In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Many important real-world problems require meshing, that is the approximation of a given geometry by a set of simpler elements such as triangles or quadrilaterals in two dimensions, and tetrahedra or hexahedra in three dimensions. Applications include finite element analysis and computer graphics. This work focuses on the former. A physically-based model of interacting "particles" is introduced to uniformly spread points over a 2-dimensional polygonal domain. The set of points is triangulated to form a triangle mesh. Delaunay triangulation is used because it guarantees a low computational cost and reasonably well-shaped elements. Several particle interaction (repulsion and attraction) models are investigated ranging from Gaussian energy potentials to Laplacian smoothing. Particle population control mechanisms are introduced to make the size of the mesh elements converge to the desired size. In most applications spatial mesh adaptivity is desirable. Triangles should not only adapt in si...

A key 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 whose vertices are almost coplanar and whose circumradius is not much larger than its shortest edge length. We present two new algorithms to generate sliver-free Delaunay meshes. The rst algorithm locally moves the vertices of an almost-good mesh, whose tetrahedra have small circumradius to shortest edge length ratio. We show that the Delaunay triangulation of the perturbed mesh vertices is still almost good. Furthermore, most slivers disappear after a mild perturbation of the mesh vertices. The remaining slivers migrate to the boundary where they can be peeled o or can be treated with boundary enforcement heuristics. The second algorithm adds points to generate well-shaped meshes. It is based on the following observations. Any tetrahedron will disappear from the Delaunay triangulation if a point is added inside the circumsphere of the tetrahedron. Among the tetrahedra created by

Abstract. When drawing graphs whose nodes contain text or graphics, the non-trivial node sizes must be taken into account, either as part of the initial layout or as a post-processing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using little additional area. This paper presents a new node overlap removal algorithm that does well by these measures. 1

A functional language to implement

Abstract—L-system is a tool commonly used for modeling and simulating the growth of fractal plants. The aim of this paper is to join some problems of the computational geometry with the fractal geometry by using the L-system technique to generate fractal plant in 3D. L-system constructs the fractal structure by applying rewriting rules sequentially and this technique depends on recursion process with large number of iterations to get different shapes of 3D fractal plants. Instead, it was reiterated a specific number of iterations up to three iterations. The vertices generated from the last stage of the L-system rewriting process are used as input to the triangulation algorithm to construct the triangulation shape of these vertices. The resulting shapes can be used as covers for the architectural objects and in different computer graphics fields. The paper presents a gallery of triangulation forms which application in architecture creates an alternative for domes and other traditional types of roofs. Keywords—Computational geometry, Fractal geometry, L-system, Triangulation.