Showing papers on "Polygon published in 1996"

OBBTree: a hierarchical structure for rapid interference detection

Abstract: We present a data structure and an algorithm for efficient and exact interference detection amongst complex models undergoing rigid motion. The algorithm is applicable to all general polygonal models. It pre-computes a hierarchical representation of models using tight-fitting oriented bounding box trees (OBBTrees). At runtime, the algorithm traverses two such trees and tests for overlaps between oriented bounding boxes based on a separating axis theorem, which takes less than 200 operations in practice. It has been implemented and we compare its performance with other hierarchical data structures. In particular, it can robustly and accurately detect all the contacts between large complex geometries composed of hundreds of thousands of polygons at interactive rates. CR

Real-time, continuous level of detail rendering of height fields

Abstract: We present an algorithm for real-time level of detail reduction and display of high-complexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screen-space threshold to bound the maximum error of the projected image. A coarse level of simplification is performed to select discrete levels of detail for blocks of the surface mesh, followed by further simplification through repolygonalization in which individual mesh vertices are considered for removal. These steps compute and generate the appropriate level of detail dynamically in real-time, minimizing the number of rendered polygons and allowing for smooth changes in resolution across areas of the surface. The algorithm has been implemented for approximating and rendering digital terrain models and other height fields, and consistently performs at interactive frame rates with high image quality.

Fitting smooth surfaces to dense polygon meshes

Abstract: Recent progress in acquiring shape from range data permits the acquisition of seamless million-polygon meshes from physical models. While dense polygon meshes are an adequate representation for some applications, many users prefer smooth surface representations for reasons of compactness, control, manufacturability, or appearance. In this thesis, we present algorithms and an end-to-end software system for converting dense irregular polygon meshes of arbitrary topology into tensor product B-spline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for interactive modification and animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries onto the polygonal surface. In many applications, the placement of patch boundaries is considered part of the creative process and is not amenable to automation. We present efficient techniques for representing, creating and editing curves on dense polygonal surfaces. The second step in our process consists of finding a gridded resampling of each bounded section of the mesh. Our resampling algorithm lays a grid of springs across the polygon mesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, which is initially unparameterized. Our parameterization algorithm is automatic, efficient, and robust, even for complex polygonal surfaces. Prior algorithms have lacked one or more of these properties, making them unusable for dense meshes. Our strategy also provides the user a flexible method to design parameterizations--an ability that previous literature in surface approximation does not address. The third and final step of our process consists of fitting a hybrid of B-spline surfaces and displacement maps to our gridded re-sampling. The displacement map is an image representation of the error between the fitted B-spline surfaces and our spring grid. Since displacement maps are just images our hybrid representation facilitates the use of image processing operators for manipulating the geometric detail of an object. Our resampling and fitting steps are fast enough to surface a million polygon mesh in under 10 minutes--important for an interactive system.

Superfaces: polygonal mesh simplification with bounded error

Abstract: The algorithm presented simplifies polyhedral meshes within prespecified tolerances based on a bounded approximation criterion. The vertices in the simplified mesh are a proper subset of the original vertices. The algorithm, called Superfaces, makes two major contributions to the research in this area: it uses a bounded approximation approach, which guarantees that a simplified mesh approximates the original mesh to within a prespecified tolerance (that is, every vertex v in the original mesh will lie within a user specified distance /spl epsiv/ of the simplified mesh); its face merging procedure is efficient and greedy-that is, it does not backtrack or undo any merging once completed and thus, the algorithm is practical for simplifying very large meshes.

A Novel Type of Skeleton for Polygons

Abstract: A new internal structure for simple polygons, the straight skeleton, is introduced and discussed. It is composed of pieces of angular bisectores which partition the interior of a given n-gon P in a tree-like fashion into n monotone polygons. Its straight-line structure and its lower combinatorial complexity may make the straight skeleton preferable to the widely used medial axis of a polygon. As a seemingly unrelated application, the straight skeleton provides a canonical way of constructing a polygonal roof above a general layout of ground walls.

Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping

Abstract: The Schwarz-Christoffel transformation and its variations yield formulas for conformal maps from standard regions to the interiors or exteriors of possibly unbounded polygons. Computations involving these maps generally require a computer, and although the numerical aspects of these transformations have been studied, there are few software implementations that are widely available and suited for general use. The Schwarz-Christoffel Toolbox for MATLAB is a new implementation of Schwarz-Christoffel formulas for maps from the disk, half-plane, strip, and rectangle domains to polygon interiors, and from the disk to polygon exteriors. The toolbox, written entirely in the MATLAB script language, exploits the high-level functions, interactive environment, visualization tools, and graphical user interface elements supplied by current versions of MATLAB, and is suitable for use both as a standalone tool and as a library for applications written in MATLAB, Fortran, or C. Several examples and simple applications are presented to demonstrate the toolbox's capabilities.

Spatial light modulator and directional display

Abstract: A liquid crystal spatial light modulator comprises columns and rows of picture elements (24-26). The columns are arranged as groups of columns, for instance under respective parallax generating elements in an autostereoscopic 3D display. The picture elements (24-26) are arranged as sets to form colour picture elements such that the picture elements (24-26) of each set are disposed at the apices of a polygon, such as a triangle (21), and are disposed in corresponding columns of the groups of columns.

Positioning system having an RF-measurements databank

Abstract: An improved positioning system and method for use in a wireless communication system including a plurality of base stations each having a corresponding coverage area. Scaled contour shapes are generated having minimum and maximum boundaries based upon determined RF measurements of each of the base stations. The intersections of the contour shapes define a bounding polygon area that describes the position of a mobile unit in terms of minimum and maximum error estimate. Once the bounding polygon area has been defined, the latitude and longitude of the center of the polygon area is determined whereupon corresponding street addresses may be obtained through reference to one or more databases.

Hierarchical polygon tiling with coverage masks

Abstract: Contact author at greene@apple.com, Apple Computer, 1 Infinite Loop, Cupertino, CA 95014 We present a novel polygon tiling algorithm in which recursive subdivision of image space is driven by coverage masks that classify a convex polygon as inside, outside, or intersecting cells in an image hierarchy. This approach permits Warnock-style subdivision with its logarithmic search properties to be driven very efficiently by bit-mask operations. The resulting hierarchical polygon tiling algorithm performs subdivision and visibility computations very rapidly while only visiting cells in the image hierarchy that are crossed by visible edges in the output image. Visible samples are never overwritten. At 512 512 resolution, the algorithm tiles as rapidly as traditional incremental scan conversion, and at high resolution (e.g. 4096 4096) it is much faster, making it well suited to antialiasing by oversampling and filtering. For densely occluded scenes, we combine hierarchical tiling with the hierarchical visibility algorithm to enable hierarchical object-space culling. When we tested this combination on a densely occluded model, it computed visibility on a 4096 4096 grid as rapidly as hierarchical z-buffering [Greene-Kass-Miller93] tiled a 512 512 grid, and it effectively antialiased scenes containing hundreds of thousands of visible polygons. The algorithm requires strict front-toback traversal of polygons, so we represent a scene as a BSP tree or as an octree of BSP trees. When maintaining depth order of polygons is not convenient, we combine hierarchical tiling with hierarchical z-buffering, resorting to z-buffering only in regions of the screen where the closest object is not encountered first. I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism Hidden line/surface removal; I.3.3 [Computer Graphics]: Picture/Image Generation. tiling, coverage mask, antialiasing, visibility, BSP tree, octree, recursive subdivision.

Method and apparatus for span and subspan sorting rendering system

Abstract: The invention provides for a data shifting capability that permits sorting the data in addition to searching for obtaining real-time performance in color, with high quality imagery through a simple search of a spatial database based on a rectangularly shaped search region or range search (fig. 13). A sorting Magnitude Comparison Content Addressable Memory (SMCCAM) performs a range search, introducing a conservative approximation of the ideal Occluding Region, and provides a MCCAM wherein the data words stored in the fields is shifted to corresponding fields in an adjacent word, based on the magnitude comparisons (fig. 7). The 3D graphics method stores the parameters of a polygon span in a spatial database (804-814) and a query operation is performed on the database to determine which of those spans, or portions of spans, are visible (816 and 818), and applies a rule for comparing new span portion to an old span portion on a subspan-by-subspan basis, thereby providing additional polygon edge information within a raster line, providing anti-aliasing.

Wavelet approximations for first kind boundary integral equations on polygons

Abstract: An elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent first kind boundary integral equation. Its Galerkin discretization with $N$ degrees of freedom on the boundary with spline wavelets as basis functions is analyzed. A truncation strategy is presented which allows to reduce the number of nonzero elements in the stiffness matrix from $O(N^2)$ to $O(N\log N)$ entries. The condition numbers are bounded independently of the meshwidth. It is proved that the compressed scheme thus obtained yields in $O(N(\log N)^2)$ operations approximate solutions with the same asymptotic convergence rates as the full Galerkin scheme in the boundary energy norm as well as in interior points. Numerical examples show the asymptotic error analysis to be valid already for moderate values of $N$ .

Site-specific harvest statistics analyzer

Abstract: Disclosed herein is a method and apparatus for analyzing statistical data for a region of a farming field defined by a boundary on a set of georeferenced agricultural maps of the field Input data includes digital maps of the field which represent spatially-variable characteristics The characteristics may represent soil properties, crop properties and farming inputs applied to the field The characteristic data is georeferenced to specific field locations by longitude and latitude coordinates An electronic display is used to display a visual map of the field together with a visual representation of a first characteristic of the field An input device is used to draw a boundary around an area of the display, thereby defining a geographic area of the field Analysis of a second characteristic of the field which correlates to the defined geographic area is then performed Typically, a farmer draws a polygon on the display based upon similar characteristic values and calculates crop yield and moisture content within the geographic area defined by the polygon

Note on A Linear-Time Algorithm for Computing$K$-Terminal Reliability in a Series-Parallel Network

Abstract: In an original and very interesting paper (Satyanarayana and Wood [1]) concerning polygon-to-chain reductions in a stochastic network, a small inconsistency occurs in the proof of Theorem 1. In particular, this happens in cases where the whole set of {\bit K}-vertices lies in the remaining polygon. Such an example is the case of polygon type 5, where the appropriate note has been made by the authors for $|\hbox{\bit K}| = 2$. Analogous notes must also be made for polygon types 4, 6, and 7, when {\bit K}$ = 2$, 3, and 4, respectively. The correct transformations are given in Table 1 (note that dark vertices are {\bit K}-vertices).

Method and apparatus for shading graphical images in a data processing system

Abstract: The present invention provides an apparatus for displaying an image of an object, as illuminated by a light source, on a display within a computer graphics display system. The image is graphically represented by a mesh of polygons and each polygon within the mesh has a surface defined by a set of vertices. The vertices define the surface of the polygon. The apparatus includes a processor, such as a rasterizer, that is responsive to each set of vertices for rendering each surface within the mesh of polygons in response to ambient lighting to produce a number of initially rendered surfaces within the mesh of polygons. Phong shading is utilized by the present invention. The processor produces a specular highlight contribution for each surface within the mesh of polygons utilizing a halfway vector, pointing from each surface to a direction halfway between a light vector and a vector pointing towards a viewpoint, associated with a vector normal to each surface. Diffuse color contributions are generated within the processor using a light vector from a surface pointing to an illumination source associated with a vector normal to each surface. The specular highlight contribution and the diffuse color contribution for each surface of the initially rendered surfaces are summed to produce finally rendered surfaces within the mesh of polygons. These finally rendered polygons are used to display the image within the computer graphics display system.

Image composition schemes for sort-last polygon rendering on 2D mesh multicomputers

Abstract: In a sort-last polygon rendering system, the efficiency of image composition is very important for achieving fast rendering. In this paper, the implementation of a sort-last rendering system on a general purpose multicomputer system is described. A two-phase sort-last-full image composition scheme is described first, and then many variants of it are presented for 2D mesh message-passing multicomputers, such as the Intel Delta and Paragon. All the proposed schemes are analyzed and experimentally evaluated on Caltech's Intel Delta machine for our sort-last parallel polygon renderer. Experimental results show that sort-last-sparse strategies are better suited than sort-last-full schemes for software implementation on a general purpose multicomputer system. Further, interleaved composition regions perform better than coherent regions. In a large multicomputer system. Performance can be improved by carefully scheduling the tasks of rendering and communication. Using 512 processors to render our test scenes, the peak rendering rate achieved on a 282,144 triangle dataset is dose to 4.6 million triangles per second which is comparable to the speed of current state-of-the-art graphics workstations.

Color image forming device

Abstract: A color image forming device that can certainly correct uniform velocity error associated with the characteristic of each optical system and can realize high-quality color image printing by performing a fine laser beam irradiating position control, in consideration of an error in surface accuracy of each mirror surface of a rotary polygon mirror. The color image forming device includes a storage unit for holding uniform velocity correction data previously created for each mirror surface of a rotary polygon mirror to correct a distortion in expansion or contraction of the electrostatic latent image in the main scanning direction due to the characteristic of an optical system, and an image clock generating unit for reading uniform velocity correction data on each mirror surface used in the rotary polygon mirror at a scanning time out of the storage unit and then generating image clock pulses for image signal creation with a period corresponding to the uniform velocity correction data. The color image forming device is applicable to printers of electro-photographic systems, electrostatic-recording systems, and the like.

Generalized unstructured decimation [computer graphics]

Abstract: Decimation describes the process of removing entities (such as polygons) from a geometric representation. The goal is to intelligently reduce the number of primitives required to accurately model the problem of interest. The work described in the article was originally motivated by the need for efficient and robust decimation of volume tessellations, that is, unstructured tetrahedrizations. Existing surface-based decimation schemes do not generalize to volumes. The technique allows local, dynamic vertex removal from an unstructured tetrahedrization while preserving the initial tessellation topology and boundary geometry. The research focuses on vertex removal methodology, not on the formulation of decimation criteria. In practice, criteria for removing vertices are application specific. The basis of the algorithm is a unique and general method to classify a triangle with respect to a nonconvex polygon. The resulting decimation algorithm (applicable to both surface and volume tessellations) is robust and efficient because it avoids floating-point classification computations.

Generating random polygons with given vertices

Abstract: The problem of generating “random” geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random x-monotone polygon on a given set of n vertices. Here, “random” is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algorithm that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n

Method and system for efficiently drawing subdivision surfaces for 3D graphics

Abstract: A process for efficiently drawing subdivision surfaces. The present invention operates within a computer system for visually displaying 3 dimensional (3D) surfaces on a display. The present invention pulls polygons from a polygon mesh of a 3D surface. The polygons are stored into a 2 dimensional array such that the vertices of the polygons occupy nodes of the 2 dimensional array and are readily accessed. The polygons are subsequently divided into a plurality of resulting polygons. The resulting polygons are then sent to a graphics pipeline, wherein the graphics pipeline renders the resulting polygons into a 3D image on the computer display.

Image processing apparatus

Abstract: In the radiosity calculation, the intersection decision is effected by the ray-casting method with respect to one portion of element of the polygon interior with the use of the coherence of the dodow so as to obtain the illumination intention and the interpolation domain of the form-factor from the intersection decision results. As the radiosity calculation is effected in accordance with the algorithm that the linear, non-linear interpolation equations are properly used in accordance with the precision to use the interpolation calculation in the interior portion the interpolation domain, the intersection decision frequency is sharply reduced so that the whole processing can be effected with higher speed.

Interacting self-avoiding walks and polygons in three dimensions

Abstract: Self-interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the -point. We consider self-avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon. We prove that these walks and polygons have the same limiting free energy if the interactions between nearest-neighbour vertices are repulsive. The attractive interaction regime is investigated using Monte Carlo methods, and we find evidence that the limiting free energies are also equal here. In particular, this means that these models have the same -point, in the asymptotic limit. The dimensions and shapes of walks and polygons are also examined as a function of the interaction strength.

Simple and efficient polygonization of implicit surfaces

Abstract: This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In this way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three-dimensional search to two dimensions.

Apparatus and method for clipping primitives using information from a previous bounding box process

Abstract: In apparatus for processing image data representing multi-dimensional objects, data is stored defining the position of a light source, a viewing position, an arrangement of polygons defining an object and a local transform for transforming said object into viewable 3-dimensional space. Processing means defines the extent of points for an object in each dimension, performs said local transform on said points and determines the extent to which said points are transformed into viewing space. Thus, an evaluation can be made as to where the object will lie in viewing space before polygons are transformed. Culling may then be performed at the object level, rather than at the polygon level.

Voronoi diagrams of polygons: a framework for shape representation

Abstract: This paper describes an efficient shape representation framework for planar shapes using Voronoi skeletons. This paper makes the following significant contributions. First a new algorithm for the construction of the Voronoi diagram of a polygon with holes is described. The main features of this algorithm are its robustness in handling the standard degenerate cases (colinearity of more than two points; co-circularity of more than three points), and its ease of implementation. It also features a robust numerical scheme to compute non-linear parabolic edges that avoids having to solve equations of degree greater than two. The algorithm has been fully implemented and tested in a variety of test inputs. Second, the Voronoi diagram of a polygon is used to derive accurate and robust skeletons for planar shapes. The shape representation scheme using Voronoi skeletons possesses the important properties of connectivity as well as Euclidean metrics. Redundant skeletal edges are deleted in a pruning step which guarantees that connectivity of the skeleton will be preserved. The resultant representation is stable with respect to being invariant to perturbations along the boundary of the shape. A number of examples of shapes with and without holes are presented to demonstrate the features of this approach.

SCROOGE:Perceptually‐Driven Polygon Reduction

Abstract: Many real-time 3D graphics renderers represent each object as a collection of simple polygons. The complexity of this polygon structure is of practical relevance because it can manifestly affect the performance of the graphics system. It is therefore common place to find techniques to reduce the polygonal complexity of a model with the ultimate aim of improving the interactivity of the application. In the past, many of these schemes have not been concerned with the perceptual side-effects of this reduction and as a result a number of visual incongruities are often perceivable when these correspondingly-reduced representations are employed. As an attempt to circumvent these problems, this paper presents a methodology for reducing the polygonal complexity of a model, whilst retaining a degree of perceptual predictability. This allows the visual consequences of the degradation to be quantified and accurately modelled.

Automated Determination of the Distribution of Local Void Ratio from Digital Images

Abstract: The frequency distribution of local void ratio is believed to be an important parameter, in addition to the void ratio, for describing the mechanical behavior of granular materials. Oda proposed a method to determine experimentally the distribution of local void ratio from 2-D plane sections. To date, implementations of Oda's method have depended to varying extents on operator judgment to form polygons by joining the centers of gravity of all particles that surround a void. Furthermore, the studies have involved a significant amount of manual work in making the required measurements. This paper describes a fully automated implementation of the method, which uses high-level, image-processing techniques. The proposed method eliminates operator judgment and manual work and makes the determination of the distribution of local void ratio from 2-D plane sections both repeatable and efficient. The method is illustrated with measurements performed on synthetic and real images. The importance of correcting the images to account for factors such as thickness of segmentation lines is demonstrated. Measurements that confirm the stability of the proposed polygon network generation procedure are also presented.

A fuzzy approach to digital image warping

Abstract: Digital image warping addresses the problem of how to smoothly transform one digital image into another. The warping process has wide applications in computer animation and can be divided into two classes depending on the type of images being transformed. Gray image warping considers the transformation of one gray-scale image into another-a process also known as image metamorphosis. Binary image warping, on the other hand, addresses the transformation of binary images such as polygonal shapes. The focus in this article is on warping polygons. We can approach the warping of polygonal shapes in two steps. The first establishes a correspondence between the vertices of two given polygons. The second step interpolates the corresponding vertices to generate vertices of an intermediate polygon. This article presents new approaches to both steps. This new algorithm uses fuzzy techniques to warp polygons that have different locations, orientations, sizes and numbers of vertices. The algorithm is robust and extensible to curved shapes.