Why 2D CDT does not require steiner points?

In this post I would like to discuss a proof of the fact that although three dimensional Constrained Delaunay triangulation can be constructued from incremental modification of corresponding Delaunay triangulation, its 2D counter-part does not require such measures. That is,...

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Understanding Jordan Curve Theorem

In this post, I will discuss Jordan Curve Theorem. It is deceptively simple to state:_ Any continous simple curve in the plane, separates the plane into two disjoint regions, the inside and the outside_.

I will first discuss the theorem...

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On Self intersection problem

These days I have been trying to solve the problem of detecting and removing self-intersections from a three-dimensional(3D) polygonal mesh. In this post(or even possibly in the upcoming posts), I will discuss this problem in detail and my ideas to...

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Understanding the symbolic perturbation adopted in CGAL

I am studying a paper by CGAL authors describing their approach to symbolic perturbation technique. This approach has been used in Delaunay_triangulation_3 class to be able to compute unique Delaunay triangulation even in the presence of degneracies in the...

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Why GitHub chose octocat?

One day while browsing whole variety of octocats available in Octodex, my mind started reasoning about why GitHub might have chosen Octocat as their mascot. Octocat is hybrid of cat and octopus, so how does it relate to programming?

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Hash functions for 3D points

I have been trying to implement the solution to 3-cell marking problem that I discussed earlier. In order to avoid duplicate points of intersection while counting number of intersections of a random ray from the barycenter of each tetrahedron...

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Open problems in Tetrahedral mesh generation

As has been the nature of articles listing Open problems in any domain, expect this post to be under construction forever. I want to enter in the field of Tetrahedral mesh generation for which I am gathering the list of...

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Learning Combinatorial Maps

In an attempt to implement Constrained Delaunay tetrahedralization algorithm proposed by Hang Si, the CDTGenerator, I have started to learn about a beautiful concept in topology called Combinatorial Maps. This datastructure can be used to represent orientable subdivided d-dimensional...

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Added new project site

I have now added a new github page for my project on Constrained Delaunay Tetrahedralization. This is an implementation of a paper by Hang Si et. al. “Meshing Piecewise Linear Complexes using CDT”. I have used CGAL extensively in...

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