A study of basic concepts of matrices and vectors. Fundamentals of motion and examination of mathematical concepts that apply to game programming and simulations. Instruction in code optimization.
| Topic |
Approximate Hours |
| Overview |
2 |
Vectors
• Vector properties
• Dot products
• Cross products
• Vector spaces |
3 |
Matrices
• Matrix properties
• Linear systems
• Matrix inverse
• Determinants
• Diagonalization |
3 |
Transforms
• General transforms
• Scaling transforms
• Rotation transforms
• Homogenous coordinates
• Transforming normal vectors
• Quaternion |
6 |
3D Engine Geometry
• Lines in 3D space
• Plane in 3D space
• View Frustum
• Interpolation
• Projection |
6 |
Ray Tracing
• Surface intersections
• Normal vector calculations
• Reflection and refraction vectors |
3 |
llumination
• RBG color
• Light sources
• Diffuse lighting
• Texture mapping
• Specular lighting
• Emission
• Shading
• Bump mapping |
3 |
Visibility Determination
• Bounding volume construction
• Bounding volume test
• Spatial portioning
• Portal systems |
6 |
Collision Detection
• Environmental collision
• Interobject collision |
6 |
Polygonal Techniques
• Depth value offset
• Decal application
• Stencil shadows |
3 |
| Fluid simulation |
4 |
Complex numbers
• Definition
• Addition and multiplication
• Conjugate and inverse |
3 |
| Total (lectures, labs and exams) |
48 |
