A k ey step in the nite element method is to generate well-shaped meshes in 3D. A mesh is well-shaped if every tetrahedron element has a small aspect ratio. It is an old outstanding problem to generate well-shaped Delaunay meshes in three or more dimensions. Existing algorithms do not completely solve this problem, primarily because they can not eliminate all slivers. A sliver is a tetrahedron ...

We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on δ-generic point sets, we establish sampling criteria which ensure that the intrinsic Delaunay complex coincides with the restricted Delaunay complex and also with the recently in...

We consider a new construction, the weak Delaunay triangulation of a finite point set in a metric space, which contains as a subcomplex the traditional (strong) Delaunay triangulation. The two simplicial complexes turn out to be equal for point sets in Euclidean space, as well as in the (hemi)sphere, hyperbolic space, and certain other geometries. There are weighted and approximate versions of ...

We show that any planar PSLG with n vertices has a conforming triangulation by O(n) nonobtuse triangles, answering the question of whether a polynomial bound exists. The triangles may be chosen to be all acute or all right. A nonobtuse triangulation is Delaunay, so this result improves a previous O(n) bound of Eldesbrunner and Tan for conforming Delaunay triangulations. In the special case that...

The traditional image matching algorithms adopt more complex strategies when dealing with mismatch caused by a lot of noise. In this paper, a simple, intuitive and effective noise processing algorithm is proposed based on Delaunay triangulation in computational geometry. The algorithm extracts feature points using SIFT method, respectively establishes Delaunay triangulation in multi-spectral an...

Computing the Delaunay triangulation of n points requires usually a minimum of (n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time.

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay trian...