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Abstract. We prove an O(n(k+1)1/3) upper bound for planar k -sets. This is the first considerable improvement on this bound after its early solution approximately 27 years ago. Our proof technique… Expand
Surface reconstruction from unorganized sample points is an important problem in computer graphics, computer aided design, medical imaging and solid modeling. Recently a few algorithms have been… Expand
Many applications in geometric modeling, computer graphics, visualization and computer vision benefit from a reduced representation called curve-skeletons of a shape. These are curves possibly with… Expand
The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm1 using the… Expand
We present an algorithm that provably reconstructs a curve in the framework introduced by Amenta, Bern and Eppstein. The highlights of the algorithm are: (i) it is simple, (ii) it requires a sampling… Expand
Medial axis as a compact representation of shapes has evolved as an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis… Expand
We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles… Expand
Chapman and Hall / CRC computer and information…
Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging… Expand
Geometric shapes are identified with their features. For computational purposes a concrete mathematical definition of features is required. In this paper we use a topological approach, namely… Expand
Abstract
The medial axis of a surface in 3D is the closure of all points that
have two or more closest points on the surface.
It is an essential geometric structure in a number of applications… Expand