Projective Geometry and Transformations of 2D
Planar Geometry
2D Projective Plane
Homegeneous representation of points and lines
Ideal points and the line at infinity
Conics and dual conics
Projective Transformation
Transformations of lines and conies
A hierarchy of transformations
Class I: Isometries
Class II: Similarity transformations
Class III: Affine transformations
Class IV: Projective transformations
Comparison
Decomposition of projective transformation
Number of invariants
Projective Geometry of 1D
Topology of projective planes
Recovery of affine transformation
Angles on the projective plane
Properties of Conics
The pole-polar relationship
Affine classification of conics
Fixed points and lines