CDTGenerator

This project is a C++ implementation of the paper "Meshing piecewise linear complex using CDT" by Hang Si et. al for generating Constrained Delaunay tetrahedralization for a given domain specified using set of points and constraint polygons.

Building

Following sequence of commands work on Ubuntu 14.04 LTS(64-bit):
mkdir build
cd build
cmake ..
make
Currently, it only builds the segment recovery module along with unit tests.

Dependencies

It atleast works with following versions of dependencies:

• CMake(>=2.8.12)
• CGAL(4.6)
• gtest(1.7.0)[optional, please see GTEST_ON switch in CMakeLists in root directory]
• gcc-4.8

Extension

Main objective is to extend this implementation to support adaptive Constrained Delaunay tetrahedralization for 3D domain.

TODO:

• Why One_dart_per_incident_cell_range<0, 2> produces segfault here but Dart_of_orbit_range<1> does not?

• Template definition of isInfinite and other such functions.

• Adding steiner point in PLC and current mesh using edge flipping and combination of edge flipping and face flipping(Refer Si's thesis).

• Search for candidate reference point only in the vertices of tetrahedrons intersecting the missing segment in function computeReferencePoint instead of all points of PLC.

• Replace loop in current definition of sew2CellsFromEdge with efficient alternative so that it can be used for larger domains as well.

• CGAL's Delaunay triangulation deals with cospherical points using symbolic perturbation. How to modify the corresponding PLC accordingly?

• Input should allow for more file options than ply.

• Why g++ -lgmp -lCGAL rply.cpp cdtCode.cpp does not link whereas, g++ rply.cpp cdtCode.cpp -lgmp -lCGAL does? Also there is issue in example usage of -l option given in 'man gcc' :(

• Replace naive code for finding all possible pairs of segments.

• How to remove hardcoded seeds for CGAL random number generator?

• Add termination criteria using local feature size for each vertex.

• Add functionality for Algorithm execution visualization.

• Add function in CGAL fork for iterating vertices of a 2-cell using One_dart_per_incident_cell_range<0, 2> in counterclockwise order. It is useful while writing polygons to data file for visualization.

• Generic sew2CellsFromEdge for both LCC and LCCWithDartInfo.

• How local degeneracy removal alone can guarantee uniqueness of Delaunay triangulation? What if a set of 5 non-local points are cospherical?