09-triangulation-in-R.Rmd

# Triangulation in R

Triangulation is available in several R packages, including triangulation by the Delaunay riangulation and/or Voronoi Tesselation, and "Constrained Delaunay" triangulation. 

What is triangulation? 

- not inference from remote signals
- rule for connecting vertices in 2-space (we touch on higher dimensional topology and geometry here, but only briefly)
- Wikipedia "... of a planar object is a subdivision into triangles . . . into simplices."

What is Delaunay triangulation? 

- a Delaunay triangulation satisifies the Delaunay condition that ["that the circumcircles of all triangles have empty interiors"](Wikipedia)
- this is good for interpolation and visulization of physical surfaces

What is Constrained Delaunay triangulation? 

- interestingly this is a triangulation that *does not* satisfy the Delaunay condition, but it aims to be "mostly Delaunay" while including additional rules, such as
- inclusion of input edges
- minimum triangle area
- minimum triangle interior angle
- many other nuances (see Shewchuk)

Where is triangulation used? 

- visualization
- vector fusion
- geometry algorithms
- interpolation
- GIS stuff
- etc. 

## Packages that include Delaunay triangulation for R

tripack?