A polygonal domain P with n corners V and h holes is a connected polygonal region of genus h whose boundary consists of h + 1 closed chains of n total line segments. The holes and the outer boundary of P are regarded as obstacles. Then, the geodesic distance d(p, q) between any two points p, q in polygonal domain P is defined to be the (Euclidean) length of a shortest obstacle-avoiding path bet...

This paper describes a new spline formulation that supports deformation of polygonal shapes into smooth spline surface models. Once a polygonal shape with underlying rectangular topology is specified by the user, it is deformed into a smooth surface that interpolates all the polygonal vertices. The user can then modify the default smooth surface by increasing or decreasing the amount of deforma...

We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n ) for any > 0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(n log n)-time algorithm is known by Pollack et al. ...

In this paper we present a novel method to compute Boolean operations on polygonal meshes. Given a Boolean expression over an arbitrary number of input meshes we reliably and efficiently compute an output mesh which faithfully preserves the existing sharp features and precisely reconstructs the new features appearing along the intersections of the input meshes. The term "hybrid" applies to our ...

Given a simple polygon P with m vertices and a set S of n points in the plane, we consider the problem of finding a rigid motion placement of P that contains the maximum number of points in S. We present two solutions to this problem that represent time versus space tradeoffs. The first algorithm runs in O(n3m3) expected time using O(n2m2) space. The second algorithm runs in O(n3m3 log(nm)) det...

Polygonal meshes can be created in several different ways. In this paper we focus on the reconstruction of meshes from point clouds, which are sets of points in 3D. Several algorithms that tackle this task already exist, but they have different benefits and drawbacks, which leads to a large number of possible reconstruction results (i.e., meshes). The evaluation of those techniques requires ext...

We present a topology simplifying approach that can be used for genus reductions, removal of protuberances, and repair of cracks in polygonal models in a unified framework. Our work is complementary to the existing work on geometry simplification of polygonal datasets and we demonstrate that using topology and geometry simplifications together yields superior multiresolution hierarchies than is...

In this paper, we propose a method for creating a threedimensional polygonal model reflecting precise boundary of physical objects from a point cloud which has strong anisotropic distribution of points obtained by a mobile mapping system. Our method creates boundary information of physical objects based on the planar region segmentation by the line-based region growing approach from a point clo...

Symmetric polygonal fuzzy number is employed to build an improved feedforward fuzzy neural network (FNN). First, a novel fuzzy arithmetic and extension principle for the polygonal fuzzy numbers is derived. Second, the topological architecture of a three layer feedforward FNN is presented, and the input-output law of this network is systematically studied. Third, a fuzzy BP learning algorithm fo...

Smoothing techniques are essential in providing high quality renderings out of polygonal objects that are described with a minimal amount of geometrical information. In order to remove the "polygonal" aspect of rough polygonal meshes, several techniques are available, such as shading or interpolation techniques. Combining the benefits of polygonal interpolation with a very simple and straightfo...