A 2D Advancing-Front Delaunay Mesh Refinement Algorithm

by   Shankar Prasad Sastry, et al.

I present a generalization of Chew's first algorithm for Delaunay mesh refinement. In his algorithm, Chew splits the line segments of the input planar straight line graph (PSLG) into shorter subsegments whose lengths are nearly identical. The constrained Delaunay triangulation of the subsegments is refined based on the length of the radii of the circumcircles of the triangles. This algorithm produces a uniform mesh, whose minimum angle can be at most π/6. My algorithm generates both truly Delaunay and constrained Delaunay size-optimal meshes. In my algorithm, I split the line segments of the input PSLG such that their lengths are asymptotically proportional to the local feature size (LFS) by solving ordinary differential equations (ODEs) that map points from a closed 1D interval to points on the input line segments in the PSLG. I then refine the Delaunay triangulation (truly or constrained) of the PSLG by inserting off-center Steiner vertices of "skinny" triangles while prioritizing such triangles with shortest edges first. As in Chew's algorithm, I show that the Steiner vertices do not encroach upon any subsegment of the PSLG. The off-center insertion algorithm places Steiner vertices in an advancing front manner such that we obtain a size-optimal Delaunay mesh (truly or constrained) if the desired minimum angle is less than π/6. In addition, even in the presence of a small angle ϕ < π/2 in the PSLG, the bound on the minimum angle "across" the small angle tends to arctan((sinϕ)/(2-cos(ϕ)) as the PSLG is progressively refined. Also, the bound on the maximum angle across any small input angle tends to π/2 + ϕ/2 as the PSLG is progressively refined.


page 1

page 2

page 3

page 4


A 3D Advancing-Front Delaunay Mesh Refinement Algorithm

I present a 3D advancing-front mesh refinement algorithm that generates ...

Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is...

Graphs with large total angular resolution

The total angular resolution of a straight-line drawing is the minimum a...

Recurrent Neural Networks as Optimal Mesh Refinement Strategies

We show that an optimal finite element mesh refinement algorithm for a p...

Rectangular mesh contour generation algorithm for finite differences calculus

In this work, a 2D contour generation algorithm is proposed for irregula...

On Designing GPU Algorithms with Applications to Mesh Refinement

We present a set of rules to guide the design of GPU algorithms. These r...

Please sign up or login with your details

Forgot password? Click here to reset