Simplicial Maps and Approximations
- The simplicial property refers to the behavior of a map (in our
case, the Nyquist map) relative to triangulations of both the domain
of definition, assuming it is a polyhedron, and the image, properly
embedded in a polyhedron
- We use the Q-triangulation to decompose the domain of definition
into simplexes
- We fast compute the triangulation of the image points, by first
computing the Voronoi Diagram associated with them. With the Voronoi
Diagram computed, we easily generate its dual, the Delaunay Triangulation
- The Nyquist map will be simplicial if and only if every simplex of
the domain is mapped to a simplex in the image
- Following is the formal definition of the Simplicial Approximation
Theorem
