Rajaditya Mukherjee

Rajaditya Mukherjee

raj [at] rajaditya [dot] com  •  Resume  •   Github  •   LinkedIn

I'm a PhD candidate in the Department of Computer Science and Engineering at The Ohio State University, working with Prof. Huamin Wang. My research focuses on physically based simulation and object modelling.
NEWS
  • Passed my PhD Candidacy Examination.
  • Paper accepted at Pacific Graphics 2016.
  • Interned in Walt Disney Animation Studios at Burbank CA.

 

 

THEORY

 

A triangulation of a set of point is defined as a maximal planar subdivision whose vertex set is same as the point set. A Delaunay Triangulation is one such triangulation but with the special property that no point in the point set is inside the circumcenter of any of the triangles of the triangulation. Delaunay triangles have a special property that they tend to maximize the minimum angles of all the triangles in the triangulation and so they tend to avoid skinny triangles. This property makes it useful for a bunch of applications in reconstruction and sampling of point clouds, etc.

Bezier curves and B-Splines are some of the most fundamental types of curves used in geometric modelling. Their usage is widespread.

 

IMPLEMENTATION

 

I have used the incremental algorithm of Bowyer-Watson for Delaunay Triangulation. You can read more details about this algorithm in here.

I have used the deCasteljau subdivision algorithm for Bezier Curve. You can read more details about this algorithm in here.

Standard Matrix based multiplication was used for the generation of the uniform Cubic B-Spline curve..

For drawing the figures on your webbrowser, I have used the Canvas Element in HTML5 standard. For all the buttons and everything, I have used the default button class and alert notifications available in Bootstrap. Also the event handlers for mouse is using JQuery Cross-browser Javascript Library.

 

RESULTS

 

 

 

 

 

 

Number of Points :

Usage is very simple. Just click on the Canvas area to select the points. Then press the appropriate button to get the triangulation. I am still trying to iron out some possible issues with the implementation so you may have some problems when you are using points that are nearly collinear. Hope I can resolve this issue soon.