Showing papers on "Polygon published in 1995"

Shape blending using the star-skeleton representation

Abstract: Shape blending, the metamorphosis of one shape into another, is a central problem in two-dimensional computer animation. In spite of impressive uses of morphing in film and video productions, the problem is far from solved. In particular, shape blending still requires considerable manual effort. By decomposing two polygons into equivalent star-shaped pieces and a connecting skeleton, the paper presents a blending method which can represent polygon interiors, not just boundaries, and generate high-quality results with minimal user intervention. >

Fast sparse aerial-image calculation for OPC

Abstract: Fast sparse aerial image simulation and its use in optical proximity correction (OPC) is the topic of this paper. The primary result is a new lookup table formulation of aerial image calculation for a partially coherent optical system. As a generalization of our previous work for Manhattan geometry, the new technique extends the fast lookup technique to arbitrary polygonal mask geometry. Using the new method, the computation required for a sample point of the image intensity is proportional to the number of polygon edges in the local mask region. Moreover, the method is particularly well suited for perturbations to the mask such as those OPC might produce. Our implementation of the new technique achieves intensity calculation speeds of 6 msec/point and perturbational update speeds of 26 microsecond(s) ec/point on a Sun SPARC 10.

Flow visualization using moving textures

Abstract: An intuitive way to visualize a flow is to watch particles or textures move in the flow. In this paper, the authors show how texture mapping hardware can produce near-real-time texture motion, using a polygon grid, and one fixed texture. However, the authors make no attempt to indicate the flow direction in a still frame. As discussed here, any anisotropic stretching comes from the velocity gradient, not the velocity itself. The basic idea is to advect the texture by the flow field. In a cited paper, they gave an indication of the wind velocity by advecting the 3D texture coordinates on the polygon vertices of a cloudiness contour surface in a climate simulation. This was slow, because the 3D texture was rendered in software, and because advecting the texture was difficult for time-varying flows. In this paper, they replace the 3D textures by 2D texture maps compatible with hardware rendering, and give techniques for handling time-varying flows more efficiently. The next section gives their technique for the case of 2D steady flows, and the following one discusses the problems of texture distortion. Then they discuss the problems with extending method to time-varying flows, and two solutions. Next they develop compositing methods for visualizing 3D flows. The final section gives their results and conclusions.

Reconstructing polygons from moments with connections to array processing

Abstract: We establish a set of results showing that the vertices of any simply connected planar polygonal region can be reconstructed from a finite number of its complex moments. These results find applications in a variety of apparently disparate areas such as computerized tomography and inverse potential theory, where in the former, it is of interest to estimate the shape of an object from a finite number of its projections, whereas in the latter, the objective is to extract the shape of a gravitating body from measurements of its exterior logarithmic potentials at a finite number of points. We show that the problem of polygonal vertex reconstruction from moments can in fact be posed as an array processing problem, and taking advantage of this relationship, we derive and illustrate several new algorithms for the reconstruction of the vertices of simply connected polygons from moments. >

Stratified sampling of spherical triangles

Abstract: We present an algorithm for generating uniformly distributed random samples from arbitrary spherical triangles The algorithm is based on a transformation of the unit square and easily accommodates stratified sampling, an effective means of reducing variance With the new algorithm it is straightforward to perform stratified sampling of the solid angle subtended by an arbitrary polygon; this is a fundamental operation in image synthesis which has not been addressed in the Monte Carlo literature We derive the required transformation using elementary spherical trigonometry and provide the complete sampling algorithm CR

Polygonization of non-manifold implicit surfaces

Abstract: A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by real-valued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these surfaces yield edges of degree two. The new method allows the definition of implicit surfaces with boundaries (i.e., edges of degree one) and intersections (i.e., edges of degree three or more). These non-manifold implicit surfaces are defined by a multiple regionalization of space. The definition includes a list of those pairs of regions whose separating surface is of interest. Also presented is an implementation that converts a nonmanifold implicit surface definition into a collection of polygons. Although following conventional implicit surface polygonization, there are significant differences that are described in detail. Several example surfaces are defined and polygonized. CR

Conservative bias in classification accuracy assessment due to pixel-by-pixel comparison of classified images with reference grids

Abstract: The use of reference grids derived from aerial photography for a pixel-by-pixel comparison with classified images can yield conservative estimales of classification accuracy. Even if the class assignment of each polygon is 100 per cent correct, and there is no change in cover type due to temporal differences between the reference data and the classified image, conservative bias in estimales of classification accuracy are still possible. In this letter, we discuss two major sources of this potential bias: 1. positional errors, and 2. difference between polygon minimum mapping unit (MMU) area and pixel size of the classified image.

Computational Geometry and Computer Graphics in C

Abstract: I. BASICS. 1. Introduction. Framework. Our Use of the C++ Language. Robustness. 2. Analysis of Algorithms. Models of Computation. Complexity Measures. Asymptotic Analysis. Analysis of Recursive Algorithms. Problem Complexity. Chapter Notes. Exercises. 3. Data Structures. What are Data Structures? Linked Lists. Lists. Stacks. Binary Search Trees. Braided Binary Search Trees. Randomized Search Trees. Chapter Notes. Exercises. 4. Geometric Data Structures. Vectors. Points. Polygons. Edges. Geometric Objects in Space. Finding the Intersection of a Line and a Triangle. Chapter Notes. Exercises. II. APPLICATIONS. 5. Incremental Insertion. Insertion Sort. Finding Star-Shaped Polygons. Finding Convex Hulls: Insertion Hull. Point Enclosure: The Ray-Shooting Method. Point Enclosure: The Signed Angle Method. Line Clipping: The Cyrus-Beck Algorithm. Polygon Clipping: The Sutherland-Hodgman Algorithm. Triangulating Monotone Polygons. Chapter Notes. Exercises. 6. Incremental Selection. Selection Sort. Finding Convex Hulls: Gift-Wrapping. Finding Complex Hulls: Graham Scan. Removing Hidden Surfaces: The Depth-Sort Algorithm. Intersection of Convex Polygons. Finding Delaunay Triangulations. Chapter Notes. Exercises. 7. Plane-Sweep Algorithms. Finding the Intersections of Line Segments. Finding Convex Hulls: Insertion Hull Revisited. Contour of the Union of Rectangles. Decomposing Polygons into Monotone Pieces. Chapter Notes. Exercises. 8. Divide-and-Conquer Algorithms. Merge Sort. Computing the Intersection of Half-Planes. Finding the Kernel of a Polygon. Finding Voronoi Regions. Merge Hull. Closest Points. Polygon Triangulation. Chapter Notes. Exercises. 9. Spatial Subdivision Methods. The Range Searching Problem. The Grid Method. Quadtrees. Two-Dimensional Search Trees. Removing Hidden Surfaces: Binary Space Partition Trees. Chapter Notes. Exercises. Bibliography. Index.

Bounding box and projections detection of hidden polygons in three-dimensional spatial databases

Abstract: An image is generated from a database of three-dimensional object data where each the objects is formed from at least one polygon having at least one edge. Successively determinations are made as to whether a particular one of the object polygons designated as the test polygon is not visible to an observer located at a predetermined location by virtue of being hidden by other objects in the database. If the test polygon is determined to be not visible, then it does not need to be rendered by an image renderer and may be discarded. The decision is made by successively selecting one of the three-dimensional object in the database. After an object is selected, each of the object polygon is selected to determining whether the polygon is occulted by another object. This determination is performed by determining the exterior region of the object as the union of bounding boxes of exterior polygons, determining the interior region of the object as the union of bounding boxes of interior polygons, and testing for overlap between the projected bounding box of the polygon and the projected bounding boxes of the exterior polygons and the projected bounding boxes of the interior polygons. The test polygon is determined to possible be visible or to be not visible based on overlaps between the projected bounding boxes of the test polygon, the interior polygons, the exterior polygons, and coordinate values. Polygons that are not visible are discarded while polygons that may be visible are retained.

The Knotting of Equilateral Polygons in R3

Abstract: It was proved in [4] that the knotting probability of a Gaussian random polygon goes to 1 as the length of the polygon goes to infinity. In this paper, we prove the same result for the equilateral random polygons in R3. More precisely, if EPn is an equilateral random polygon of n steps, then we have provided that n is large enough, where ∊ is some positive constant.

Fast Polygon Triangulation Based on Seidel's Algorithm

Abstract: Publisher Summary This chapter describes fast polygon triangulation based on Seidel's algorithm. Computing the triangulation of a polygon is a fundamental algorithm in computational geometry. In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, such as those described by splines. Methods of triangulation include algorithms, convex hull differences, and horizontal decompositions. This chapter describes an implementation based on Seidel's algorithm for triangulating simple polygons having no holes. It is an incremental randomized algorithm whose expected complexity is O(n log*n). In practice, it is almost linear time for a simple polygon having n vertices. The triangulation does not introduce any additional vertices and decomposes the polygon into n − 2 triangles. Furthermore, the algorithm generates a query structure that can be used to determine the location of a point in logarithmic time. All the data structures used in the implementation are statically allocated.

Method and apparatus for mapping texture

Abstract: In a real-time texture mapping system, a more solid and naturally-mapped image is obtained with a minimum of computation volume. The texture-mapping system adds a texture image to an area of a polygon which forms a fundamental unit of three-dimensional image information of an object to be displayed on a screen. A geometry transfer engine (GTE) 61 extracts representing points from the polygonal area. Then, coordinates of the thus extracted representing points are subjected to the perspective transformation. Thereafter, the representing points, after the perspective transformation, are subjected to the linear interpolation in a graphic processing unit (GPU) 62 so that the image is formed.

Voronoi diagrams for planar shapes

Abstract: Although many algorithms compute Voronoi diagrams for polygons, few do so for shapes bounded by arbitrary closed curves. The paper presents an algorithm which does this. It also traces the diagrams directly from their differential properties. >

Searching for a Mobile Intruder in a Corridor - The Open Edge Variant of the Polygon Search Problem

Abstract: The polygon search problem is the problem of searching for mobile intruders in a simple polygon by a single mobile searcher having various degrees of visibility. This paper considers the “open edge” variant of the problem in which the given polygon P must be searched without allowing undetected intruders to reach a given edge u, under an additional assumption that any number of intruders can leave and enter P through another edge v at any time. One may view P as representing a corridor with two open exits u and v, and the task of the searcher is to force all the intruders out of P through v (but not u). We present a simple necessary condition for a polygon to be searchable in this manner by the searcher having a light bulb, and then show that the same condition is sufficient for the polygon to be searchable by the searcher having two flashlights. The time complexity of generating a search schedule is also discussed.

Evolutions of planar polygons

Abstract: Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygo nal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the well-known Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.

Robot navigation in unknown generalized polygonal terrains using vision sensors

Abstract: This paper considers the problem of navigating a point robot in an unknown two-dimensional terrain populated by disjoint generalized polygonal obstacles. A generalized polygon consists of a connected sequence of circular arcs and straight-line segments. The terrain model is not known a priori, but the robot is equipped with a vision sensor. A discrete vision sensor detects all visible (from a single position) portions of the obstacle boundaries in a single scan operation. The navigation problem deals with moving the robot through the terrain from a source position to a destination position, and the terrain model acquisition problem deals with autonomously building a model of the terrain. A complete solution to either problem is shown to require an infinite number of scan operations in cusp regions formed by a pair of convex and concave obstacle edges. Either problem is considered solved with a precision /spl epsiv/ if the points that have not been scanned are those in a cusp region with a clearance less than /spl epsiv/ from two obstacle edges. Three methods are proposed to solve both problems with a precision /spl epsiv/ based on extensions of the generalized visibility graph, the generalized Voronoi diagram, and the trapezoidal decomposition. Then simplified versions of these structures are proposed to exactly solve the navigation and terrain model acquisition problems using a continuous vision sensor that detects all visible obstacle boundaries as the robot navigates along a path. >

Shape model generation device for generating shape models with a reduced number of polygons while maintaining quality of the two-dimensional image of the generated shape models

Abstract: An image generation system having a shape model generation device for generating a set of polygons which approximates a given solid having a curved surface and output vertex coordinates of each polygon in a screen coordinate system. An image generation device is provided for generating images for each polygon on receiving the vertex coordinates, and an image display device displays the generated images. The shape model generation device divides the solid into a set of polygons in a virtual-space, where the number of polygons used for dividing the solid into polygons is minimized while maintaining a high-quality display image. The set of polygons are projected onto a screen based on a designated view point and direction in the virtual-space, and the vertex coordinates of each polygon is transformed into two-dimensional screen coordinates. An edge judgment unit is provided in the shape model generation device for judging whether any side of each screen-projected polygon constitutes a part of an outline of the set of screen-projected polygons. An edge change unit in the shape model generation device generates a new vertex in the virtual-space on any side which constitutes a part of the outline, and the coordinates of the new vertex are transformed into two-dimensional screen coordinates. A polygon division unit is provided for dividing a screen-projected polygon including any side which constitutes a part of the outline into smaller screen-projected polygons at the new vertex.

Three-dimensional sound system

Abstract: An object incorporated in image data is formed with a plurality of polygons. An object table defines each polygon by means of coordinates at an apex in a view coordinate system and the sound generated from the polygon. The sound source processor unit controls sound to be generated from each polygon according to the position and direction of the polygon when the object is viewed from a viewpoint.

Generating multiple levels of detail from polygonal geometry models

Abstract: This paper presents a new method for solving the following problem: Given a polygonal model of some geometric object generate several more and more approximative representations of this object containing less and less polygons. The idea behind the method is that small detail in the model is represented by many spatially close points. A hierarchical clustering algorithm is used to generate a hierarchy of clusters from the vertices of the object’s polygons. The coarser the approximation the more points are found to lie within one cluster of points. Each cluster is replaced by one representative point and polygons are reconstructed from these points. A static detail elision algorithm was implemented to prove the practicability of the method. This paper shows examples of approximations generated from different geometry models, pictures of scenes rendered by a detail elision algorithm and timings of the method at work.

Searching for the kernel of a polygon—a competitive strategy

Abstract: We present a competitive strategy for walking into the kernel of an initially unknown star-shaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to the closest kernel point, k, whose length does not exceed 5:3331...times the distance from s to k. This is complemented by a general lower bound of v2. Our analysis relies on a result about a new and interesting class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. We show a tight upper bound of 5:3331... for the length of a self-approaching curve over the distance between its endpoints.

An Optimal Algorithm for Computing Visibility in the Plane

Abstract: The authors give an algorithm to compute the visibility polygon from a point among a set of $h$ pairwise-disjoint polygonal obstacles with a total of $n$ vertices. Our algorithm uses $O(n)$ space and runs in optimal time $\Theta(n+h\log h)$, improving the previous upper bound of $O(n\log n)$. A direct consequence of the algorithm is an $O(n+h\log h)$ time algorithm for computing the convex hull of $h$ disjoint simple polygons.

Efficient geometric algorithms on the EREW PRAM

Abstract: We present a technique that can be used to obtain efficient parallel geometric algorithms in the EREW PRAM computational model. This technique enables us to solve optimally a number of geometric problems in O(log n) time using O(n/log n) EREW PRAM processors, where n is the input size of a problem. These problems include: computing the convex hull of a set of points in the plane that are given sorted, computing the convex hull of a simple polygon, computing the common intersection of half-planes whose slopes are given sorted, finding the kernel of a simple polygon, triangulating a set of points in the plane that are given sorted, triangulating monotone polygons and star-shaped polygons, and computing the all dominating neighbors of a sequence of values. PRAM algorithms for these problems were previously known to be optimal (i.e., in O(log n) time and using O(n/log n) processors) only on the CREW PRAM, which is a stronger model than the EREW PRAM. >

Automatic generation of triangular irregular networks using greedy cuts

Abstract: Proposes a new approach to the automatic generation of triangular irregular networks (TINs) from dense terrain models. We have developed and implemented an algorithm based on the greedy principle used to compute minimum-link paths in polygons. Our algorithm works by taking greedy cuts ("bites") out of a simple closed polygon that bounds the yet-to-be triangulated region. The algorithm starts with a large polygon, bounding the whole extent of the terrain to be triangulated, and works its way inward, performing at each step one of three basic operations: ear cutting, greedy biting, and edge splitting. We give experimental evidence that our method is competitive with current algorithms and has the potential to be faster and to generate many fewer triangles. Also, it is able to keep the structural terrain fidelity at almost no extra cost in running time and it requires very little memory beyond that for the input height array.

Competitive Searching in Polygons - Beyond Generalised Streets

Abstract: We consider a robot inside an unknown polygon P which has to find a path from a starting point s to a target point t. It is equipped with on-board cameras through which it can get the visibility map of its immediate surroundings. We define two new classes of polygons and provide strategies for searching these classes of polygons.

Texture Mapping as an Alternative for Meshing During Walkthrough Animation

Abstract: Mesh-based radiosity calculation requires many mesh elements to reconstruct subtle details of shading. On the other hand, the excessive number of polygons slows down rendering, impairing the sensation of interactivity when a user-navigated walkthrough in complex environment is performed. When distribution of illumination over a scene is to be quickly rendered, then the Gouraud shaded polygon becomes an inefficient drawing primitive, which can be successfully replaced by texture mapping.