Essential mathematics for computer graphics fast:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Springer
2001
|
| Schriftenreihe: | Essential series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 229 S. graph. Darst. |
| ISBN: | 1852333804 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | JOHN VINCE ESSENTIAL MATHEMATICS FOR COMPUTER GRAPHICS FAST SPRINGER
CONTENTS 1. MATHEMATICS 1 IS MATHEMATICS DIFFICULT? 3 WHO SHOULD READ
THIS BOOK? 4 AIMS AND OBJECTIVES OF THIS BOOK 4 ASSUMPTIONS MADE IN THIS
BOOK 5 HOW TO USE THE BOOK 5 2. NUMBERS 7 NATURAL NUMBERS 8 PRIME
NUMBERS 8 INTEGERS 9 RATIONAL NUMBERS 9 IRRATIONAL NUMBERS 10 REAL
NUMBERS 10 THE NUMBER LINE 10 COMPLEX NUMBERS 10 SUMMARY 13 3. ALGEBRA
15 NOTATION 16 ALGEBRAIC LAWS 17 ASSOCIATIVE LAW 18 COMMUTATIVE LAW 18
DISTRIBUTIVE LAW 19 SOLVING THE ROOTS OF A QUADRATIC EQUATION 19 INDICES
20 LAWS OF INDICES 21 EXAMPLES 21 LOGARITHMS 21 FURTHER NOTATION 23
SUMMARY 23 4. TRIGONOMETRY 25 THE TRIGONOMETRIC RATIOS 26 EXAMPLE 28
INVERSE TRIGONOMETRIC RATIOS 28 TRIGONOMETRIC RELATIONSHIPS 29 THE SINE
RULE 29 ESSENTIAL MATHEMATICS FOR CG FAST THE COSINE RULE . . 30
COMPOUND ANGLES 30 PERIMETER RELATIONSHIPS 31 SUMMARY 32 5. CARTESIAN
COORDINATES 33 THE CARTESIAN XY-PLANE 34 FUNCTION GRAPHS 36 GEOMETRIC
SHAPES 37 POLYGONAL SHAPES 37 AREAS OF SHAPES 38 THEOREM OF PYTHAGORAS
IN 2D 39 3D COORDINATES 40 THEOREM OF PYTHAGORAS IN 3D 40 3D POLYGONS 41
EULER S RULE 41 SUMMARY 42 6. VECTORS 43 2D VECTORS 45 VECTOR NOTATION
45 GRAPHICAL REPRESENTATION OF VECTORS 45 MAGNITUDE OF A VECTOR 47 3D
VECTORS 49 VECTOR MANIPULATION 49 MULTIPLYING A VECTOR BY A SCALAR 50
VECTOR ADDITION AND SUBTRACTION 50 POSITION VECTORS 51 UNIT VECTORS *.
52 CARTESIAN VECTORS 53 VECTOR MULTIPLICATION 54 SCALAR PRODUCT 55
EXAMPLE OF THE DOT PRODUCT 57 THE DOT PRODUCT IN LIGHTING CALCULATIONS
58 THE DOT PRODUCT IN BACK-FACE DETECTION 59 THE VECTOR PRODUCT 60 THE
RIGHT-HAND RULE 64 DERIVING A UNIT NORMAL VECTOR FOR A TRIANGLE 65 AREAS
66 CALCULATING 2D AREAS 67 SUMMARY 68 CONTENTS 7. TRANSFORMATIONS 69 2D
TRANSFORMATIONS 70 TRANSLATION 70 SCALING 70 REFLECTION 71 MATRICES 72
SYSTEMS OF NOTATION 75 THE DETERMINANT OF A MATRIX 76 HOMOGENEOUS
COORDINATES 77 2D TRANSLATION 79 2D SCALING 79 2D REFLECTIONS 80 2D
SHEARING 82 2D ROTATION 83 2D SCALING 86 2D REFLECTIONS 87 2D ROTATION
ABOUT AN ARBITRARY POINT 88 3D TRANSFORMATIONS 89 3D TRANSLATION 89 3D
SCALING 90 3D ROTATIONS 90 GIMBAL LOCK 95 ROTATING ABOUT AN AXIS 96 3D
REFLECTIONS 98 CHANGE OF AXES 98 2D CHANGE OF AXES 99 DIRECTION COSINES
100 POSITIONING THE VIRTUAL CAMERA 102 DIRECTION COSINES 103 EULER
ANGLES 106 QUATERNIONS 110 ADDING AND SUBTRACTING QUATERNIONS 110
MULTIPLYING QUATERNIONS 111 THE INVERSE QUATERNION 111 ROTATING POINTS
ABOUT AN AXIS 112 ROLL, PITCH AND YAW QUATERNIONS 116 QUATERNIONS IN
MATRIX FORM 118 FRAMES OF REFERENCE 119 TRANSFORMING VECTORS 120
DETERMINANTS 122 PERSPECTIVE PROJECTION 126 SUMMARY 128 ESSENTIAL
MATHEMATICS FOR CG FAST 8. INTERPOLATION 129 LINEAR INTERPOLANT 130
NON-LINEAR INTERPOLATION 133 TRIGONOMETRIC INTERPOLATION 133 CUBIC
INTERPOLATION 135 INTERPOLATING VECTORS 141 INTERPOLATING QUATERNIONS
145 SUMMARY 147 9. CURVES AND PATCHES 149 THE CIRCLE 150 THE ELLIPSE 151
BEZIER CURVES 152 BERNSTEIN POLYNOMIALS 152 QUADRATIC BEZIER CURVES 157
CUBIC BERNSTEIN POLYNOMIALS 158 A RECURSIVE BEZIER FORMULA 162 BEZIER
CURVES USING MATRICES 162 LINEAR INTERPOLATION 164 B-SPLINES 167 UNIFORM
B-SPLINES 168 CONTINUITY 171 NON-UNIFORM B-SPLINES 172 NON-UNIFORM
RATIONAL B-SPLINES 172 SURFACE PATCHES 173 PLANAR SURFACE PATCH 173
QUADRATIC BEZIER SURFACE PATCH 174 CUBIC BEZIER SURFACE PATCH 177
SUMMARY 180 10. ANALYTIC GEOMETRY 181 REVIEW OF GEOMETRY 182 ANGLES 182
INTERCEPT THEOREMS 183 GOLDEN SECTION 184 TRIANGLES 185 CENTER OF
GRAVITY OF A TRIANGLE 185 ISOSCELES TRIANGLE 186 EQUILATERAL TRIANGLE
187 RIGHT TRIANGLE 187 THEOREM OF THALES 187 THEOREM OF PYTHAGORAS 188
QUADRILATERAL 188 CONTENTS TRAPEZOID 189 PARALLELOGRAM 189 RHOMBUS 190
REGULAR POLYGON (N-GON) 190 CIRCLE 192 2D ANALYTIC GEOMETRY 193 EQUATION
OF A STRAIGHT LINE 193 THE HESSIAN NORMAL FORM 194 SPACE PARTITIONING
197 THE HESSIAN NORMAL FORM FROM TWO POINTS 198 INTERSECTION POINTS 199
INTERSECTION POINT OF TWO STRAIGHT LINES 199 INTERSECTION POINT OF TWO
LINE SEGMENTS 199 POINT INSIDE A TRIANGLE 202 AREA OF A TRIANGLE 202
HESSIAN NORMAL FORM 205 INTERSECTION OF A CIRCLE WITH A STRAIGHT LINE
207 3D GEOMETRY 209 EQUATION OF A STRAIGHT LINE 209 POINT OF
INTERSECTION OF TWO STRAIGHT LINES 211 EQUATION OF A PLANE 215 SPACE
PARTITIONING 216 POINT OF INTERSECTION OF A LINE AND A PLANE 216 POINT
OF INTERSECTION OF A LINE SEGMENT AND A PLANE 218 SUMMARY 219 11.
CONCLUSION 221 REFERENCES 223 INDEX 225
|
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| dewey-full | 006.60151 006.6/0151 |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:51:17Z |
| institution | BVB |
| isbn | 1852333804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009397212 |
| oclc_num | 247948471 |
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| owner | DE-739 DE-824 DE-522 DE-83 DE-B768 |
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| physical | IX, 229 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Essential series |
| spelling | Vince, John 1941- Verfasser (DE-588)120106604 aut Essential mathematics for computer graphics fast John Vince London [u.a.] Springer 2001 IX, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Essential series Computergraphik - Mathematik Mathematik (DE-588)4037944-9 gnd rswk-swf Computergrafik (DE-588)4010450-3 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=009397212&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vince, John 1941- Essential mathematics for computer graphics fast Computergraphik - Mathematik Mathematik (DE-588)4037944-9 gnd Computergrafik (DE-588)4010450-3 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4010450-3 |
| title | Essential mathematics for computer graphics fast |
| title_auth | Essential mathematics for computer graphics fast |
| title_exact_search | Essential mathematics for computer graphics fast |
| title_full | Essential mathematics for computer graphics fast John Vince |
| title_fullStr | Essential mathematics for computer graphics fast John Vince |
| title_full_unstemmed | Essential mathematics for computer graphics fast John Vince |
| title_short | Essential mathematics for computer graphics fast |
| title_sort | essential mathematics for computer graphics fast |
| topic | Computergraphik - Mathematik Mathematik (DE-588)4037944-9 gnd Computergrafik (DE-588)4010450-3 gnd |
| topic_facet | Computergraphik - Mathematik Mathematik Computergrafik |
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