Showing papers on "Constrained Delaunay triangulation published in 2021"
TL;DR: In this paper, the authors proposed a generalization of Chew's first algorithm for Delaunay mesh refinement by splitting the line segments of an input planar straight line graph such that the lengths of split segments are asymptotically proportional to the local feature size at their endpoints.
Abstract: I present a generalization of Chew's first algorithm for Delaunay mesh refinement. I split the line segments of an input planar straight line graph (PSLG) such that the lengths of split segments are asymptotically proportional to the local feature size at their endpoints. By employing prior algorithms, I then refine the truly or constrained Delaunay triangulation of the PSLG by inserting off-center Steiner vertices of "skinny" triangles while prioritizing triangles with shortest edges first. This technique inserts Steiner vertices in an advancing front manner such that we obtain a size-optimal, truly or constrained Delaunay mesh if the desired minimum angle is less than 30° (in the absence of small input angles). This is an improvement over prior algorithms that produce size-optimal meshes with minimum angles of about 26.4°and 28.6°for truly and constrained Delaunay meshes, respectively. Even in the presence of small input angles, the upper bound on the maximum angle is an angle strictly greater than 120° (an improvement from about 137°). The lower bound on the minimum angle in the presence of small angles is identical to prior bounds.
5 citations
01 Jan 2021
TL;DR: In this paper, a medial surface mesh in a constrained Delaunay triangulation is constructed to detect the safe marching space of front points, and the distance between front points and the medial surface is computed by walking through tetrahedra in sequence without additional data structures.
Abstract: Boundary layer meshes as an important part of hybrid mesh are often constructed via advancing layer method for CFD fluid simulations. One major difficulty in implementing a robust boundary layer meshing tool is to handle mesh collisions. In this work, the authors propose to enhance the Jump-and-Walk method by constructing a medial surface mesh in a constrained Delaunay triangulation to detect the safe marching space of front points. Medial surface can build a separation wall between adjacent boundary surfaces to prevent the intersection of boundary layer elements, and the computation of the distance between front points and the medial surface can be accelerated by walking through tetrahedra in sequence without additional data structures. A range of tests were performed for several complex configurations to demonstrate the capability of the method.
07 Jun 2021
TL;DR: The restricted constrained Delaunay triangulation (restricted CDT) as mentioned in this paper is a generalization of both the restricted DELA and the constrained DELA, which is the dual of a restricted Voronoi diagram defined on a surface that was extended by topological surgery.
Abstract: We introduce the restricted constrained Delaunay triangulation (restricted CDT), a generalization of both the restricted Delaunay triangulation and the constrained Delaunay triangulation. The restricted CDT is a triangulation of a surface whose edges include a set of user-specified constraining segments. We define the restricted CDT to be the dual of a restricted Voronoi diagram defined on a surface that we have extended by topological surgery. We prove several properties of restricted CDTs, including sampling conditions under which the restricted CDT contains every constraining segment and is homeomorphic to the underlying surface.