Research

My research fields concentrate on:

• 1. Longest Edge Bisection in 2D and 3D

  2. Triangle/Tetrahedra Mesh Generation

  3. Mesh Refinement algorithms

  4. Discrete Computer Aided Geometric Design

Also past perojects in:

• 5. 3D GIS software for Desktop and Mobile devices

  6. Information systems and Applied Innovation

Some graphical samples of my research:

• Sextuple Representation of an arbitrary tetrahedron. A revolutionary and powerful manner of representing tetrahedral elements. See the paper at ScienceDirect

- Empirical evidence on the non-degeneracy property of the tetrahedral meshes obtained by iterative application of the 8-tetrahedra longest-edge (8T-LE) partition. Sensitivity tests are used to study the non-degeneracy property of refinement. (a) the apex is moved along the vertical axis, (b) the apex is moved along one edge, (c) the apex is moved along a quarter-arc, (d) the apex is moved along the vertical axis away from the supporting face.

The generation graph of the families emerging from the SCLEB of . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

-We have solved the propagation problem in longest-edge refinement. In Longest Edge based partition, LE are progressively bisected and hence all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the initial triangulation. The average propagation zone for each triangle is reduced in each uniform refinement stage, and asymptotically approaches a constant neighbor triangles.

- Algorithm to convert a tri to quad mesh similar to that by Velho (2000). Our method here offers an ‘on the fly’ tri to quad conversion mainly adequate for such applications

that need simultaneously tri/quad meshes under an iterative refinement procedure

- Geometrical Normalized Diagram to study the improvement in shape of triangles generated by iterative application of triangle subdivision. Traceback curves showing antecedents in successive regions: (a) traceback from equilateral triangle apex with antecedents on border curves

and (b) traceback from acute triangles interior to region.

- Coarsening surface meshes by 4 triangle Longest Edge partition. Adaptive quality meshes are resulted from dense point clouds.

- A 2D initial triangle mesh is iteratively refined following the 4 Triangles Longest-Edge partition, where some initial targeted triangles are picked up for the local refinement.

- This is a test problem in which refinement and coarsening techniques are used to simulate an adaptivity problem in a L-shape 3D domain. The criterion for refining or derefining the 3D mesh is based on a simple error indicator who makes a linear singularity to move along a path in the domain.

- A ball-singularity moving across a 3D mesh. The simulated ball penetrates a 3D domain from upper-right side to lower-left corner. 3D Local refinement and derefinement are iteratively performed following the 8 Tetrahedra Longest Edge partition.