Showing papers on "Polygon published in 1999"

Fast computation of generalized Voronoi diagrams using graphics hardware

Abstract: We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolation-based polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a bounded-error approximation of a (possibly) non-linear function of the distance between a site and a 2D planar grid of sample points. For each sample point, we compute the closest site and the distance to that site using polygon scan-conversion and the Z-buffer depth comparison. We construct distance meshes for points, line segments, polygons, polyhedra, curves, and curved surfaces in 2D and 3D. We generalize to weighted and farthest-site Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points. We also show how to adaptively refine the solution through a simple windowing operation. The algorithm has been implemented on SGI workstations and PCs using OpenGL, and applied to complex datasets. We demonstrate the application of our algorithm to fast motion planning in static and dynamic environments, selection in complex user-interfaces, and creation of dynamic mosaic effects. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; I.3.3 [Computer Graphics]: Picture/Image Generation. Additional

A visibility-based pursuit-evasion problem

Abstract: This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ(lg n). For multiply-connected free spaces, the bound is pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

Enclosing a polygonal cavity in a two-dimensional bounded domain from Cauchy data

Abstract: We consider a reconstruction problem of the shape of an unknown open set D in a two-dimensional bounded domain from the Cauchy data on of a nonconstant solution u of the equation u = 0 in \ D. We assume that the Neumann derivative of u vanishes on D and that D is a convex open polygon. We give a formula for the calculation of the support function of D from such data.

Animation of three-dimensional characters along a path for motion video sequences

Abstract: A character is represented in a character generator as a set of polygons The character may be manipulated using three-dimensional animation techniques A code for a character may be used to access a set of curves defining the outline of the character This set of curves is transformed into a set of polygons The set of polygons may be rendered as a three-dimensional object The set of polygons may be created by converting the curves into sets of connected line segments and then tessellating the polygon defined by the line segments Animation properties are represented using a normalized scale along a path or over time Animation may be provided in a manner that is independent of the spatial and temporal resolution of the video to which it is applied Such animation may be applied to characters defined by a set of polygons Various three-dimensional spatial transformations, lighting effects and other colorizations may be provided A user interface for editing a character string may provide two alternate displays A first display allows a user to input and view any desired portion of the character string for the purpose of editing A second display allows a user to view how the character string appears at a selected point in time during a titling effect for the purpose of animation In both displays, the text is displayed in a three-dimensional form This interface may be combined with a timeline editing interface for editing an associated video program, or other user interface, to permit layering of titling effects and adjustment of animation properties, positioning and timing

System and method for enhanced 9-1-1 address development, maintenance and call routing using road access zones

Abstract: System and method for enhanced 9-1-1 address development, maintenance and call routing using road access zones (RAZs). RAZs are geographic areas accessible by a particular road. RAZs are formed from geographic data in vector form which includes a plurality of road names, address numbers, and road center lines. The steps for forming the RAZ include: first assigning a number to each road name, then creating a roadname route system based on the plurality of road names and the address numbers, then creating a plurality of polygons, wherein each polygon is associated with a different road name number, and then overlaying the road center lines with the polygons so as to define a left side and a right side of each road center line. RAZs efficiently provide for the verification, maintenance and determination of road names, address parity, geo-coding and emergency service zones (ESZ). In addition, an emergency service zone data layer (ESZ) can be created from the RAZs, which allows for, among other things, an enhanced E-911 system suitable for use with wireless communication devices, such as cell phones.

Finding the shortest watchman route in a simple polygon

Abstract: We present the first polynomial time algorithm that finds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n 6 ) time, but it is adaptive, making it run faster on polygons with a simple structure.

Automatic camera placement for image-based modeling

Abstract: We present an automatic camera placement method for generating image-based models from scenes with known geometry. Our method first approximately determines the set of surfaces visible from a given viewing area and then selects a small set of appropriate camera positions to sample the scene from. We define a quality measure for a surface as seen, or covered, from the given viewing area. Along with each camera position, we store the set of surfaces which are best covered by this camera. Next, one reference view is generated from each reference view that do not belong to the selected set of polygons are masked out. The image-based model generated by our method, covers every visible surface only once, associating it with a camera position from which it is covered with quality that exceeds a user-specified quality threshold. The result is a compact non-redundant image-based model with controlled quality. The problem of covering every visible surface with a minimum number of cameras (guards) can be regarded as an extension to the well-known Art Gallery Problem. However, since the 3D polygonal model is textured, the camera-polygon visibility relation is not binary; instead, it has a weight-the quality of the polygon's coverage.

Ray intersection reduction using directionally classified target lists

Abstract: A method and apparatus, in a computer graphics display system, for reducing the number of polygon intersection tests required to test a ray against a set of polygons. With this method, a multitude of polygons that represent images of object or parts of objects are identified, and these polygons are grouped into a plurality of groups on the basis of the general orientations of the polygons. Also, a ray is identified that represents a line of sight, and the general direction of the ray is compared with the general orientations of the polygons in the above-mentioned groups of polygons. On the basis of this comparison, selected groups of polygons are eliminated from further consideration. Polygons in other groups may be tested to determine if the ray intersects the polygons. The preferred embodiment of the invention described herein in detail has a number of important features. These include (1) a compressed representation of the general direction of displacement of a 3D vector called the directional classification code and a method for computing it given a vector, and (2) a conservative but efficient technique for determining whether the dot product of two vectors of equal length will result in a positive or negative value by comparing their directional classification codes using boolean logic.

A framework for streaming geometry in VRML

Abstract: We introduce a framework for streaming geometry in VRML that eliminates the need to perform complete downloads of geometric models before starting to display them. This framework for the progressive transmission of geometry has three main parts, as follows: 1) a process to generate multiple levels-of-detail (LODs); 2) a transmission process (preferably in compressed form); and 3) a data structure for receiving and exploiting the LODs generated in the first part and transmitted in the second. The processes in parts 1 and 2 have already received considerable attention. We concentrate on a solution for part 3. Our basic contribution is a flexible LOD storage scheme, which we refer to as a progressive multilevel mesh. This scheme, primarily intended as a data structure in memory, has a low memory footprint and provides easy access to the various LODs (thus suitable for efficient rendering). This representation is not tied to a particular automated polygon reduction tool. In fact, we can use the output of any polygon reduction algorithm based on vertex clustering (including the edge collapse operations used in several algorithms). The progressive multilevel mesh complements compression techniques such as those developed by M. Deering (1995), H. Hoppe (1996) or G. Taubin et al. (1998). We discuss the integration of some of these compression techniques. However, for the sake of simplicity, we use a simple file format to describe the algorithm.

Polygon Evolution by Vertex Deletion

Abstract: We propose a simple approach to evolution of polygonal curves that is specially designed to fit discrete nature of curves in digital images. It leads to simplification of shape complexity with no blurring (i.e., shape rounding) effects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a finite number of discrete evolution steps which are just the iterations of a basic procedure of vertex deletion.

The use of spatial cognitive abilities in geographical information systems : the map overlay operation

Abstract: Spatial cognitive abilities play an important role in the use of GIS, although they have yet to be examined in a controlled experimental setting. This study aimed to develop an experimental design which measures spatial cognitive abilities in the use of GIS, specifically the map overlay operation. Subjects (n = 134) received three map overlay tests in which they were given two of the following input map layers, logical operator(s), or output map layer(s). Subjects were required to select the correct logical operator for Test 1, to select the correct output map layer for Test 2, and to select the correct input map layers for Test 3. Each test contained a total of 16 questions, based on a 4 (’and’, ’or’, ’xor’, ’not’ operators) x 2 (one two polygons per map layer) x 2 (three or five polygon edges) factorial design. Results indicated a significant main effect of logical operators and number of polygons on performance; however, there was no effect of the number of polygon edges on performance Significant two-way interactions revealed an effect of the number of polygon edges and the number of polygons using various logical operators on performance, in addition, performance was not significantly different between males and females or between GIS users and non-users. Overall, results show that map overlays in which a visual correspondence can be made between the same polygons in the input and output map layers are cognitively less demanding than map overlays in which the shape of the polygons have been radically transformed between the input and output map layers. This study helps further develop our understanding of the spatial cognitive abilities which are required in the use of GIS, and whether certain sub-populations differ in these cognitive abilities. These results may contribute to more effective and efficient GIS teaching and interface design by taking into account individual spatial cognitive abilities.

Mixing translucent polygons with volumes

Abstract: We present an algorithm which renders opaque and/or translucent polygons embedded within volumetric data. The processing occurs such that all objects are composited in the correct order, by rendering thin slabs of the translucent polygons between volume slices using slice-order volume rendering. We implemented our algorithm with OpenGL on current general-purpose graphics systems. We discuss our system implementation, speed and image quality, as well as the renderings of several mixed scenes.

The Use of Spatial Cognitive Abilities in Geographical Information Systems: The Map Overlay Operation

Abstract: Spatial cognitive abilities play an important role in the use of GIS, although they have yet to be examined in a controlled experimental setting. This study aimed to develop an experimental design which measures spatial cognitive abilities in the use of GIS, specifically the map overlay operation. Subjects (n = 134) received three map overlay tests in which they were given two of the following: input map layers, logical operator(s), or output map layer(s). Subjects were required to select the correct logical operator for Test 1, to select the correct output map layer for Test 2, and to select the correct input map layers for Test 3. Each test contained a total of 16 questions, based on a 4 (‘and’, ‘or’, ‘xor’, ‘not’ operators) × 2 (one or two polygons per map layer) × 2 (three or five polygon edges) factorial design. Results indicated a significant main effect of logical operators and number of polygons on performance; however, there was no effect of the number of polygon edges on performance. Significant two-way interactions revealed an effect of the number of polygon edges and the number of polygons using various logical operators on performance. In addition, performance was not significantly different between males and females or between GIS users and non-users. Overall, results show that map overlays in which a visual correspondence can be made between the same polygons in the input and output map layers are cognitively less demanding than map overlays in which the shape of the polygons have been radically transformed between the input and output map layers. This study helps further develop our understanding of the spatial cognitive abilities which are required in the use of GIS, and whether certain sub-populations differ in these cognitive abilities. These results may contribute to more effective and efficient GIS teaching and interface design by taking into account individual spatial cognitive abilities.

Method and apparatus for adaptive hierarchical visibility in a tiled three-dimensional graphics architecture

Abstract: A data processing system providing high performance three-dimensional graphics includes at least one system processor, chipset core logic, a graphics processor, and a Z-buffer. In one embodiment an adaptive hierarchical visibility (AHV) method performs occlusion-culling in a tiled 3D graphics hardware architecture. Polygon bins for each tile are bucket-sorted in order of increasing depth Z. Polygon bins are rendered starting with the bin closest to the viewer. After some number of bins are rendered, a single layer, hierarchical Z-buffer (HZ) may be constructed from the Z-buffer thus far accumulated for the rendered bins, if it would be cost effective to do so. Subsequent bins are rendered by first testing their polygons against the HZ buffer to see if they are hidden. Also described are an integrated circuit for implementing the AHV algorithm, and a computer-readable medium storing a data structure for implementing the AHV method and apparatus.

A Computer Program for Soil Textural Classification

Abstract: Manual classification of soils into textural classes with the USDA textural triangle is tedious. This computer program can perform the same task easier and faster. The algorithm is based on the fact that each point in the textural triangle represents a unique combination of sand and clay content. For a given textural class, all combinations of sand and clay content are bound by a polygon. Finding the textural class is equivalent to finding the polygon where a particular combination of sand and clay is located. Both a World Wide Web interactive version and a Windows 95 console program are available. On a 133 MHz Pentium microcomputer, the Windows version can classify 1000 soil samples in about a second.

Watermarking of 3D-polygon-based models with robustness against mesh simplification

Abstract: This paper presents a watermarking algorithm suitable for embedding private watermarks into three dimensional polygon based models. The algorithm modifies the models normal distribution to store information solely in the geometry of the model. The watermarks show significant robustness against mesh simplifying methods.

Locally controllable manipulation by stable pushing

Abstract: When a polygonal object is pushed with line contact along an edge, the push is called stable if the object remains fixed to the pusher. The object is small-time locally controllable by stable pushing if, by switching among pushing edges, it can be pushed to follow any path arbitrarily closely. Since the pushes are stable by the frictional mechanics, pushing plans can be executed without position feedback of the object. We derive a necessary and sufficient condition for a polygon to be small-time locally controllable by stable pushing: the pushing friction coefficient must be nonzero and the set of feasible pure forces (forces applied through a polygon edge and passing through the center of friction) must positively span the plane. We interpret this condition in terms of the polygon shape, the location of the center of friction, and the pushing friction coefficient, allowing us to characterize classes of polygons with this fundamental "manoeuvrability" property.

Automatic generation of high-level contact state space

Abstract: Planning in contact state space is very important for many robotics tasks. This paper introduces a general and novel approach for automatic creation of high-level, discrete contact state space between two objects, called contact formation (CF) graphs. A complete CF graph is the result of merging several special subgraphs, called the goal-contact relaxation graphs. We have implemented our algorithm for arbitrary contacting polygons, and the results obtained are presented in this paper. The implementation is extended for arbitrary contacting polyhedra. The time complexity of our algorithm is bounded by O(M/sup 2/), where M characterizes the maximum complexity of the two objects.

Graphics processor with pipeline state storage and retrieval

Abstract: A deferred graphics pipeline processor comprised of a mode extraction unit and a Polygon Memory associated with the polygon unit. The mode extraction unit receives a data stream from a geometry unit and separates the data stream into vertices data, and non-vertices data which is sent to the Polygon Memory for storage. A mode injection unit receives inputs from the Polygon Memory and communicates the mode information to one or more other processing units. The mode injection unit maintains status information identifying the information that is already cached and not sending information that is already cached, thereby reducing communication bandwidth.

Shading 3-dimensional computer generated images

Abstract: A method and apparatus for shading 3-dimensional computer generated images represents each object in the image as a set of polygons. An image plane on which the image is to be displayed is divided into a plurality of rectangular areas. Data defining the location of each polygon is then supplied. The rectangular areas which are required to show the whole of the polygon are then determined. Then, for each pixel in each rectangular area, the depth value is determined for the distance of a surface of the polygon from the image plane and a determination is made as to whether or not the surface is visible at that pixel. The pixel is shaded on dependence on the result of this determination.

Finding the Constrained Delaunay Triangulation and Constrained Voronoi Diagram of a Simple Polygon in Linear Time

Abstract: In this paper, we present an $\Theta (n)$ time worst-case deterministic algorithm for finding the constrained Delaunay triangulation and constrained Voronoi diagram of a simple n-sided polygon in the plane. Up to now, only an O(n log n) worst-case deterministic and an O(n) expected time bound have been shown, leaving an O(n) deterministic solution open to conjecture.

System and method for data visualization

Abstract: A system and method for visualizing information on a computer system by generating and displaying a number of axes on a computer monitor, selecting points along respective axes which correspond to an information entry using a mouse or any other spatially-based input device, and forming a polygonal shape therefrom, the vertices of the polygon being the respective selected points. Multiple such polygons may be serially displayed or overlaid to facilitate visualization and interpretation of the information. The system and method of the present invention are further directed to facilitating the entry, modification and storage of a record in a computer system by displaying it on a polar chart, selecting a point on the polar chart with a mouse or any other spatially-based input device, and respectively entering, modifying and storing the record.

Image forming device

Abstract: PROBLEM TO BE SOLVED: To provide an image forming device wherein a polygon mirror does not get dirty with an air flow containing dust suck into a polygon mirror cover and an optical system such as an image forming lens and a filter is not contaminated with an air flow containing dust blown out of the opening part of the polygon mirror cover and which can maintain shape image formation long. SOLUTION: This device is equipped with an image formation part which forms a toner image to be transferred to a recording material and an optical deflector which rotates the polygon mirror 21 coupled with a driving part 22 by a rotary shaft 23 and deflects and scans illumination light emitted by a light source through the optical system and those light source, the optical system, and the optical deflector are put in an optical box 26 to constitute the image forming device, which is characterized in that the optical deflector is installed in the optical box 26 so that the axial direction of the rotary shaft 23 of the optical deflector and the gravitational direction are almost at right angles to each other.

Rotational polygon containment and minimum enclosure using only robust 2D constructions

Abstract: An algorithm and a robust floating point implementation is given for rotational polygon containment: given polygons P1,P2,P3,…,Pk and a container polygon C, find rotations and translations for the k polygons that place them into the container without overlapping. A version of the algorithm and implementation also solves rotational minimum enclosure: given a class C of container polygons, find a container C∈ C of minimum area for which containment has a solution. The minimum enclosure is approximate: it bounds the minimum area between (1−e)A and A. Experiments indicate that finding the minimum enclosure is practical for k=2,3 but not larger unless optimality is sacrificed or angles ranges are limited (although these solutions can still be useful). Important applications for these algorithm to industrial problems are discussed. The paper also gives practical algorithms and numerical techniques for robustly calculating polygon set intersection, Minkowski sum, and range intersection: the intersection of a polygon with itself as it rotates through a range of angles. In particular, it introduces nearest pair rounding, which allows all these calculations to be carried out in rounded floating point arithmetic.

Predicting geometrical properties of random packed beds from computer simulation

Abstract: Using advances in computational geometry and collision-detection algorithms, an algorithm was developed to analyze and predict the geometrical properties of a randomly packed structure using packing objects of arbitrary shape. A 3-D polygonal model was used to describe an arbitrarily complex packing object and a simple container object. The dynamics of the packing process is not simulated, but a search algorithm finds stable equilibrium positions for the packing objects of arbitrary shapes using a collision-detection algorithm in a 3-D space. A modified conjugate gradient optimization method determines the packing object's final packing location and orientation. Once the bed is packed, both macroscopic quantities like the overall porosity, the specific surface area, and the number of packing objects per unit volume and microscopic properties like the porosity variation in any direction could be determined. For accurate porosity calculation inside a given 3-D polygonal sample space, the Sutherland-Hodgman polygon clipper algorithm was used. Predicted results are validated against available experimental data for spheres, Raschig rings, Pall rings, and cascade minirings.

Covering rectilinear polygons with axis-parallel rectangles

Abstract: We give an O( log n) factor approximation algorithm for covering a rectilinear polygon with holes using axis-parallel rectangles. This is the first polynomial time approximation algorithm for this problem with an o(log n) approximation factor. 1. Introduction. We consider the problem of covering rectilinear polygons with axis-parallel rectangles. Given a rectilinear polygon P with complexity n (complexity refers to the minimum of the number of vertical edges and the number of horizontal edges in the polygon), this problem requires determining the minimum number of axis-parallel rectangles whose union covers P. The polygon P may have holes in it. Applications. Cheng, Iyengar, and Kashyap (5) showed that this problem has applications to image compression. They claim that representing an image using a rectangle covering of its white pixels gives compression superior to that achieved by quadtrees. It also has applications to printing integrated circuits (9). Hardness. Much effort has gone into determining the computational complexity of this problem. In spite of this, the exact complexity of this problem has remained open for many years and continues to do so. Masek (19) showed that this problem is NP-complete. Later, Culberson and Reckhow (6) used a clever reduction from 3-SAT to show that this is the case even when P has no holes. The next natural question is whether the number of rectangles needed to cover P can be computed approximately. Berman and Dasgupta (2) showed that this problem is MaxSNP-Hard for polygons with holes, ruling out the possibility of a polynomial time approximation scheme. Approximation results. Note that the rectangle covering problem is a special case of the general set covering problem. Therefore, it admits an approximation algorithm with a performance guarantee of O(log n), using the greedy scheme due to Johnson (10) and Lovasz (16). This was the best approximation factor known for the rectangle covering problem until now. Further, it is known that the general set covering problem cannot be approximated any better, modulo constant terms, unless NP = P (17, 18). However, this proof of hardness assumes certain properties about the set system which do not hold for the rectangle covering problem. In this paper, we address the issue of whether the Ω(log n) approximation factor barrier can be broken in polynomial time for the rectangle covering problem. There seem to be only a few examples of nontrivial algorithms breaking this