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| Dunn F., Parberry I. — 3D Math Primer for Graphics and Game Development |
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| Предметный указатель |
Homogenous matrices, general 135
Homogenous matrix, general affine transformations 140
Homogenous matrix, projection 140
Homogenous matrix, translation 137
Hoppe, Hugues 335—336
Hotspot of specular highlight 363
Hotspot of spot light 361
Hotspot, falloff 367
ID math 6—8
Identities, concerning determinants 128
Identities, concerning matrix inverse 131
Identities, concerning matrix multiplication 89 90
Identities, concerning quaternions 166 167
Identities, concerning transposition 86
Identities, concerning vectors 65 90
Identities, trig 257—258 (see also Trig identities)
Identity matrix 85 88 218 225
Identity quaternions 163 208
Illumination (see Lighting)
imaginary numbers (see Complex numbers)
Implicit form, for circle/sphere (see Sphere)
Implicit form, for representing geometric primitive 239—240
Incenter of triangle 267—268
Indexed triangle mesh 320—322
Inertial space 28—29
infinity 6—7
Information hiding 77
Initialization, lack of default initialization 77
Inner product (see Dot product)
Int (data type) 8
Integers 7
Interpolation of AABB and plane 285 310—312
Interpolation of Euler angles (see Euler angles)
Interpolation of implicit lines in 2D 282
Interpolation of quaternions (see Slerp intersection)
Interpolation of ray and AABB 297 307—309
Interpolation of ray and circle/sphere 287—288
Interpolation of ray and plane 284
Interpolation of sphere and AABB 291 307
Interpolation of three planes 286
Interpolation of two AABBs 297—299 312—315
Interpolation of two circles/spheres 288—291
Interpolation of two rays in 3D 283
Interpolation with view frustum (see View frustum clipping)
Interpolation, linear (see Linear interpolation)
Interpolation, static vs. dynamic 281
Interpolation, tests 281—300
Inverse matrix 130 151 236—237
Inverse matrix of orthogonal matrix 132
Invertible matrices (see Inverse matrix)
Invertible transformations 122
Isolated vertices (see Topology of triangle mesh)
Lambert’s law for diffuse reflection 366
Latitude 25
Law of Cosines (see Identities trig)
Law of Sines (see Identities trig)
Left-hand rule 17 106
Left-hand rule for ordering vertices (see vertex order)
Left-handed coordinate space 16
Length of vector (see Magnitude)
Lerp (see Linear interpolation)
Level of detail (see LOD)
Light attenuation 366—367
Light sources 360—361
Light sources, ambient (see Ambient light)
Light sources, directional (see Directional light)
Light sources, omni (see Point light)
Light sources, point (see Point light)
lighting 358—371
Lighting equation 361 367—368 378—379
Lighting model (see also Lighting equation)
Lighting model, local 358 368
Lighting model, standard 358 361 368
Lighting, stored at the vertex level 330
Line (see also Ray)
Line, 2D representations 243—245
Line, segment (see Ray)
Linear algebra 46
Linear algebra, identities (see Identities)
Linear fog (see Fog)
Linear interpolation 157 173 367 369
Linear running time (see Algorithm running time)
Linear transformation 91 121
Linear transformation, does not contain translation 97 101 121 137 140
Location, specifying in 2D 13 14
Location, specifying in 3D 15 16
LOD (level of detail) 336 375
Logarithmic running time (see Algorithm running time)
longitude 25
Loose quadtrees (see Quadtree)
Magnitude of a complex number 160
Magnitude of a vector 37
Magnitude, quaternion 163 166
Magnitude, vector, computing 49
Magnitude, vectors with a given magnitude 47
Malformed 151
Malformed, redundancy 151
Manifold 330
Mapping 120
Mapping texture (see Texture mapping)
material 362
math utilities 196—198
MathUtil.cpp 197—198
MathUtil.h 196—197
Matrix 4 3
Matrix chain problem 89
Matrix creep 134 152 179
Matrix form (for orientation), advantages/disadvantages 150—151
Matrix form (for orientation), converting to/from Euler angles (see Euler angles)
Matrix form (for orientation), converting to/from quaternion (see Quaternion)
Matrix, class (see Classes)
Matrix, classical adjoint (see classical adjoint)
Matrix, cofactor (see Cofactor)
Matrix, concatenation of transformations 119
Matrix, cpp 224—238
Matrix, definition 83
Matrix, determinant (see Determinant)
Matrix, diagonal 84
Matrix, dimensions and notation 83
Matrix, homogenous (see Homogenous matrix)
Matrix, identity (see Identity matrix)
Matrix, implementing (see Classes)
Matrix, inverse (see Inverse matrix)
Matrix, invertible (see Inverse matrix)
Matrix, linear algebra identities (see Identities mathematical)
Matrix, minor (see Minor)
Matrix, multiplication by scalar 86
Matrix, multiplication does linear transformation 91 93
Matrix, multiplication of two matrices 86 151 235—236
Matrix, multiplication of vector and matrix 89 235
Matrix, orthogonal 122 132
Matrix, representing angular displacement 149—152
Matrix, representing orientation using (see Matrix form)
Matrix, singular vs. non-singular 122 130
Matrix, square 84
Matrix, trace (see Trace)
Matrix, transposition (see Transposition)
Matrix, variables, typeface used for 46
Matrix, visualizing 93—97
Member functions vs. nonmember 75
Memory, used by Euler angles 156
Memory, used by matrices 151
mesh (see Triangle mesh)
Minor (of a matrix) 127
Mirroring (see Reflection)
Model transform from object to world space 354 378
Modeling space (see Object space)
Moller, Thomas 297
Multiplication of complex numbers (see Complex numbers)
Natural numbers 6
| Near clip plane 351
Negation, quaternion (see Quaternion)
Negation, vector 48 52
negative numbers 7
Nested coordinate space 30 31
Non-uniform scale (see Scale)
Norm of vector (see Magnitude)
normal 53
Normal, best fit (see Plane in triangle meshes)
Normalizing a vector 53
Normalizing to plane (see Plane)
Normalizing to polygon (see Polygon)
Normalizing, averaging 329—330
Normalizing, color (see Color)
Normalizing, determinant (see Determinant)
Normalizing, notation (see also Conventions)
Normalizing, triangulation to triangle (see Triangle normals)
Normalizing, vertex 328—329
Notation (see Algorithm running time)
OBB (oriented bounding box) 247
Object space 26—27 354
Occlusion of a bounding volume 390
Occlusion of a single pixel 386
Occlusion, high level techniques 402—406
Octree 393—398
Omni Light (see Point light)
On the Heavens and Physics 24
Onto arbitrary line of plane 117
Onto cardinal axis or plane 116
Opacity (see Alpha open edge)
OpenGL, clip matrix 357
OpenGL, column vectors in 91
Operator overloading 73 74
Operator precedence, cross product 62
Operator precedence, dot product 58 62
Optimization of vector code 78
Order in 3D 147—193
Order of the axes in 2D 12
Order of vertices (see Vertex)
Order vs. angular displacement 149 215
Order vs. direction 148
Order vs. rotation 149
Order, comparison of representation methods 179—180
Order, converting between representation methods 180—192
Order, orientation 148
Oriented bounding box (see OBB)
Origin of the universe 24
Origin, used to define a coordinate space 11 31
Orthogonal basis 134
Orthogonal matrix (see Matrix)
Orthogonal transformations 122
Orthogonalizing a matrix 134
Orthographic projection by using zero scale 112 117
Orthographic projection, implementation 232—233
Orthonormal basis 134
Outcode 387—389
Outer product (see Cross product)
Output window 349 358
Overview of the graphics pipeline (see Graphics pipeline)
Page flipping 372
parallel (see Orthographic projection)
Parallel lines and linear transformations 121
Parallel projection (see Orthographic projection)
Parallel, portion of vector 61
Parallel, vectors 60 63
Parallelepiped 129
Parallelogram 129
Parametric for representing geometric primitives 240
Parametric for representing rays (see Ray)
Parametric point of intersection (see Intersection)
Parent coordinate space (see Nested coordinate space)
Perimeter of triangle 258
Perpendicular, axis (see axis Bisector)
Perpendicular, cross product yields perpendicular vector 63
Perpendicular, portion of vector 61
Perpendicular, vectors 60 63
Perspective (see Perspective projection)
Perspective projection 141—142
Perspective projection from camera to screen space 355—358
Phong exponent (see Glossiness in specular lighting)
Phong shading 370 378
Phong specular lighting model 362—363
PI 7 8 196 247 410
Pigeonholing 392
Pinhole camera 142—145
Pitch 154
Pivoting 131
Pixel, aspect ratio (see Aspect ratio)
Pixel, shading 383
Pixel, size of 350
Pixel, tests 383
Planar graph 330
Plane 252—256
Plane equation (see Plane implicit
Plane, best fit 254—256
Plane, definition using three points 253
Plane, distance to point 256
Plane, front and back side 253
Plane, implicit definition 252—253
Plane, intersection tests (see Intersection)
Playstation II 326 336
Point light 360
Point of concavity (see Polygon separate class)
Point, closest (see Closest)
Points at infinity 136 139
Points vs. vector (see Vector)
Points, homogenous 136
Points, locating in 2D 13 14
Points, locating in 3D 15 16
Points, notation 14
Polar coordinates 25 148
Polygon 269—275
Polygon, convex vs. concave 271—274
Polygon, fanning 274—275
Polygon, self-intersecting 270
Polygon, simple vs. complex 269—270
Polygon, triangulation 274—275
Portal techniques 403—406
POSITION (see also Points Locating)
Position vs. displacement 38
Position, relative vs. absolute 25 26 38 41
Potentially visible set (see PVS)
Precedence precision, floating-point 73
Precedence, operator (see Operator)
Primitives private class members 77
Primitives, geometric (see Geometric)
Procedural modeling 375
PRODUCT (see Cross product vector dot)
Product of scalar and vector (see Vector)
Progressive mesh 336 375
Projected light map 361 363
Projecting one vector onto another 61 110 113
projection plane 141—145
Projection, orthographic (see Orthographic projection)
Projector 141
Proper transformation (see Rigid body transformation)
Public class members 77
PVS (potentially visible set) 402—403
Pyramid spot light (see Spot light)
Pythagorean Theorem 50 287
Quadratic formula 290
Quadratic running time (see Algorithm running time)
Quadtree 393—398
Quadtree, loose 398
Quatemion.cpp 207—215
Quatemion.h 205—207
Quaternion as a complex number 160—162
Quaternion as an axis angle pair 162
Quaternion implementing (see Classes)
Quaternion, advantages/disadvantages 178
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