Study Guide COMP557 2018 09
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I Introduction
Disclaimer
About This Guide
II Transformations
Notation
Implicit Representation
Explicit (Parametric) Representation
Linear Transformations
Combining Linear Transforms with Translation
Homogeneous Coordinates
Affine Transformations
Rigid Motions
Composing to change axes
Points vs. Vectors
Change of Coordinates
Aside: Classes of transforms
3D Transformations
Rotations in 3D
Euler Angles
Gimbal Lock
Interpolation of Euler Angles
Scene Graphs
Transforms on the Graph
Quaternions
Considerations For Choosing Rotations
Linear Interpolation
Building Rotations
Transforming Normal Vectors
III Viewing and Projection
Image Order and Object Order
Camera Transformation
Lookat Transformation
Orthographic Projection
Orthographic Viewport Transformation
Planar Perspective Projection
Homogeneous Coordinates Revisited
Carrying Depth Through Perspective
OpenGL Transformation Pipeline
Frustum Applications
Projection Taxonomy
Parallel Projection
Orthographic
Oblique
Perspective
Shifted Perspective
Field of View
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