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| Dunn F., Parberry I. — 3D Math Primer for Graphics and Game Development |
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| Предметный указатель |
Quaternion, conjugate 164 214
Quaternion, converting to/from Euler angles (see Euler angles)
Quaternion, converting to/from matrix 185—189 218—219 230
Quaternion, cross product (see Cross product)
Quaternion, dot product (see Dot product)
Quaternion, exponential 170
Quaternion, exponentiation 171 214—215
Quaternion, geometric interpretation 162
Quaternion, identity (see Identity)
Quaternion, magnitude (see Magnitude)
Quaternion, multiplication by scalar 170
Quaternion, negation 163
Quaternion, notation 160
Quaternion, squad 177—178
Quaternion, unit quaternion 164
RADIANS 409—410
Radius of AABB (see AABB)
Radius of circle/sphere (see Circle Sphere)
Rasterization 383
Rational numbers 7
Ray 241—245
Ray as moving point 281
Ray, intersection (see Intersection)
Ray, parametric form 242
Ray, representation methods 242—245
Ray, skew 283
Ray, two points form 242
Raytrace (see Intersection)
Raytracing, quadtree 395—398
Real numbers 6 7
Rectangular spot light (see Spot light)
Redundancy by using negative scale 112 118
Redundancy in barycentric coordinates 262
Redundancy in matrices (see Matrix)
Redundancy in parameterization of geometric primitive (see Geometric primitives reflection)
Redundancy, matrix 118 233—235
Redundancy, specular (see Specular lighting contribution two)
Reflection vector, used in Phong specular model 362—363
Reflections is same as a rotation 118
Reflex vertex (see Polygon Convex
retina 142
RGB color model (see Color)
Right-hand rule 17 107
Right-handed coordinate space 16
Rigid body transformation 123
Rise (see Slope-intercept)
ROLL (see Bank)
Roll-pitch-yaw 155
Room (in portal rendering) 403 404
Root node of a tree 393 399—400
Rotation class (see Classes)
Rotation vs. orientation (see Orientation which way is positive)
Rotation, between object and inertial space 28
Rotation, complex numbers in 2D (see Complex numbers in 2D about the origin)
Rotation, complex numbers in 3D about arbitrary axis 109
Rotation, complex numbers in 3D about cardinal axis 108
Row vector (see Vector)
Run (see Slope-intercept)
Sand — Reckoner 24
scalar 36
Scalar variables, typeface used for 46
Scale in arbitrary direction 113 231
Scale, along cardinal axes 112 230
Scale, transformation matrix 112—115
Scale, uniform vs. non-uniform 112
Scale, vector (see Vector multiplication)
Scissoring 383
Screen coordinate space 12 16
Screen space mapping from clip space to 358
Self-intersecting polygon (see Polygon)
Semiperimeter of a triangle 258
Shading Gouraud (see Gouraud)
Shading Phong (see Phong)
Shading pixel (see Pixel)
Shading, comparison of interpolation methods 370—371
Shading, flat (see Flat)
shearing 118 231—232
Sheep, animating 30 31
Sheep, dead 6
Shininess (see Glossiness in specular lighting Specular
Shoemake, Ken 188
Short (data type) 8
Sigma notation 409
Simple polygon (see Polygon)
Singular matrix (see Matrix)
Skew box 96 129
Skew rays (see Ray)
Skew transformation (see Shearing)
Slerp 173—177 212—214
Sliver triangles, caused by fanning 275
Sliver triangles, collapse after vertex welding 332—333
Slope-intercept, representation of 2D line 243
Space partitioning techniques 390—402
Specular color 363
Specular lighting contribution 362—365
Specular map (see Gloss map)
Sphere 246—247 (see also Circle)
Sphere, implicit form 239—240 247
Sphere, testing against view frustum 389
Sphere, unit sphere 53
Spherical fog (see Fog)
Spherical light (see Point light)
Spherical linear interpolation (see Slerp)
Spline, quaternion (see Quaternion)
Squad spot light 361
Square matrices (see Matrix)
Standard position, drawing an angle in 411
Static intersection test (see Intersection tests)
Strip (see Triangle strip)
| Stripe 325
Stripification (see Triangle strip)
Subscript notation (see Notation)
Suggested reading 407
Summation notation 409
Surface area of sphere (see Sphere)
Surface normal (see also Normal)
Surface normal, used in lighting equation 362
Sutherland — Hodgman polygon clipping 381
Syntax, overloaded operators 73
Syntax, weird syntax caused by member functions 76
T&L (transformation and lighting) 377—379
Tail of vector (see Vector temporary)
Texture mapping 373—374
Texture mapping, coordinates 328 373
Theory of relativity 41
Topology of triangle mesh 330—331
Trace (matrix) 187
Transform, model (see Model transform)
Transform, view (see View transform
Transformation 331
Transformation, AABB (see AABB)
Transposition 85
triangle 257—269
Triangle mesh 319—343
Triangle rule for vector addition/subtraction 55
Triangle stri 323—327
Triangle, area 258—260
Triangulation (see Polygon trig)
Trig identities 413—414
Triple product 62 126 127
Tripod formed by 3
Trivial accept 389
Trivial rejection (see VSD)
Typeface conventions (see Conventions)
Uniform scale (see Scale)
Unit circle 410 (see also Circle)
Unit quaternion (see Quaternion)
Unit sphere (see Sphere)
Unit vector (see Normal angle)
Univariate Functions 240
utilities, math (see Math utilities)
V-intercept (see Slope-intercept)
Variables 46
Variables vs. point 40 41 57 78 139 149
Variables vs. scalar 36
Variables, typeface used for 46
Vector as a matrix 85
Vector from one point to another 57
Vector processing unit 79
Vector, addition and subtraction 54
Vector, angle between 59
Vector, direction (see Direction)
Vector, geometric interpretation 37
Vector, head and tail 37 64 65
Vector, magnitude (see Magnitude)
Vector, mathematical definition 36
Vector, multiplication by matrix (see Matrix)
Vector, multiplication/division by scalar 51
Vector, negation (see Negation)
Vector, normal (see Normal)
Vector, notation 36
Vector, row vs. column 36 85 89 90
Vector, sequence of displacements 39 56 92
Vector, specifying 38
Vector, transposition (see Transposition)
Velocity 36 38
Vertex, caching 323
Vertex, convex vs. concave shaders 377
Vertex, duplicate 330
Vertex, formats 376—377
Vertex, isolated 330 332
Vertex, lighting 378—379
Vertex, normal (see Normals)
Vertex, order 253—256 257 269 271 274 320—321 329 381
Vertex, reflex (see Polygon)
Vertex, split 335
Vertex, triangle mesh 320
Vertex, welding 329 331—334
View frustum 351 381
View frustum, testing bounding volume against 387—389
View transform from world to camera space 354 378
View volume (see View)
virtual functions 77
Visibility (see VSD)
Visible surface determination (see VSD)
Volume of sphere (see sphere
VSD (visible surface determination) 385—406
Web page 2
Welding vertices (see Vertex)
Window, rendering (see View parameters)
Winged edge model 322
Woo, Andrew 297
World space 24—26 354
WrapPi (see Angles Wrapping)
Wrapping angles (see Angles Wrapping)
Yaw (see Heading)
Z-checking 390
Zero (see Zero vector)
Zero vector 47
Zero vector, cannot be normalized 53
Zero vector, global constant variable 78
Zero vector, interpreted by cross product 64
Zero vector, interpreted by dot product 60
Zero vector, not affected by linear transformation 97 121
Zero, invention of 6
Zoom 351
Zoom, converting between field of view and 352
Zoom, inserting into the clip matrix 357 428
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