Jan 6, 2019- Examples of how Nature uses mathematics to optimize development. In mathematics, a Voronoi diagram is a way of dividing space into a number of regions. The dual to this process is the Delaunay triangulation to maximize the minimum angle of all the angles of the triangles. Each output line is a triple i j k, which are the indices of the three points in a Delaunay triangle. Points are numbered starting at 0. If option -v is present, the Voronoi diagram is produced. Voronoi Delaunay Classical example Boris N. Delaunay (1890-1980) Voronoi Delaunay Classical example Voronoi - geometry Delaunay - topology Boris N. Delaunay (1890-1980) faces of the Voronoi diagram Voronoi. faces of the Voronoi diagram Voronoi. Centroidal Voronoi Tessellation Algorithms for Image Processing (to appear in Journal of Mathematical Imaging and Vision) Given an image u, let U= {u(i,j)} (i,j)?D denote the set of (not necessarily distinct) color values in the original image. Then, for any set of replacement A New Approach to Output-Sensitive Voronoi Diagrams and Delaunay Triangulations Don Sheehy INRIA Saclay, France Joint work with Gary Miller at CMU. Voronoi k-face Delaunay (d-k)-face. Delaunay triangulations and Voronoi diagrams are projections of polyhedra. Regularized image gradient (Shen-Castan), Manual segmentation, Multivariate Statistical Analysis (MSA), Principal Component Analysis (PCA), 53 plugins, including Alpha Blending, Histogram Equalization, Delaunay_Voronoi (Delaunay/Voronoi diagrams from point selections) This is a short recap of how to draw the Voronoi Diagram using the Delaunay Triangulation system. This is a short recap of how to draw the Voronoi Diagram using the Delaunay Triangulation system. A video generated by a processing.org sketch, which demonstrates: animated Delaunay triangulation and the corresponding dual graph, a Voronoi diagram. Deluanay Triangulation & Voronoi Diagram Delaunay Triangulation and Voronoi Diagrams (withmateria