Alex Rand

Research

Software

Teaching

Papers

• Alexander Rand and Noel Walkington.
  Collars and Intestines: Practical Conforming Delaunay Refinement.
  To appear in the Proceedings of the 18th International Meshing Roundtable, 2009.
  An extended version containing proofs of the theorems can be found here.


• Alexander Rand and Noel Walkington.
  Delaunay Refinement Algorithms for Estimating Local Feature Size
  Submitted, 2009.


• Alexander Rand.
  Delaunay Refinement Algorithms for Numerical Methods.
  Carnegie Mellon University Ph.D. thesis, 2009.


• Alexander Rand and Noel Walkington.
  3D Delaunay Refinement of Sharp Domains Without a Local Feature Size Oracle.
  In the Proceedings of the 17th International Meshing Roundtable, 2008.


• Alexander Rand.
  Reordering Ruppert's Algorithm.
  18th Fall Workshop on Computational Geometry, 2008.
  An extended version containing proofs of the theorems can be found here.


• Maria Emelianenko, Lili Ju, and Alexander Rand.
  Nondegeneracy and Weak Global Convergence of the Lloyd Algorithm in $R^d$.
  SIAM Journal on Numerical Analysis. 46(3): 1423-1441, 2008.

Media

Here are some videos of some 3D meshes generated by the algorithm described in the IMR paper listed above.



Here are some examples of Ruppert's algorithm on simple 2D input, contrasted with a reordered approach which prioritizes mesh quality over mesh conformity.