Animation maths:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | Dutch |
| Veröffentlicht: |
Leuven
Lannoo Campus
[2021]
Amsterdam |
| Ausgabe: | New edition |
| Schriftenreihe: | Campus handbook
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 409 pagina's Illustrationen, Diagramme 24 cm |
| ISBN: | 9789401474955 9401474958 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | ANIMATION MATHS б Contents Functions 67 4.1 Basic concepts on real functions 4.2 Polynomial functions 68 69 69 71 73 75 76 78 78 78 82 82 82 84 84 85 86 89 apter 4 ■ Linear functions Quadratic functions Acknowledgements Chapter 1 ■ Arithmetic refresher 1.1 Algebra Real numbers Real polynomials 1.2 Equations in one variable Linear equations Quadratic equations 1.3 Logarithms 1.4 Exercises Chapter 2 ■ Linear systems 2.1 Definitions 2.2 Methods for solving linear systems Solving by substitution Solving by elimination 2.3 Exercises Chapter 3 ■ Trigonometry 3.1 Angles 3.2 Triangles 3.3 Right triangle 3.4 Unit circle 3.5 Special angles Trigonometric ratios for an angle of 45°= į rad Trigonometric ratios for an angle of 30°= | rad Trigonometric ratios for an angle of 60°= Ş rad Overview 3.6 Pairs of angles 3.7 Sum identities 3.8 Inverse trigonometric functions 3.9 Exercises 15 17 18 18 23 25 25 26 31 34 37 38 40 40 41 45 4.3 Intersection of functions 4.4 Logarithmic functions 4.5 Exponential functions 4.6 Trigonometric functions Elementary sine function General sine function Transversal oscillations 4.7 arcsine arccosine arctangent atan2 4.8 Maclaurin expansions 4.9 Exercises apter 5 · The Golden Section 91 5.1 The golden number 5.2 The golden section 92 94 94 95 96 98 98 99 99 100 103 105 The golden triangle The golden rectangle The golden spiral The golden pentagon The golden ellipse 47 48 50 54 55 57 58 58 59 59 60 60 63 65 Inverse trigonometric functions 5.3 Golden arithmetic Golden identities The Fibonacci numbers 5.4 The golden section worldwide 5.5 Exercises lapter 6 ■
Coordinate systems 6.1 Cartesian coordinates 6.2 Parametric curves 6.3 Polar coordinates 6.4 Polar curves 6.5 Exercises 107 108 108 112 115 118
CONTENTS Chapter 7 ■ Vectors 7.1 7.2 7.3 7.4 The concept of a vector 121 ANIMATION MATHS 8 Chapter 8 · Parameters 149 Parametric equations Vector equation of a Une Intersecting straight lines 150 123 8.1 8.2 8.3 126 8.4 Vector equation of a plane 157 126 8.5 Exercises 161 122 Vectors as arrows 122 Vectors as arrays Free vectors Base vectors 151 155 Addition of vectors 127 Vectors as arrows 127 Vectors as arrays 127 9.1 Measures 164 Vector addition summarised 128 9.2 9.3 Deltatime Translational motion Rectilinear motion with constant velocity (RMCV) 165 Scalar multiplication of vectors 129 Chapter 9 ՛ Kinematics 163 165 Vectors as arrows 129 Vectors as arrays 129 Rectilinear motion with constant acceleration (RMCA) 168 Scalar multiplication summarised Normalisation 130 171 130 Free fall Summary Properties 130 Vector subtraction 9.4 131 Circular motion Uniform circular motion (UCM) 168 174 176 176 Creating free vectors 131 Nonuniform circular motion (NCM) 183 Euler’s method for trajectories 132 133 Summary 186 7.5 Decomposition of vectors 7.6 Decomposition of a plane vector Base vectors defined Dot product Definition 7.7 7 Geometric interpretation Orthogonality Cross product 9.5 Planar curvilinear motion 187 133 Normal-tangential components 188 134 Radial-angular components 191 194 135 9.6 135 136 139 Independence of Motion Combined rectilinear motions with constant velocities Projectile motion (PM) 9.7 Exercises 194 195 200 140 Definition 140 Geometric interpretation Parallelism 142 144 Chapter 10 ՛ Collision detection 10.1 Collision detection using circles and spheres 203
204 Normal vectors 145 Circles and spheres Intersecting line and circle 204 7.8 7.9 Exercises 147 Intersecting circles and spheres 208 206 Altitude to a straight line 211 211 212 Altitude to a plane 214 Frame rate issues Location of a point with respect to a polygon 216 10.2 Collision detection using vectors Location of a point with respect to other points 10.3 Exercises 217 220
CONTENTS 9 Chapter 11 ■ Matrices 11.1 The concept of a matrix 11.2 Determinant of a square matrix 11.3 Addition and scalar multiplication of matrices ANIMATION MATHS 10 223 224 Cubic Bezier segment 12.5 B-splines 225 227 Cubic B-spiines Matrix representation Addition of matrices 111 De Boor’s algorithm Scalar multiplication of a matrix 229 11.4 Transpose of a matrix 11.5 Dot product of matrices Introduction Condition Definition 12.6 Exercises 262 264 264 265 267 269 230 230 230 232 Properties 232 233 11.6 Inverse of a matrix 235 Introduction Definition 235 Conditions 236 235 Chapter 13 · Transformations 13.1 Transistion 13.2 Scaling 13.3 Rotation Rotation in 2D Rotation in 3D 13.4 Reflection 13.5 Shearing 13.6 Combining standard transformations 2D rotation around an arbitrary centre 271 272 277 280 280 282 284 286 288 Row reduction 236 Matrix inversion 237 3D scaling about an arbitrary centre Inverse of a product 240 2D reflection over an axis through the origin 293 294 Solving systems of linear equations 241 2D reflection over an arbitrary axis 295 243 3D combined rotation 298 11.7 The Fibonacci operator 11.8 The matrix exponential 245 Structures 245 Matrix exponential 245 247 11.9 Exercises 13.7 Row-representation 13.8 Exercises Chapter 14 ՝ Transformation A a I y s is Typesetting Chapter 12 · Bezier curves 12.1 Vector equation of segments Linear Bezier segment 249 250 250 251 Quadratic Bezier segment Cubic Bezier segment 252 Bezier segments of higher degree 254 14.1 14.2 14.3 14.4 14.5 14.6 Translation analysis Scaling analysis Rotation analysis Composite transformation
analysis Conventions Applications 290 299 300 303 304 304 308 311 315 318 319 12.2 De Casteljau algorithm 12.3 Bezier curves 255 256 Orbit transformation 319 320 Concatenation 256 Look-at transformation 322 Linear transformations Illustrations 258 12.4 Matrix representation Linear Bezier segment Quadratic Bezier segment Pivot transformation 14.7 Exercises 326 258 260 Chapter 15 ■ Scene Graphs 329 260 261 15.1 Concept of a scene graph 15.2 Bone structures 330 332
ч CONTENTS 11 15.3 Solar systems 15.4 Exercises Chapter 16 · ViewTransformation 16.1 The Rendering Pipeline The concept of the pipeline The stages of the pipeline 16.2 16.3 16.4 16.5 16.6 Camera transformation View transformation View operator Camera with zoom Exercises ANIMATION MATHS 12 336 339 341 342 342 342 344 345 349 351 354 Quaternion exponentiation The quest for the quaternion rotation 381 Unit rotation quaternion 385 17.8 Exercises Annex A · Real numbers in computers A.l Scientific notation A.2 The decimal computer A.3 Special values Annex В · Notations and Conventions B.l Alphabets 382 389 391 39! 391 392 393 393 Latin alphabet 393 357 Greek alphabet 394 35g B.2 Mathematical symbols 394 362 362 Sets Mathematical symbols 394 Addition and subtraction 362 Mathematical keywords 396 Multiplication З63 Numbers 396 Exponentiation З65 Division 366 Chapter 17 ■ Hypercomplexnumbers 17.1 Complex numbers 17.2 Complex number arithmetic Complex conjugate 17.3 Complex numbers and transformations Translation 368 36g Standard rotation 369 Standard scaling 37O Composite transformation 17.4 Complex continuation of theFibonacci numbers Integer Fibonacci numbers Complex Fibonacci numbers 17.5 Quaternions 17.6 Quaternion arithmetic C.l C.2 C.3 C.4 SI Prefixes SI Base measures SI Supplementary measure SI Derived measures 37O 371 37! 372 374 375 Addition and subtraction 375 Scalar multiplication 376 Normalisation Quaternion multiplication 376 376 Quaternion conjugate 37g Inverse quaternion 379 17.7 Quaternions and rotations 379 Trigonometrical representation oí quaternions Euler
representation of quaternions Annex C ■ The International System of Units (SI) З8О З8О 395 397 397 398 398 399 Bibliography 400 Index 403
|
| adam_txt |
ANIMATION MATHS б Contents Functions 67 4.1 Basic concepts on real functions 4.2 Polynomial functions 68 69 69 71 73 75 76 78 78 78 82 82 82 84 84 85 86 89 apter 4 ■ Linear functions Quadratic functions Acknowledgements Chapter 1 ■ Arithmetic refresher 1.1 Algebra Real numbers Real polynomials 1.2 Equations in one variable Linear equations Quadratic equations 1.3 Logarithms 1.4 Exercises Chapter 2 ■ Linear systems 2.1 Definitions 2.2 Methods for solving linear systems Solving by substitution Solving by elimination 2.3 Exercises Chapter 3 ■ Trigonometry 3.1 Angles 3.2 Triangles 3.3 Right triangle 3.4 Unit circle 3.5 Special angles Trigonometric ratios for an angle of 45°= į rad Trigonometric ratios for an angle of 30°= | rad Trigonometric ratios for an angle of 60°= Ş rad Overview 3.6 Pairs of angles 3.7 Sum identities 3.8 Inverse trigonometric functions 3.9 Exercises 15 17 18 18 23 25 25 26 31 34 37 38 40 40 41 45 4.3 Intersection of functions 4.4 Logarithmic functions 4.5 Exponential functions 4.6 Trigonometric functions Elementary sine function General sine function Transversal oscillations 4.7 arcsine arccosine arctangent atan2 4.8 Maclaurin expansions 4.9 Exercises apter 5 · The Golden Section 91 5.1 The golden number 5.2 The golden section 92 94 94 95 96 98 98 99 99 100 103 105 The golden triangle The golden rectangle The golden spiral The golden pentagon The golden ellipse 47 48 50 54 55 57 58 58 59 59 60 60 63 65 Inverse trigonometric functions 5.3 Golden arithmetic Golden identities The Fibonacci numbers 5.4 The golden section worldwide 5.5 Exercises lapter 6 ■
Coordinate systems 6.1 Cartesian coordinates 6.2 Parametric curves 6.3 Polar coordinates 6.4 Polar curves 6.5 Exercises 107 108 108 112 115 118
CONTENTS Chapter 7 ■ Vectors 7.1 7.2 7.3 7.4 The concept of a vector 121 ANIMATION MATHS 8 Chapter 8 · Parameters 149 Parametric equations Vector equation of a Une Intersecting straight lines 150 123 8.1 8.2 8.3 126 8.4 Vector equation of a plane 157 126 8.5 Exercises 161 122 Vectors as arrows 122 Vectors as arrays Free vectors Base vectors 151 155 Addition of vectors 127 Vectors as arrows 127 Vectors as arrays 127 9.1 Measures 164 Vector addition summarised 128 9.2 9.3 Deltatime Translational motion Rectilinear motion with constant velocity (RMCV) 165 Scalar multiplication of vectors 129 Chapter 9 ՛ Kinematics 163 165 Vectors as arrows 129 Vectors as arrays 129 Rectilinear motion with constant acceleration (RMCA) 168 Scalar multiplication summarised Normalisation 130 171 130 Free fall Summary Properties 130 Vector subtraction 9.4 131 Circular motion Uniform circular motion (UCM) 168 174 176 176 Creating free vectors 131 Nonuniform circular motion (NCM) 183 Euler’s method for trajectories 132 133 Summary 186 7.5 Decomposition of vectors 7.6 Decomposition of a plane vector Base vectors defined Dot product Definition 7.7 7 Geometric interpretation Orthogonality Cross product 9.5 Planar curvilinear motion 187 133 Normal-tangential components 188 134 Radial-angular components 191 194 135 9.6 135 136 139 Independence of Motion Combined rectilinear motions with constant velocities Projectile motion (PM) 9.7 Exercises 194 195 200 140 Definition 140 Geometric interpretation Parallelism 142 144 Chapter 10 ՛ Collision detection 10.1 Collision detection using circles and spheres 203
204 Normal vectors 145 Circles and spheres Intersecting line and circle 204 7.8 7.9 Exercises 147 Intersecting circles and spheres 208 206 Altitude to a straight line 211 211 212 Altitude to a plane 214 Frame rate issues Location of a point with respect to a polygon 216 10.2 Collision detection using vectors Location of a point with respect to other points 10.3 Exercises 217 220
CONTENTS 9 Chapter 11 ■ Matrices 11.1 The concept of a matrix 11.2 Determinant of a square matrix 11.3 Addition and scalar multiplication of matrices ANIMATION MATHS 10 223 224 Cubic Bezier segment 12.5 B-splines 225 227 Cubic B-spiines Matrix representation Addition of matrices 111 De Boor’s algorithm Scalar multiplication of a matrix 229 11.4 Transpose of a matrix 11.5 Dot product of matrices Introduction Condition Definition 12.6 Exercises 262 264 264 265 267 269 230 230 230 232 Properties 232 233 11.6 Inverse of a matrix 235 Introduction Definition 235 Conditions 236 235 Chapter 13 · Transformations 13.1 Transistion 13.2 Scaling 13.3 Rotation Rotation in 2D Rotation in 3D 13.4 Reflection 13.5 Shearing 13.6 Combining standard transformations 2D rotation around an arbitrary centre 271 272 277 280 280 282 284 286 288 Row reduction 236 Matrix inversion 237 3D scaling about an arbitrary centre Inverse of a product 240 2D reflection over an axis through the origin 293 294 Solving systems of linear equations 241 2D reflection over an arbitrary axis 295 243 3D combined rotation 298 11.7 The Fibonacci operator 11.8 The matrix exponential 245 Structures 245 Matrix exponential 245 247 11.9 Exercises 13.7 Row-representation 13.8 Exercises Chapter 14 ՝ Transformation A a I y s is Typesetting Chapter 12 · Bezier curves 12.1 Vector equation of segments Linear Bezier segment 249 250 250 251 Quadratic Bezier segment Cubic Bezier segment 252 Bezier segments of higher degree 254 14.1 14.2 14.3 14.4 14.5 14.6 Translation analysis Scaling analysis Rotation analysis Composite transformation
analysis Conventions Applications 290 299 300 303 304 304 308 311 315 318 319 12.2 De Casteljau algorithm 12.3 Bezier curves 255 256 Orbit transformation 319 320 Concatenation 256 Look-at transformation 322 Linear transformations Illustrations 258 12.4 Matrix representation Linear Bezier segment Quadratic Bezier segment Pivot transformation 14.7 Exercises 326 258 260 Chapter 15 ■ Scene Graphs 329 260 261 15.1 Concept of a scene graph 15.2 Bone structures 330 332
ч CONTENTS 11 15.3 Solar systems 15.4 Exercises Chapter 16 · ViewTransformation 16.1 The Rendering Pipeline The concept of the pipeline The stages of the pipeline 16.2 16.3 16.4 16.5 16.6 Camera transformation View transformation View operator Camera with zoom Exercises ANIMATION MATHS 12 336 339 341 342 342 342 344 345 349 351 354 Quaternion exponentiation The quest for the quaternion rotation 381 Unit rotation quaternion 385 17.8 Exercises Annex A · Real numbers in computers A.l Scientific notation A.2 The decimal computer A.3 Special values Annex В · Notations and Conventions B.l Alphabets 382 389 391 39! 391 392 393 393 Latin alphabet 393 357 Greek alphabet 394 35g B.2 Mathematical symbols 394 362 362 Sets Mathematical symbols 394 Addition and subtraction 362 Mathematical keywords 396 Multiplication З63 Numbers 396 Exponentiation З65 Division 366 Chapter 17 ■ Hypercomplexnumbers 17.1 Complex numbers 17.2 Complex number arithmetic Complex conjugate 17.3 Complex numbers and transformations Translation 368 36g Standard rotation 369 Standard scaling 37O Composite transformation 17.4 Complex continuation of theFibonacci numbers Integer Fibonacci numbers Complex Fibonacci numbers 17.5 Quaternions 17.6 Quaternion arithmetic C.l C.2 C.3 C.4 SI Prefixes SI Base measures SI Supplementary measure SI Derived measures 37O 371 37! 372 374 375 Addition and subtraction 375 Scalar multiplication 376 Normalisation Quaternion multiplication 376 376 Quaternion conjugate 37g Inverse quaternion 379 17.7 Quaternions and rotations 379 Trigonometrical representation oí quaternions Euler
representation of quaternions Annex C ■ The International System of Units (SI) З8О З8О 395 397 397 398 398 399 Bibliography 400 Index 403 |
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| index_date | 2024-07-03T18:31:15Z |
| indexdate | 2024-07-10T09:15:14Z |
| institution | BVB |
| isbn | 9789401474955 9401474958 |
| language | Dutch |
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| spelling | De Pauw, Ivo Verfasser (DE-588)1249179041 aut Animation maths Ivo de Pauw, Bieke Masselis New edition Leuven Amsterdam Lannoo Campus [2021] 409 pagina's Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Campus handbook Computeranimation (DE-588)4199710-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf wiskunde Computeranimation (DE-588)4199710-4 s Mathematik (DE-588)4037944-9 s DE-604 Masselis, Bieke ca. 20./21. Jh. Verfasser (DE-588)1249187621 aut Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032959360&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Pauw, Ivo Masselis, Bieke ca. 20./21. Jh Animation maths Computeranimation (DE-588)4199710-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4199710-4 (DE-588)4037944-9 |
| title | Animation maths |
| title_auth | Animation maths |
| title_exact_search | Animation maths |
| title_exact_search_txtP | Animation maths |
| title_full | Animation maths Ivo de Pauw, Bieke Masselis |
| title_fullStr | Animation maths Ivo de Pauw, Bieke Masselis |
| title_full_unstemmed | Animation maths Ivo de Pauw, Bieke Masselis |
| title_short | Animation maths |
| title_sort | animation maths |
| topic | Computeranimation (DE-588)4199710-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Computeranimation Mathematik |
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