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| Dunn F., Parberry I. — 3D Math Primer for Graphics and Game Development |
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| Предметный указатель |
3D Studio Max 21 343 360
AABB (axially aligned bounding box) 247—252
AABB (axially aligned bounding box), computing 249
AABB (axially aligned bounding box), intersection tests (see Intersection)
AABB (axially aligned bounding box), representing 248
AABB (axially aligned bounding box), testing against view frustum 389
AABB (axially aligned bounding box), transforming 251—252 304—305
AABB3 class (see classes)
AABB3.cpp 302—315
AABB3.h 300—302
Absolute position (see Position)
Accessor functions 77
acos 196 197
Adaptive subdivision 393—395
Addition of complex numbers (see Complex numbers)
Addition of vectors (see Vector)
Additive identity 47 48
Additive inverse 48
Affine transformation 101 122
Algorithm running time 334 391 401
Aliasing Euler angles (see Euler angles)
Alpha 376 383
Alpha blending 383
Alpha test 383
Ambient color 366
Ambient light, light source 361
Ambient light, lighting contribution 366
Angle, between vectors 59
Angle, degrees and radians 409
Angle-preserving transformation 122
angles 409
Angles, wrapping 158 196 197
Angular displacement (see Orientation)
API 150
API, delivering geometry to 375—377
API, distribution of work 346
Archimedes 24
Area of circle, see sphere of parallelogram 63 258
Area of parallelogram 63
Area of rectangle 64
Area of skew box 129
Area of triangle (see Triangle)
Aristarchus 24
Aristotle 24
Array as vector 36
ASIN 182
Aspect ratio 350
Assembly language 79
atan 2 183
Attenuation of light (see Light attenuation)
Axes, possible orientations in 2D 12
Axes, possible orientations in 3D 19 20
Axes, transforming (see Transformations)
Axes, usually perpendicular 11 15 16 31
Axis, a line about which something rotates 106 162
Axis, third axis in 3D 15
Axis, used to define a coordinate space 11 31
Axis-angle pair 162
Backface culling 380—381 385
Baiycentric coordinates 260—267 (see also Baiycentric)
Baiycentric coordinates space computing in 2D 262
Baiycentric coordinates space computing in 3D 263—267
Baiycentric coordinates space, correspondence with Cartesian 260—262
Baiycentric coordinates space, tessellate the plane 261
Bank 154
Basis vectors 93
Basis vectors, rows of a matrix as 93 94
Billboard, problems with averaging normals 329
Binary space partition (see BSP tree)
Bits, size of data types 8
Bivariate functions 240 417
Blending, alpha (see Alpha blending)
Blinn specular lighting model 364
Body space (see Object space)
Bounding box (see AABB)
Bounding volume (see also Sphere AABB)
Bounding volume, AABB vs. sphere 250
Bounding volume, brute force 389
Bounding volume, occlusion of 390
Bounding volume, visibility tests 386—390
BSP (binary space partition) tree 398—402
BSP (binary space partition) tree, constructing 400—402
BSP (binary space partition) tree, example 399—400
BSP (binary space partition) tree, traversing 400
Buffer, depth (see Depth buffer)
Buffer, frame (see Frame buffer)
Buffer, z-buffer (see Depth buffer)
C++ 3
Camera space 27—28 351 354
Camera space in this book 19—20
Camera space, Euler angles (see Euler angles)
Camera space, typeface 46
Camera, specifying (see View parameters)
Canonical Euler angles (see Euler angles)
Canonical view volume (see Clip space)
Cardinal spline 177
Cartesia 9—14 24 26
Cartesian coordinate system 5 6 9—20
Cartesian coordinate system, 2D 9—14
Cartesian coordinate system, 3D 14—20
Center of AABB (see AABB)
Center of circle/sphere (see Sphere)
Center of gravity, of triangle 267
Center of projection 141—145
Centroid (see Center of gravity)
Child coordinate space (see Nested coordinate space)
circle 246—247 (see also Sphere)
Circle, circumscribed about triangle (see Circumcenter)
Circle, inscribed in triangle (see Incenter)
Circle, parametric form 240
Circle, tangent to three lines (see Incenter)
Circle, through three points (see Circumcenter)
Circle, unit circle 53
Circumcenter 268—269
Circumference of circle/sphere (see Sphere)
Clamping, color (see Color)
Class, design 73—82 196
Classes, AABB3 249 300—315
Classes, EditTriMesh 336—343
Classes, EulerAngles 199—205
Classes, Matrix4x3 220—238
Classes, Quaternion 205—215
Classes, RotationMatrix 215—220
Classes, Vector3 69—82
Classical adjoint 130
Clip matrix 355 378 387
Clip plane 351 356 381—383 387
Clip space 355 378
Clipping, polygon 381—383 385
Closed mesh 330
Closest point on AABB 280—281
Closest point on circle/sphere 280
Closest point on parametric ray 278—279
Closest point on plane 279
Closest point tests 277—281
Closest point to 2D implicit line 277—278
Closest point to AABB 306
Cofactor (of a matrix) 127
Collision detection 281
color space (see Color)
Color, math on 359
Color, RGB model 359
Color, space 359
Column vector (see Vector)
complex numbers 160—162 (see also Quaternion)
Complex numbers, addition, subtraction, and multiplication of 160
Complex numbers, conjugate 161
Complex numbers, rotation in 2D 161
Complex polygon (see Polygon)
Computational geometry 1
| Concave (see Polygon)
Conical spot light (see Spot light conjugate)
Const reference arguments 75
Constraint (see Redundancy)
Constructor, avoiding redundant calls 80
Constructor, no default initialization 77
Continuous mathematics 7
Convex (see Polygon)
Convex partitioning (see Polygon)
Coordinate space, camera (see Camera space)
Coordinate space, examples 25—29
Coordinate space, inertial (see Inertial space)
Coordinate space, left vs. right-handed 16
Coordinate space, object (see Object space)
Coordinate space, screen (see Screen coordinate space)
Coordinate space, specifying 31
Coordinate space, transformations (see Transformation)
Coordinate space, which to use for lighting 379
Coordinate space, world (see World space)
Coordinate spaces, multiple 23—25
Copernicus, Nicholas 24
Counting numbers 6
Cross product, quaternion 165 166 210
Cross product, vector 62 65 74
Culling of backfacing polygons (see Backface culling)
da Vinci, Leonardo 13
De Revolutionibus Orbium Coelestium 24
Decimation of triangle mesh (see Triangle mesh decimation)
Degenerate triangles, topology problem 331
Degenerate triangles, used to seam triangle strips 325
Degenerate triangles, vertex welding sliver polygons 332—333
DEGREES 409—410
Degrees of freedom (see also Redundancy)
Degrees of freedom in parameterization of geometric primitive (see Geometric primitives)
Degrees of freedom, AABB vs. sphere 250
Depth buffer 372 383 385 390
Depth test 383
Descartes. Rene 5 6
Detaching faces 329 334—335
Determinant (matrix) 125 236
Determinant (matrix), classifying transformations 123 129
Determinant (matrix), used to compute inverse 131
Diagonal, elements of a matrix 84
Diagonal, matrix 84
Diameter of circle/sphere (see Sphere)
Difference, between points 57
Difference, between quaternions (see Quaternion diffuse)
Difference, lighting contribution 365—366
Diffuse color 366
Dimension of matrix (see Matrix)
Dimension of vector 36
Direction of vector 37
Direction vs. orientation (see Orientation)
Directional light 360
DirectX, clip matrix 357
DirectX, discrete mathematics 7
DirectX, flexible vertex format 376
DirectX, row vectors in 91
DirectX, vertex shaders 377
Displacement vs. distance 36 38
Displacement vs. position (see Position)
Displacement, vectors as a sequence of (see Vector)
Distance from point to plane (see Plane)
Distance vs. displacement 36 38
Distance, between two points 57
Distance, signed 13 14 15 244 256
Division of a vector by a scalar (see Vector)
Domino effect during vertex welding (see Vertex Welding)
Doorway (in portal rendering) 403 404
Dot product, quaternion 169 419
Dot product, vector 58
Double (data type) 8 73
Double angle formula (see Trig identities)
Double buffering 372
Duplicate vertices (see Vertex)
Dynamic intersection test (see Intersection)
Edge collapse 335
EditTriMesh class (see Classes)
EditTriMesh.h 336—342
Euler angles, advantages/disadvantages 156—158
Euler angles, aliasing 156—158
Euler angles, canonical 156—157 201
Euler angles, class (see Classes)
Euler angles, conventions 153 155
Euler angles, converting to/from matrix 180—185 203—205 218
Euler angles, converting to/from quaternion 190—193 201—203 209-210
Euler angles, definition 153
Euler angles, implementing (see Classes)
Euler angles, interpolation problems 157—159
Euler, Leonhard 153 162
EulerAngles.cpp 200—205
EulerAngles.h 198—199
Euler’s equation for planar graphs 330
Eye space (see Camera space)
Falloff, angle 361 367
Falloff, distance 360—361 367
Fanning (see Polygon Triangle
Far clip plane 351
Field of view (see Zoom)
First law of computer graphics 8 19
Fixed-point math 80
Flat shading 370
Flexible vertex format 376
Float (data type) 8 73
Floating point 8
Floating-point coordinates 383
Floating-point error (see Matrix creep)
floating-point math 80
Focal distance 355
Fog 368—370
Fog, color 370
Fog, density 369
Foreshortening, perspective (see Perspective projection)
Fractions 7
Frame buffer 350 372
Function, mathematical 120
Galilei, Galileo 24
Gaussian elimination 131
Geocentric universe 24
Geometric primitives, AABB (see AABB)
Geometric primitives, circle (see Circle)
Geometric primitives, degrees of freedom in parameterization 241
Geometric primitives, representation of 239—241
Geometric primitives, sphere (see Sphere)
Gimbel lock 157—158
Glassner, Andrew 329
Global coordinate system (see World space)
Gloss map 363 379
Glossiness in specular lighting 363—365
Gouraud shading 330 371 378
Gouraud shading, problems with averaged normals 329
Gram — Schmidt orthogonalization 134
Graph of rooms 404
Graph planar (see Planar graph)
graphics pipeline 346—349
Grid lines, in Cartesian coordinate space 11
Grid, partitioning space using 392—393
GS (Graphics Synthesizer) (see Playstation II)
Halfway vector used in Blinn specular model 364
Hamilton, William 161
Handedness of coordinate system 16—19
Head of vector (see Vector)
Heading 153
Heading vs. yaw 155
Heading-pitch-bank 153
Heliocentric universe 24
Heron’s formula for triangle area 258
Hierarchy of coordinate spaces (see Nested coordinate space)
Hierarchy, grouping objects for VSD 391
Homogenous coordinates 136
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