triangulation_refine_local, an Octave code which tries to locally refine a triangulation by replacing one triangular element by four smaller ones.
The refinement process introduces three new nodes, at the midsides of the original element. This, in turn, will create what is called "hanging nodes" on the neighboring elements, an undesirable feature. Therefore, each hanging node is used to divide the neighboring element into two new elements. This removes the hanging node problem.
Information about the triangulation is updated. In particular, the coordinates of the three new nodes are assigned indexes, and added to the node coordinate array. Four old elements are replaced by 10 new, smaller ones. This requires modifications to the element-node array and to the element-neighbor array.
This process of refinement does not take into account the shape of the new elements. The refinement process could create a new triangulation which no longer has the Delaunay property. If this is a concern, then a simple expedient is to retriangulate the nodes.
The program presented here presumed the triangulation involves order 3 elements, that the element-node array lists the nodes in counter-clockwise order, and that the element neighbor array indexes the element neighbors by the element node that is opposite to them. If any of these assumptions do not hold for the given data, the calculation will need to be modified.
The information on this web page is distributed under the MIT license.
triangulation_refine_local is available in a MATLAB version and an Octave version.
triangulation_refine_local_test
triangulation, an Octave code which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.
triangulation_boundary_edges, an Octave code which reads data defining a triangulation, determines which edges lie on the boundary, organizes them into connected components, and writes this information to a file.
triangulation_boundary_nodes, an Octave code which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.
triangulation_corner, an Octave code which patches triangulations so that no triangle has two sides on the boundary.
triangulation_delaunay_discrepancy, an Octave code which measures the amount by which a triangulation fails the local delaunay test;
triangulation_display, an Octave code which displays the nodes and elements of a triangulation on the MATLAB graphics screen;
triangulation_order3, a data directory which contains a description and examples of order 3 triangulations.
triangulation_orient, an Octave code which reads data defining a triangulation, makes sure that every triangle has positive orientation, and if not, writes a corrected triangle file.
triangulation_plot, an Octave code which reads data defining a triangulation and creates a postscript image of the nodes and triangles.
triangulation_quality, an Octave code which reads data defining a triangulation and computes a number of quality measures.
triangulation_refine, an Octave code which refines a triangulation.
triangulation_triangle_neighbors, an Octave code which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.