Results 1  10
of
15
Efficient Binary Space Partitions for HiddenSurface Removal and Solid Modeling
, 1990
"... We consider schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated. Such a binary space partition, or BSP, is naturally considered as a binary tree where each internal node corresponds to a division. The goal is to choose the hyperplanes properly ..."
Abstract

Cited by 91 (0 self)
 Add to MetaCart
We consider schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated. Such a binary space partition, or BSP, is naturally considered as a binary tree where each internal node corresponds to a division. The goal is to choose the hyperplanes properly so that the size of the BSP, i.e., the number of resulting fragments of the objects, is minimized. For the twodimensional case, we construct BSPs of size O(n log n) for n edges, while in three dimensions, we obtain BSPs of size O(n²) for n planar facets and prove a matching lower bound of Ω(n²). Two applications of efficient BSPs are given. The first is an O(n²)sized data structure for implementing a hiddensurface removal scheme of Fuchs et al. [6]. The second application is in solid modeling: given a polyhedron described by its n faces, we show how to generate an O(n²)sized CSG (constructivesolidgeometry) formula whose literals correspond to halfspaces supporting the faces of the polyhedron. The best previous results for both of these problems were O(n³).
An Efficient Algorithm for Finding the CSG Representation of a Simple Polygon
, 1989
"... Modeling twodimensional and threedimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometr ..."
Abstract

Cited by 32 (10 self)
 Add to MetaCart
Modeling twodimensional and threedimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary. We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedron P are based on the halfspaces supporting the faces of P . For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone...
Visibility with a moving point of view
 Algorithmica
, 1994
"... We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the ..."
Abstract

Cited by 28 (1 self)
 Add to MetaCart
We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the flightpath. Three progressively more specialized problems are considered: general scenes, terrains, and terrains with vertical flightpaths. 1.
Constructing Good Partitioning Trees
, 1996
"... Partitioning trees, a multidimensional generalization of binary search trees, is alone among the principal methods for representing geometry in combining the representation of a set with the geometric search structure required for efficient spatial operations such as set operations and visibility. ..."
Abstract

Cited by 27 (1 self)
 Add to MetaCart
Partitioning trees, a multidimensional generalization of binary search trees, is alone among the principal methods for representing geometry in combining the representation of a set with the geometric search structure required for efficient spatial operations such as set operations and visibility. Since a partitioning tree may be interpreted as specifying a program for exploring the structure induced on a space (e.g. by objects), there are many trees which represent the same spatial structure but provide different searches of the space. The issue of generating a good program to determine spatial relations between sets is then transformed into the issue of constructing good partitioning trees. The metric we choose for characterizing goodness is the expected cost of various elementary operations calculated using simple probability models. However, choosing the optimal from at least n! different trees by enumeration is not viable. Consequently, we employ heuristics that make local decisions based on the expected cost models. In addition to this quantitative methodology, we develop a qualitative understanding of what constitutes a good representation. This leads us to the notion of a good tree as one that provides a sequence or set of approximations, each obtained by various prunings of a single tree.
BrepIndex: A Multidimensional Space Partitioning Tree
, 1991
"... In this paper we present the Brepindex, a multidimensional space partitioning data structure that provides quick spatial access to the vertices, edges and faces of a boundary representation (Brep), thus yielding a single unified representation for polyhedral solids. We give an algorithm for the con ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
In this paper we present the Brepindex, a multidimensional space partitioning data structure that provides quick spatial access to the vertices, edges and faces of a boundary representation (Brep), thus yielding a single unified representation for polyhedral solids. We give an algorithm for the construction of the Brepindex and prove its correctness. We show that its size is \Omega\Gamma v + e + f), where v, e, and f are the number of vertices, edges, and faces of the Brep. The lower bound can be achieved for some Breps by compressing the structure using simple rewrite rules. We then demonstrate robust point and line/Brep classification methods given an implementation that uses finiteprecision arithmetic. Keywords: Classification, Brep, BSP Trees, Data Structures 1. Introduction Most data structures that exist for representing polyhedral solids can be categorized either as boundarybased or as volumebased. Each category has certain benefits not found in the other and therefore, ...
Shadow Volume BSP Trees for Computation of Shadows in Dynamic Scenes
 In 1995 Symposium on Interactive 3D Graphics
, 1995
"... This paper presents an algorithm for shadow calculation in dynamic polyhedral scenes illuminated by point light sources. It is based on a modification of Shadow Volume Binary Space Partition trees, to allow these be constructed from the original scene polygons in arbitrary order and to support for f ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
This paper presents an algorithm for shadow calculation in dynamic polyhedral scenes illuminated by point light sources. It is based on a modification of Shadow Volume Binary Space Partition trees, to allow these be constructed from the original scene polygons in arbitrary order and to support for fast reconstruction after a change in scene geometry. Timings using sample scenes are presented that indicate substantial savings both in terms of computation time and shadows produced. KEY WORDS: shadows, BSP Trees, SVBSP Trees, dynamic modification. 1
Multiresolution BSP Trees Applied to Terrains, Transparency, and . . .
"... We present a system for incorporating multiple level of detail (LOD) models of 3D objects within a single hierarchical data structure. This system was designed for a scientific visualization application involving terrain and volume rendering. Our data structure is a modified Binary Space Partitionin ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
We present a system for incorporating multiple level of detail (LOD) models of 3D objects within a single hierarchical data structure. This system was designed for a scientific visualization application involving terrain and volume rendering. Our data structure is a modified Binary Space Partitioning (BSP) tree. We describe how our tree construction and traversal routines may be used with a variety of LOD methods. This is demonstrated with two different LOD methods: a new method specialized for terrain elevation height fields, and an existing method for general objects. Images, timings, and storage data for our implementation are provided. Keywords: BSP trees, Virtual reality, Realtime graphics, Multiple levelsofdetail. 1 Introduction This research was motivated by a scientific visualization project in which we were asked to produce an interactive display combining renderings of terrain and volume data. The volume data, derived from simulations of radio frequency (RF) propagation...
Construction of Sparse Wellspaced Point Sets for Quality Tetrahedralizations
, 2007
"... Summary. We propose a new mesh refinement algorithm for computing quality guaranteed Delaunay triangulations in three dimensions. The refinement relies on new ideas for computing the goodness of the mesh, and a sampling strategy that employs numerically stable Steiner points. We show through experim ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Summary. We propose a new mesh refinement algorithm for computing quality guaranteed Delaunay triangulations in three dimensions. The refinement relies on new ideas for computing the goodness of the mesh, and a sampling strategy that employs numerically stable Steiner points. We show through experiments that the new algorithm results in sparse wellspaced point sets which in turn leads to tetrahedral meshes with fewer elements than the traditional refinement methods.