mathématiques Mathematik Computer graphics Mathematics Computergrafik (DE-588)4010450-3 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4010450-3 (DE-588)4037944-9 |
| title | Computer graphics through key mathematics |
| title_auth | Computer graphics through key mathematics |
| title_exact_search | Computer graphics through key mathematics |
| title_full | Computer graphics through key mathematics Huw Jones |
| title_fullStr | Computer graphics through key mathematics Huw Jones |
| title_full_unstemmed | Computer graphics through key mathematics Huw Jones |
| title_short | Computer graphics through key mathematics |
| title_sort | computer graphics through key mathematics |
| topic | Infographie Mathématiques Mathematik Computer graphics Mathematics Computergrafik (DE-588)4010450-3 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Infographie Mathématiques Mathematik Computer graphics Mathematics Computergrafik |
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