Mathematics for 3D game programming and computer graphics / Eric Lengyel.
Material type:
TextPublisher: Boston, MA : Course Technology, Cengage Learning, [2012]Copyright date: ©2012Edition: 3rd editionDescription: xviii, 545 pages : illustrations ; 25 cmContent type: - text
- unmediated
- volume
- 9781435458864
- 1435458869
- 794.81526 23 L.E.M
Contents:
Summary: Mathematics for 3D game programming and computer graphics, third edition, illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and game engines at the professional level.
Machine generated contents note: ch. 1 Rendering Pipeline --
1.1. Graphics Processors --
1.2. Vertex Transformation --
1.3. Rasterization and Fragment Operations --
ch. 2 Vectors --
2.1. Vector Properties --
2.2. Dot Product --
2.3. Cross Product --
2.4. Vector Spaces --
ch. 2 Summary --
Exercises for Chapter 2 --
ch. 3 Matrices --
3.1. Matrix Properties --
3.2. Linear Systems --
3.3. Matrix Inverses --
3.4. Determinants --
3.5. Eigenvalues and Eigenvectors --
3.6. Diagonalization --
ch. 3 Summary --
Exercises for Chapter 3 --
ch. 4 Transforms --
4.1. Linear Transformations --
4.1.1. Orthogonal Matrices --
4.1.2. Handedness --
4.2. Scaling Transforms --
4.3. Rotation Transforms --
4.3.1. Rotation About an Arbitrary Axis --
4.4. Homogeneous Coordinates --
4.4.1. Four-Dimensional Transforms --
4.4.2. Points and Directions --
4.4.3. Geometrical Interpretation of the w Coordinate --
4.5. Transforming Normal Vectors --
4.6. Quaternions --
4.6.1. Quaternion Mathematics --
4.6.2. Rotations with Quaternions --
4.6.3. Spherical Linear Interpolation --
ch. 4 Summary --
Exercises for Chapter 4 --
ch. 5 Geometry for 3D Engines --
5.1. Lines in 3D Space --
5.1.1. Distance Between a Point and a Line --
5.1.2. Distance Between Two Lines --
5.2. Planes in 3D Space --
5.2.1. Intersection of a Line and a Plane --
5.2.2. Intersection of Three Planes --
5.2.3. Transforming Planes --
5.3. View Frustum --
5.3.1. Field of View --
5.3.2. Frustum Planes --
5.4. Perspective-Correct Interpolation --
5.4.1. Depth Interpolation --
5.4.2. Vertex Attribute Interpolation --
5.5. Projections --
5.5.1. Perspective Projections --
5.5.2. Orthographic Projections --
5.5.3. Extracting Frustum Planes --
5.6. Reflections and Oblique Clipping --
ch. 5 Summary --
Exercises for Chapter 5 --
ch. 6 Ray Tracing --
6.1. Root Finding --
6.1.1. Quadratic Polynomials --
6.1.2. Cubic Polynomials --
6.1.3. Quartic Polynomials --
6.1.4. Newton's Method --
6.1.5. Refinement of Reciprocals and Square Roots --
6.2. Surface Intersections --
6.2.1. Intersection of a Ray and a Triangle --
6.2.2. Intersection of a Ray and a Box --
6.2.3. Intersection of a Ray and a Sphere --
6.2.4. Intersection of a Ray and a Cylinder --
6.2.5. Intersection of a Ray and a Torus --
6.3. Normal Vector Calculation --
6.4. Reflection and Refraction Vectors --
6.4.1. Reflection Vector Calculation --
6.4.2. Refraction Vector Calculation --
ch. 6 Summary --
Exercises for Chapter 6 --
ch. 7 Lighting and Shading --
7.1. RGB Color --
7.2. Light Sources --
7.2.1. Ambient Light --
7.2.2. Directional Light Sources --
7.2.3. Point Light Sources --
7.2.4. Spot Light Sources --
7.3. Diffuse Reflection --
7.4. Specular Reflection --
7.5. Texture Mapping --
7.5.1. Standard Texture Maps --
7.5.2. Projective Texture Maps --
7.5.3. Cube Texture Maps --
7.5.4. Filtering and Mipmaps --
7.6. Emission --
7.7. Shading Models --
7.7.1. Calculating Normal Vectors --
7.7.2. Gouraud Shading --
7.7.3. Blinn-Phong Shading --
7.8. Bump Mapping --
7.8.1. Bump Map Construction --
7.8.2. Tangent Space --
7.8.3. Calculating Tangent Vectors --
7.8.4. Implementation --
7.9. Physical Reflection Model --
7.9.1. Bidirectional Reflectance Distribution Functions --
7.9.2. Cook-Torrance Illumination --
7.9.3. Fresnel Factor --
7.9.4. Microfacet Distribution Function --
7.9.5. Geometrical Attenuation Factor --
7.9.6. Implementation --
ch. 7 Summary --
Exercises for Chapter 7 --
ch. 8 Visibility Determination --
8.1. Bounding Volume Construction --
8.1.1. Principal Component Analysis --
8.1.2. Bounding Box Construction --
8.1.3. Bounding Sphere Construction --
8.1.4. Bounding Ellipsoid Construction --
8.1.5. Bounding Cylinder Construction --
8.2. Bounding Volume Tests --
8.2.1. Bounding Sphere Test --
8.2.2. Bounding Ellipsoid Test --
8.2.3. Bounding Cylinder Test --
8.2.4. Bounding Box Test --
8.3. Spatial Partitioning --
8.3.1. Octrees --
8.3.2. Binary Space Partitioning Trees --
8.4. Portal Systems --
8.4.1. Portal Clipping --
8.4.2. Reduced View Frustums --
ch. 8 Summary --
Exercises for Chapter 8 --
ch. 9 Polygonal Techniques --
9.1. Depth Value Offset --
9.1.1. Projection Matrix Modification --
9.1.2. Offset Value Selection --
9.1.3. Implementation --
9.2. Decal Application --
9.2.1. Decal Mesh Construction --
9.2.2. Polygon Clipping --
9.3. Billboarding --
9.3.1. Unconstrained Quads --
9.3.2. Constrained Quads --
9.3.3. Polyboards --
9.4. Polygon Reduction --
9.5. T-Junction Elimination --
9.6. Triangulation --
ch. 9 Summary --
Exercises for Chapter 9 --
ch. 10 Shadows --
10.1. Shadow Casting Set --
10.2. Shadow Mapping --
10.2.1. Rendering the Shadow Map --
10.2.2. Rendering the Main Scene --
10.2.3. Self-Shadowing --
10.3. Stencil Shadows --
10.3.1. Algorithm Overview --
10.3.2. Infinite View Frustums --
10.3.3. Silhouette Determination --
10.3.4. Shadow Volume Construction --
10.3.5. Determining Cap Necessity --
10.3.6. Rendering Shadow Volumes --
10.3.7. Scissor Optimization --
ch. 10 Summary --
Exercises for Chapter 10 --
ch. 11 Curves and Surfaces --
11.1. Cubic Curves --
11.2. Hermite Curves --
11.3. Bezier Curves --
11.3.1. Cubic Bezier Curves --
11.3.2. Bezier Curve Truncation --
11.3.3. de Casteljau Algorithm --
11.4. Catmull-Rom Splines --
11.5. Cubic Splines --
11.6. B-Splines --
11.6.1. Uniform B-Splines --
11.6.2. B-Spline Globalization --
11.6.3. Nonuniform B-Splines --
11.6.4. NURBS --
11.7. Bicubic Surfaces --
11.8. Curvature and Torsion --
ch. 11 Summary --
Exercises for Chapter 11 --
ch. 12 Collision Detection --
12.1. Plane Collisions --
12.1.1. Collision of a Sphere and a Plane --
12.1.2. Collision of a Box and a Plane --
12.1.3. Spatial Partitioning --
12.2. General Sphere Collisions --
12.3. Sliding --
12.4. Collision of Two Spheres --
ch. 12 Summary --
Exercises for Chapter 12 --
ch. 13 Linear Physics --
13.1. Position Functions --
13.2. Second-Order Differential Equations --
13.2.1. Homogeneous Equations --
13.2.2. Nonhomogeneous Equations --
13.2.3. Initial Conditions --
13.3. Projectile Motion --
13.4. Resisted Motion --
13.5. Friction --
ch. 13 Summary --
Exercises for Chapter 13 --
ch. 14 Rotational Physics --
14.1. Rotating Environments --
14.1.1. Angular Velocity --
14.1.2. Centrifugal Force --
14.1.3. Coriolis Force --
14.2. Rigid Body Motion --
14.2.1. Center of Mass --
14.2.2. Angular Momentum and Torque --
14.2.3. Inertia Tensor --
14.2.4. Principal Axes of Inertia --
14.2.5. Transforming the Inertia Tensor --
14.3. Oscillatory Motion --
14.3.1. Spring Motion --
14.3.2. Pendulum Motion --
ch. 14 Summary --
Exercises for Chapter 14 --
ch. 15 Fluid and Cloth Simulation --
15.1. Fluid Simulation --
15.1.1. Wave Equation --
15.1.2. Approximating Derivatives --
15.1.3. Evaluating Surface Displacement --
15.1.4. Implementation --
15.2. Cloth Simulation --
15.2.1. Spring System --
15.2.2. External Forces --
15.2.3. Implementation --
ch. 15 Summary --
Exercises for Chapter 15 --
ch. 16 Numerical Methods --
16.1. Trigonometric Functions --
16.2. Linear Systems --
16.2.1. Triangular Systems --
16.2.2. Gaussian Elimination --
16.2.3. LU Decomposition --
16.2.4. Error Reduction --
16.2.5. Tridiagonal Systems --
16.3. Eigenvalues and Eigenvectors --
16.4. Ordinary Differential Equations --
16.4.1. Euler's Method --
16.4.2. Taylor Series Method --
16.4.3. Runge-Kutta Method --
16.4.4. Higher-Order Differential Equations --
ch. 16 Summary --
Exercises for Chapter 16 --
Appendix A Complex Numbers --
A.1. Definition --
A.2. Addition and Multiplication --
A.3. Conjugates and Inverses --
A.4. Euler Formula --
Appendix B Trigonometry Reference --
B.1. Function Definitions --
B.2. Symmetry and Phase Shifts --
B.3. Pythagorean Identities --
B.4. Exponential Identities --
B.5. Inverse Functions --
B.6. Laws of Sines and Cosines --
Appendix C Coordinate Systems --
C.1. Cartesian Coordinates --
C.2. Cylindrical Coordinates --
C.3. Spherical Coordinates --
C.4. Generalized Coordinates --
Appendix D Taylor Series --
D.1. Derivation --
D.2. Power Series --
D.3. Euler Formula --
Appendix E Answers to Exercises --
Chapter 2 --
Chapter 3 --
Chapter 4 --
Chapter 5 --
Chapter 6 --
Chapter 7 --
Chapter 8 --
Chapter 9 --
Chapter 10 --
Chapter 11 --
Chapter 12 --
Chapter 13 --
Chapter 14 --
Chapter 15 --
Chapter 16.
| Item type | Current library | Collection | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|
Books
|
Main library B10 | Computers & Information Technology ( Digital Media Tech. ) | 794.81526 L.E.M (Browse shelf(Opens below)) | Available | 00010393 |
Browsing Main library shelves, Shelving location: B10 Close shelf browser (Hides shelf browser)
| 794.81526 H.J.G Game programming all in one / | 794.81526 H.J.G Game programming all in one / | 794.81526 I.K.G Game usability : advice from the experts for advancing the player experience / | 794.81526 L.E.M Mathematics for 3D game programming and computer graphics / | 794.81526 M.J.B Beginning scripting through game creation / | 794.81526 R.G.M Macromedia Flash professional 8 game development / | 794.81526 S.A.G Game graphics programming / |
Includes index.
Machine generated contents note: ch. 1 Rendering Pipeline --
1.1. Graphics Processors --
1.2. Vertex Transformation --
1.3. Rasterization and Fragment Operations --
ch. 2 Vectors --
2.1. Vector Properties --
2.2. Dot Product --
2.3. Cross Product --
2.4. Vector Spaces --
ch. 2 Summary --
Exercises for Chapter 2 --
ch. 3 Matrices --
3.1. Matrix Properties --
3.2. Linear Systems --
3.3. Matrix Inverses --
3.4. Determinants --
3.5. Eigenvalues and Eigenvectors --
3.6. Diagonalization --
ch. 3 Summary --
Exercises for Chapter 3 --
ch. 4 Transforms --
4.1. Linear Transformations --
4.1.1. Orthogonal Matrices --
4.1.2. Handedness --
4.2. Scaling Transforms --
4.3. Rotation Transforms --
4.3.1. Rotation About an Arbitrary Axis --
4.4. Homogeneous Coordinates --
4.4.1. Four-Dimensional Transforms --
4.4.2. Points and Directions --
4.4.3. Geometrical Interpretation of the w Coordinate --
4.5. Transforming Normal Vectors --
4.6. Quaternions --
4.6.1. Quaternion Mathematics --
4.6.2. Rotations with Quaternions --
4.6.3. Spherical Linear Interpolation --
ch. 4 Summary --
Exercises for Chapter 4 --
ch. 5 Geometry for 3D Engines --
5.1. Lines in 3D Space --
5.1.1. Distance Between a Point and a Line --
5.1.2. Distance Between Two Lines --
5.2. Planes in 3D Space --
5.2.1. Intersection of a Line and a Plane --
5.2.2. Intersection of Three Planes --
5.2.3. Transforming Planes --
5.3. View Frustum --
5.3.1. Field of View --
5.3.2. Frustum Planes --
5.4. Perspective-Correct Interpolation --
5.4.1. Depth Interpolation --
5.4.2. Vertex Attribute Interpolation --
5.5. Projections --
5.5.1. Perspective Projections --
5.5.2. Orthographic Projections --
5.5.3. Extracting Frustum Planes --
5.6. Reflections and Oblique Clipping --
ch. 5 Summary --
Exercises for Chapter 5 --
ch. 6 Ray Tracing --
6.1. Root Finding --
6.1.1. Quadratic Polynomials --
6.1.2. Cubic Polynomials --
6.1.3. Quartic Polynomials --
6.1.4. Newton's Method --
6.1.5. Refinement of Reciprocals and Square Roots --
6.2. Surface Intersections --
6.2.1. Intersection of a Ray and a Triangle --
6.2.2. Intersection of a Ray and a Box --
6.2.3. Intersection of a Ray and a Sphere --
6.2.4. Intersection of a Ray and a Cylinder --
6.2.5. Intersection of a Ray and a Torus --
6.3. Normal Vector Calculation --
6.4. Reflection and Refraction Vectors --
6.4.1. Reflection Vector Calculation --
6.4.2. Refraction Vector Calculation --
ch. 6 Summary --
Exercises for Chapter 6 --
ch. 7 Lighting and Shading --
7.1. RGB Color --
7.2. Light Sources --
7.2.1. Ambient Light --
7.2.2. Directional Light Sources --
7.2.3. Point Light Sources --
7.2.4. Spot Light Sources --
7.3. Diffuse Reflection --
7.4. Specular Reflection --
7.5. Texture Mapping --
7.5.1. Standard Texture Maps --
7.5.2. Projective Texture Maps --
7.5.3. Cube Texture Maps --
7.5.4. Filtering and Mipmaps --
7.6. Emission --
7.7. Shading Models --
7.7.1. Calculating Normal Vectors --
7.7.2. Gouraud Shading --
7.7.3. Blinn-Phong Shading --
7.8. Bump Mapping --
7.8.1. Bump Map Construction --
7.8.2. Tangent Space --
7.8.3. Calculating Tangent Vectors --
7.8.4. Implementation --
7.9. Physical Reflection Model --
7.9.1. Bidirectional Reflectance Distribution Functions --
7.9.2. Cook-Torrance Illumination --
7.9.3. Fresnel Factor --
7.9.4. Microfacet Distribution Function --
7.9.5. Geometrical Attenuation Factor --
7.9.6. Implementation --
ch. 7 Summary --
Exercises for Chapter 7 --
ch. 8 Visibility Determination --
8.1. Bounding Volume Construction --
8.1.1. Principal Component Analysis --
8.1.2. Bounding Box Construction --
8.1.3. Bounding Sphere Construction --
8.1.4. Bounding Ellipsoid Construction --
8.1.5. Bounding Cylinder Construction --
8.2. Bounding Volume Tests --
8.2.1. Bounding Sphere Test --
8.2.2. Bounding Ellipsoid Test --
8.2.3. Bounding Cylinder Test --
8.2.4. Bounding Box Test --
8.3. Spatial Partitioning --
8.3.1. Octrees --
8.3.2. Binary Space Partitioning Trees --
8.4. Portal Systems --
8.4.1. Portal Clipping --
8.4.2. Reduced View Frustums --
ch. 8 Summary --
Exercises for Chapter 8 --
ch. 9 Polygonal Techniques --
9.1. Depth Value Offset --
9.1.1. Projection Matrix Modification --
9.1.2. Offset Value Selection --
9.1.3. Implementation --
9.2. Decal Application --
9.2.1. Decal Mesh Construction --
9.2.2. Polygon Clipping --
9.3. Billboarding --
9.3.1. Unconstrained Quads --
9.3.2. Constrained Quads --
9.3.3. Polyboards --
9.4. Polygon Reduction --
9.5. T-Junction Elimination --
9.6. Triangulation --
ch. 9 Summary --
Exercises for Chapter 9 --
ch. 10 Shadows --
10.1. Shadow Casting Set --
10.2. Shadow Mapping --
10.2.1. Rendering the Shadow Map --
10.2.2. Rendering the Main Scene --
10.2.3. Self-Shadowing --
10.3. Stencil Shadows --
10.3.1. Algorithm Overview --
10.3.2. Infinite View Frustums --
10.3.3. Silhouette Determination --
10.3.4. Shadow Volume Construction --
10.3.5. Determining Cap Necessity --
10.3.6. Rendering Shadow Volumes --
10.3.7. Scissor Optimization --
ch. 10 Summary --
Exercises for Chapter 10 --
ch. 11 Curves and Surfaces --
11.1. Cubic Curves --
11.2. Hermite Curves --
11.3. Bezier Curves --
11.3.1. Cubic Bezier Curves --
11.3.2. Bezier Curve Truncation --
11.3.3. de Casteljau Algorithm --
11.4. Catmull-Rom Splines --
11.5. Cubic Splines --
11.6. B-Splines --
11.6.1. Uniform B-Splines --
11.6.2. B-Spline Globalization --
11.6.3. Nonuniform B-Splines --
11.6.4. NURBS --
11.7. Bicubic Surfaces --
11.8. Curvature and Torsion --
ch. 11 Summary --
Exercises for Chapter 11 --
ch. 12 Collision Detection --
12.1. Plane Collisions --
12.1.1. Collision of a Sphere and a Plane --
12.1.2. Collision of a Box and a Plane --
12.1.3. Spatial Partitioning --
12.2. General Sphere Collisions --
12.3. Sliding --
12.4. Collision of Two Spheres --
ch. 12 Summary --
Exercises for Chapter 12 --
ch. 13 Linear Physics --
13.1. Position Functions --
13.2. Second-Order Differential Equations --
13.2.1. Homogeneous Equations --
13.2.2. Nonhomogeneous Equations --
13.2.3. Initial Conditions --
13.3. Projectile Motion --
13.4. Resisted Motion --
13.5. Friction --
ch. 13 Summary --
Exercises for Chapter 13 --
ch. 14 Rotational Physics --
14.1. Rotating Environments --
14.1.1. Angular Velocity --
14.1.2. Centrifugal Force --
14.1.3. Coriolis Force --
14.2. Rigid Body Motion --
14.2.1. Center of Mass --
14.2.2. Angular Momentum and Torque --
14.2.3. Inertia Tensor --
14.2.4. Principal Axes of Inertia --
14.2.5. Transforming the Inertia Tensor --
14.3. Oscillatory Motion --
14.3.1. Spring Motion --
14.3.2. Pendulum Motion --
ch. 14 Summary --
Exercises for Chapter 14 --
ch. 15 Fluid and Cloth Simulation --
15.1. Fluid Simulation --
15.1.1. Wave Equation --
15.1.2. Approximating Derivatives --
15.1.3. Evaluating Surface Displacement --
15.1.4. Implementation --
15.2. Cloth Simulation --
15.2.1. Spring System --
15.2.2. External Forces --
15.2.3. Implementation --
ch. 15 Summary --
Exercises for Chapter 15 --
ch. 16 Numerical Methods --
16.1. Trigonometric Functions --
16.2. Linear Systems --
16.2.1. Triangular Systems --
16.2.2. Gaussian Elimination --
16.2.3. LU Decomposition --
16.2.4. Error Reduction --
16.2.5. Tridiagonal Systems --
16.3. Eigenvalues and Eigenvectors --
16.4. Ordinary Differential Equations --
16.4.1. Euler's Method --
16.4.2. Taylor Series Method --
16.4.3. Runge-Kutta Method --
16.4.4. Higher-Order Differential Equations --
ch. 16 Summary --
Exercises for Chapter 16 --
Appendix A Complex Numbers --
A.1. Definition --
A.2. Addition and Multiplication --
A.3. Conjugates and Inverses --
A.4. Euler Formula --
Appendix B Trigonometry Reference --
B.1. Function Definitions --
B.2. Symmetry and Phase Shifts --
B.3. Pythagorean Identities --
B.4. Exponential Identities --
B.5. Inverse Functions --
B.6. Laws of Sines and Cosines --
Appendix C Coordinate Systems --
C.1. Cartesian Coordinates --
C.2. Cylindrical Coordinates --
C.3. Spherical Coordinates --
C.4. Generalized Coordinates --
Appendix D Taylor Series --
D.1. Derivation --
D.2. Power Series --
D.3. Euler Formula --
Appendix E Answers to Exercises --
Chapter 2 --
Chapter 3 --
Chapter 4 --
Chapter 5 --
Chapter 6 --
Chapter 7 --
Chapter 8 --
Chapter 9 --
Chapter 10 --
Chapter 11 --
Chapter 12 --
Chapter 13 --
Chapter 14 --
Chapter 15 --
Chapter 16.
Mathematics for 3D game programming and computer graphics, third edition, illustrates the mathematical concepts that a game developer needs to develop 3D computer graphics and game engines at the professional level.
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