GH: CS 112 - Computer Graphics

Topology is the study of continuity and connectivity.

• Manifold: made up of 1-2 triangles(2D)/tetrahedrons (3D)
  
• Dimensions
• (1) Euler characteristics (2) Genus
• Orientability
  

Dimensions - # of parameters to change and still be in the object (i.e. dimension 0 for point, b/c cannot change any parameters)
Possibility of EMBEDDED into higher dimensions
Manifolds with boundaries (1 or 2), Manifold (2), Non-Manifolds "need not" be manifold
Triangles - planar, rotationally invariant interpolation of attributes during rasterization
Parametric: P1(1-u) + PU(u) - interpolation

Euler:
e = V-E+F
Euler = Verticies - Edges + Faces

Interpolation: linear combination of points
- coefficients:
- < 1 = within convex hull
- > 1 = outside convex hull

Common Data structures: sequential, index list of vertices, or list of triangles