Polyhedron kernel computation using a geometric approach

Fast computation of geometric moments using a symmetric kernel

This paper presents a novel set of geometric moments with symmetric kernel (SGM) obtained using an appropriate transformation of image coordinates. By using this image transformation, the computational complexity of geometric moments (GM) is reduced significantly through the embedded symmetry and separability properties. In addition, it minimizes the numerical instability problem that occurs in...

Skeleton Computation of an Image Using a Geometric Approach

In this work we develop two algorithms to compute the skeleton of a binary 2D image. Both algorithms follow a geometric approach and work directly with the boundary of the image which is an orthogonal polygon (OP). One of these algorithms processes the edges of the polygon while the other one uses its vertices. Compared with a thinning method, the presented algorithms show a good performance. T...

The CGAL Kernel: A Basis for Geometric Computation

Exact Geometric Computation Using Cascading

In this paper we talk about a new efficient numerical approach to deal with inaccuracy when implementing geometric algorithms. Using various floating-point filters together with arbitrary precision packages, we develop an easy-to-use expression compiler called EXPCOMP. EXPCOMP supports all common operations +,−, ·, /,√ . Applying a new semi-static filter, EXPCOMP combines the speed of static fi...

Parallel Volume Computation of Massive Polyhedron Union

We present a parallel implementation of UNION3, an algorithm for computing the volume, surface area, center of mass, or similar properties of a boolean combination of many polyhedra. UNION3 has been implemented on the special case of the union of congruent isothetic cubes, and tested on 100,000,000 cubes. The algorithm uses a volume formula that does not require first computing the explicit uni...