polygon), along with some extra vertices, called Steiner points. Not all triangulations, however, serve equally well; numerical and discretization error depend on the quality of the triangulation, meaning the shapes and sizes of triangles. A typical quality guarantee gives a lower bound on the minimum

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improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combinations of two or more local transformations to improve a given triangulation towards an optimal triangulation. Experimental results on finite element meshes show that this algorithm is much more effective

algorithm to mesh the macromolecules surface model represented by the skin surface defined by Edelsbrunner. Our algorithm overcomes several challenges residing in current surface meshing methods. First, we guarantee the mesh quality with a provable lower bound of 21 ◦ on its minimum angle. Second, we ensure

The terminal-edge Delaunay algorithm, initially called Lepp-Delaunay algorithm, deals with the construction of size-optimal (adapted to the geometry) quality triangulation of complex objects. In two dimensions, the algorithm can be formulated in terms of the Delaunay insertion of both midpoints

In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high

. The LEPP-Delaunay algorithm for the quality triangulation problem can be formulated in terms of the Delaunay insertion of midpoints of terminal edges (the common longest-edge of a pair of Delaunay triangles) and boundary edges in the current mesh. In this paper we discuss theoretical results

We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality

The quality of a triangulation is, in many practical applications, influenced by the angles of its triangles. In the straight line case, angle optimization is not possible beyond the Delaunay triangulation. We propose and study the concept of circular arc triangulations, a simple and effective

of polygons forming a sweep. We present a method to compute compatible triangulations of planar polygons with a very small number of Steiner (interior) vertices. Being close to optimal in terms of the number of Steiner vertices, these compatible triangulations are usually not of high quality, i.e., do