delaunay

I am implementing the Bowyer-Watson algorithm as presented at Wikipedia . In my implementation, everything works as I would expect up until the last part of the pseudocode: for each triangle in triangulation // done inserting points, now clean up if triangle contains a vertex from original super-triangle remove triangle from triangulation If I follow the pseudocode here literally, I can end up with missing triangles in my Delaunay triangulation. As an example, please consider the images below. The sites I am triangulating are rendered as blue circles. The triangles are rendered with black

I have data in the form (x, y, z) where x and y are not on a regular grid. I wish to display a 2D colormap of these data, with intensity (say, grey scale) mapped to the z variable. An obvious solution is to interpolate (see below) on a regular grid, d <- data.frame(x=runif(1e3, 0, 30), y=runif(1e3, 0, 30)) d$z = (d$x - 15)^2 + (d$y - 15)^2 library(akima) d2 <- with(d, interp(x, y, z, xo=seq(0, 30, length = 30), yo=seq(0, 30, length = 50), duplicate="mean")) pal1 <- grey(seq(0,1,leng=500)) with(d2, image(sort(x), sort(y), z, useRaster=TRUE, col = pal1)) points(d$x, d$y, col="white", bg=grey(d$z

I am computing the 2D delaunay triangulation of a few thousand points. Each point has more data associated with it beyond x and y coordinates. Therefore, I was wondering if it is possible to retrieve the index of each point so that I can access my own point struct in another vector. Currently, as I access vertices from a Face_handle, it returns a point (i.e. x,y coordinates) How can I return each vertex by its ID (index) instead of its x,y coordinates? Thank you. #include <vector> #include <CGAL/Exact_predicates_inexact_constructions_kernel.h> #include <CGAL/Delaunay_triangulation_2.h> typedef

I'm working on a game where I create a random map of provinces (a la Risk or Diplomacy). To create that map, I'm first generating a series of semi-random points, then figuring the Delaunay triangulations of those points. With that done, I am now looking to create a Voronoi diagram of the points to serve as a starting point for the province borders. My data at this point (no pun intended) consists of the original series of points and a collection of the Delaunay triangles. I've seen a number of ways to do this on the web, but most of them are tied up with how the Delaunay was derived. I'd love