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Dunn F., Parberry I. — 3D Math Primer for Graphics and Game Development
Dunn F., Parberry I. — 3D Math Primer for Graphics and Game Development

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Название: 3D Math Primer for Graphics and Game Development

Авторы: Dunn F., Parberry I.

Аннотация:

3D Math Primer for Graphics and Game Development covers fundamental 3D math concepts that are especially useful for computer game developers and programmers. The authors discuss the mathematical theory in detail and then provide the geometric interpretation necessary to make 3D math intuitive. Working C++ classes illustrate how to put the techniques into practice, and exercises at the end of each chapter help reinforce the concepts.


Язык: en

Рубрика: Computer science/Обработка изображений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 428

Добавлена в каталог: 16.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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