Transformation

Model Transformation

2D transformations

• Scale
• Reflection
• Shear
• Rotate
• Inverse
• Affine Transformations
• Screen resolution

3D transformations

• Rodrigues’ Rotation Formula

View / Camera Transformation

Projection Transformation

• Orthographic
• Perspective

Viewport Transformation

Rasterization

Scanning conversion algorithms

Line

DDA

Bresenham

Polygon

X-Scan line

Active Edge Table Algorithm（AET）

Circle

Bresenham

Positive and negative method

Polygon proximity

Area-filling algorithm

Simple seed filling Algorithm

Scan line seed filling Algorithm

Clip Algorithm

Line

Cohen-Sutherland

Midpoint Displacement

Liang-Barsky

Polygon

Sutherland-Hodgman

Weiler-Atherton

Antialiasing

Aliasing

• Jaggies
• Moire
• Wagon wheel effect

Filtering

• Blurring
• Fourier Transform

Sampling

MSAA (Multisample Antialiasing)

FXAA (Fast Approximate Antialiasing)

TAA (Temporal Antialiasing)

Visibility / occlusion

Painter’s Algorithm

Z-Buffer Algorithm

Shading

Blinn-Phong Reflectance Model

Diffuse reflection

Specular highlights

Ambient lighting

Shading Frequencies

flat shading (Face)

Gouraud shading (Vertex)

Phong shading (Pixel)

Barycentric interpolation

Texture Mapping

Barycentric Coordinates

Texture Magnification

Bilinear Interpolation

Bicubic interpolation

Texture Minification

Mipmap

Trilinear Interpolation

Anisotropic Filtering

Ripmap

EWA filtering

Applications of Textures

Environment Map

Bump / Normal mapping

Displacement mapping

3D Procedural Noise

Geometry

Curves

Bezier curves

De Casteljau’s algorithm

Properties

• Interpolates endpoints
• Tangent to end segments
• Affine transformation property
• Convex hull property

Piecewise Bézier Curves

B-splines

Surfaces

Bezier surfaces

Triangles & quads

Subdivision

Loop Subdivision

Catmull-Clark Subdivision

simplification

Collapsing An Edge

• Quadric Error Metrics

regularization

Ray Tracing

Shadow Mapping

• Hard shadows vs. soft shadows

Whitted-Style Ray Tracing

Bounding Volumes

Axis-Aligned Bounding Box (AABB)

Spatial Partitions

• Oct-Tree
• KD-Tree
• BSP-Tree

Bounding Volume Hierarchy（BVH）

Object Partitions

Radiometry

Radiant Intensity

• 单位立体角上的能量

Irradiance

• 单位面积上的能量

Radiance

• 单位立体角上单位投影面积的能量

Bidirectional Reflectance Distribution Function (BRDF)

The Reflection Equation

The Rendering Equation

Path Tracing

Monte Carlo Integration

Russian Roulette (RR)

Materials and Appearances

Diffuse / Lambertian Material

Glossy material

Ideal reflective / refractive material

• Law of Refraction
• Fresnel Reflection / Term

Microfacet Material

• Microfacet Theory

Isotropic / Anisotropic Materials

Advanced Light Transport

Unbiased light transport methods

Bidirectional path tracing (BDPT)

Metropolis light transport (MLT)

Biased light transport methods

Photon mapping

Vertex connection and merging (VCM)

Instant Radiosity (IR)

Advanced Appearance Modeling

Non-surface models

Participating media

Hair / fur / fiber (BCSDF)

Granular material

Surface models

Translucent material (BSSRDF)

Subsurface Scattering

Cloth

Detailed material (non-statistical BRDF)

Procedural appearance

• Thresholding (noise -> binary noise)

Animation and Simulation

Physically Based Animation

• Cloth
• Fluids
• Mass Spring System

Rigging

Motion Capture

Single Particle Simulation

Euler’s Method

• Errors
• Instability

Midpoint method / Modified Euler

Adaptive step size

Implicit methods

Runge-Kutta Families

Position-based / Verlet integration

Rigid body simulation

Fluid simulation