Netgen_org.pdf (application/pdf Object) Surface Reconstruction from Point Sets. Authors Pierre Alliez, Laurent Saboret, Gaël Guennebaud This CGAL component implements a surface reconstruction method which takes as input point sets with oriented normals and computes an implicit function.
We assume that the input points contain no outliers and little noise. The output surface mesh is generated by extracting an isosurface of this function with the CGAL Surface Mesh Generator [4] or potentially with any other surface contouring algorithm. Algorithm - Mesh Generation from Points with X, Y and Z Co-Ordinate. COMPUTING CONSTRAINED DELAUNAY TRIANGULATIONS IN THE PLANE. Generating the Delaunay Triangulation To generate the Delaunay triangulation, we chose to implement a "divide and conquer" algorithm presented by Guibas and Stolfi , in: Guibas, L. and Stolfi, J., "Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams", ACM Transactions on Graphics, Vol.4, No.2, April 1985, pages 74-123.
The divide and conquer algorithm only computes the Delaunay triangulation for the convex hull of the point set. The first step is to put all of the points into order of increasing x-coordinates (when two points have the same x-coordinate, their order is determined by their y-coordinates). This set of 10 points has been orderedOnce the points are ordered, the ordered set is successively divided into halves until we are left with subsets containing no more than three points. These subsets may be instantly triangulated as a segment in the case of two points and a triangle in the case of three points.