Showing papers on "Polygon published in 2000"

Relief texture mapping

Abstract: We present an extension to texture mapping that supports the representation of 3-D surface details and view motion parallax. The results are correct for viewpoints that are static or moving, far away or nearby. Our approach is very simple: a relief texture (texture extended with an orthogonal displacement per texel) is mapped onto a polygon using a two-step process: First, it is converted into an ordinary texture using a surprisingly simple 1-D forward transform. The resulting texture is then mapped onto the polygon using standard texture mapping. The 1-D warping functions work in texture coordinates to handle the parallax and visibility changes that result from the 3-D shape of the displacement surface. The subsequent texture-mapping operation handles the transformation from texture to screen coordinates.

Face fixer: compressing polygon meshes with properties

Abstract: Most schemes to compress the topology of a surface mesh have been developed for the lowest common denominator: triangulated meshes. We propose a scheme that handles the topology of arbitrary polygon meshes. It encodes meshes directly in their polygonal representation and extends to capture face groupings in a natural way. Avoiding the triangulation step we reduce the storage costs for typical polygon models that have group structures and property data.

Computing n-Finger Form-Closure Grasps on Polygonal Objects

Abstract: This paper presents an efficient algorithm for computing all n-finger form-closure grasps on a polygonal object based on a new sufficient and necessary condition for form-closure. With this new condition, it is possible to transfer the problem of computing the form-closure grasp in R{sup 3} to one in R{sup 1}. The author demonstrates that the non-form-closure grasps consist of two convex polytopes in the space of n parameters representing grasp points on sides of the polygon. The proposed algorithm works efficiently for n {le} and takes O(n{sup 3n/2})time for n > 3, where n denotes the number of the fingers. The algorithm has been implemented and its efficiency has been confirmed with two examples.

Shadow volume reconstruction from depth maps

Abstract: Current graphics hardware can be used to generate shadows using either the shadow volume or shadow map techniques. However, the shadow volume technique requires access to a representation of the scence as a polygonal model, and handling the near plane clip correctly and efficiently is difficult; conversely, accurate shadow maps require high-precision texture map data representations, but these are not widely supported.We present a hybird of the shadow map and shadow volume approaches which does not have these difficulties and leverages high-performance polygon rendering. The scene is rendered from the point of view of the light source and a sampled depth map is recovered. Edge detection and a template-based reconstruction technique are used to generate a global shadow volume boundary surface, after which the pixels in shadow can be marked using only a one-bit stencil buffer and a single-pass rendering of the shadow volume boundary polygons. The simple form of our template-based reconstruction scheme simplifies capping the shadow volume after the near plane clip.

A Fast Algorithm for Computing the Closest Point and Distance Transform

Abstract: This paper presents a new algorithm for computing the closest point transform to a manifold on a rectilinear grid in low dimensional spaces. The closest point transform finds the closest point on a manifold and the Euclidean distance to a manifold for all the points in a grid, (or the grid points within a specified distance of the manifold). We consider manifolds composed of simple geometric shapes, such as, a set of points, piecewise linear curves or triangle meshes. The algorithm computes the closest point on and distance to the manifold by solving the Eikonal equation |∇u| = 1 by the method of characteristics. The method of characteristics is implemented efficiently with the aid of computational geometry and polygon/polyhedron scan conversion. The computed distance is accurate to within machine precision. The computational complexity of the algorithm is linear in both the number of grid points and the complexity of the manifold. Thus it has optimal computational complexity. Examples are presented for piecewise linear curves in 2D and triangle meshes in 3D. 1 The Closest Point Transform Let u(x), x ∈ R, be the distance from the point x to a manifold S. If dim(S) = n − 1, (for example curves in 2D or surfaces in 3D), then the distance is signed. The orientation of the manifold determines the sign of the distance. One can adopt the convention that the outward normals point in the direction of positive or negative distance. In order for the distance to be well-defined, the manifold must be orientable and have a consistent orientation. A Klein bottle in 3D for example is not orientable. Two concentric circles in 2D have consistent orientations only if the normals of the inner circle point “inward” and the normals of the outer circle point “outward”, or vice-versa. Otherwise the distance would be ill-defined in the region between the circles. For manifolds which are not closed, the distance is ill-defined in any neighborhood of the boundary. However, the distance is well-defined in neighborhoods of the manifold which do not contain the boundary. If dim(S) < n− 1, (for example a set of points in 2D or a curve in 3D), the distance is unsigned, (non-negative).

Geometry and origin of a polygonal fault system

Abstract: A fault array in South Australia, interpreted from a 3D onshore seismic survey, shows fault traces on the lowermost mapped horizon of a shale‐dominated sequence which outline polygonal cells averaging 1.4 km in diameter. The cell boundaries coincide approximately with the downward terminations and near convergence of conjugate pairs of normal faults. The pattern becomes less spatially ordered on higher horizons where faults still show a near‐isotropic strike distribution. Maximum throws, c. 80 m, occur c. 400 m above the downward terminations of the faults. The faults have a systematic geometric relationship with folds, with anticlines in the mutual hanging walls of fault pairs and broader footwall synclines that define the shallow dish forms of the polygons. Polygon boundaries coincide with anticlinal ridges on the interface between the faulted sequence and an underlying 35 m thick low velocity, low density, overpressured layer. Although the pattern of ridges defining the polygon boundaries is strikingly similar to experimental spoke and hub patterns formed at the boundaries between viscous materials with density inversion, the data do not exclude the possibility of lateral extension.

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 camera position by rendering the scene. Pixels in 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.

Interactive motion planning using hardware-accelerated computation of generalized Voronoi diagrams

Abstract: We present techniques for fast motion planning by using discrete approximations of generalized Voronoi diagrams, computed with graphics hardware. Approaches based on this diagram computation are applicable to both static and dynamic environments of fairly high complexity. We compute a discrete Voronoi diagram by rendering a 3D distance mesh for each Voronoi site. The sites can be points, line segments, polygons, polyhedra, curves and surfaces. The computation of the generalized Voronoi diagram provides fast proximity query toolkits for motion planning. The tools provide the distance to the nearest obstacle stored in the Z-buffer, as well as the Voronoi boundaries, Voronoi vertices and weighted Voronoi graphs extracted from the frame buffer using continuation methods. We have implemented these algorithms and demonstrated their performance for path planning in a complex dynamic environment composed of more than 140,000 polygons.

Consistent queries over cardinal directions across different levels of detail

Abstract: Current models for cardinal directions, such as north and northeast, are either point-based or region-based, but no models exist that apply equally, independent of the geometric data types (be it points, lines, or polygons). To allow users to formulate queries such as "Find all towns in Maine that are northeast of Augusta" without pondering about the cities' geometric data types, we extend the model of the model of the direction-relation matrix to handle arbitrary pairs of points, lines, and polygons. This new model, called the deep direction-relation matrix, retains the 3/spl times/3 structure of the direction-relation matrix with empty and non-empty tiles, while it records additionally neighbor codes for empty tiles to capture whether the tiles' boundaries are empty or not. This extension covers all intricacies imposed by line and point objects, yielding a unifying and consistent model for cardinal directions. It enables the use of cardinal directions in spatial query languages independent of the objects' geometric data types.

Device and method for creating and using data on road map expressed by polygons

Abstract: Data on roads and intersections expressed by polygons properly agreeing with the complex shapes of roads on a city map is automatically created. In a simple polygon forming processing (3), the line segments of road network data (2) where the roads are modeled to line segments are expanded in the direction of the road width, and simple road polygon data (4) on roads having widths a little thicker than those of the road widths of city map data (5). In a scissors data creating processing (6), shape lines near roads are connected from the city map data (5), and thereby scissors data (7) defining the outlines of roads is created. In a road polygon creating processing (9), simple road polygons are trimmed along the road outlines, and road polygon data (9) well agreeing with the road shapes on the city map data is created.

Proximity correction software for wafer lithography

Abstract: A system for computing a pattern function for a polygonal pattern having a finite number of predetermined face angles. One method includes the steps of decomposing the polygon into a set of flashes, computing the pattern function by summing together all flashes evaluated at a point (x,y), and the pattern function returning a 1 if point (x,y) is inside a polygon and otherwise will return a 0. Another method for computing a two-dimensional convolution value for any point (x,y) on a polygonal pattern includes the steps of identifying a set of half-plane basis functions corresponding to each face angle of the polygonal pattern, convolving each half-plane basis function with a convolution kernel using integration to find convolved flash (cflash) x,y values, storing the cflash (x,y) values to a two-dimensional look-up table, decomposing the polygonal pattern into a set of flashes where each of the flashes is an instance of the half-plane basis functions, and computing a convolution value for point (x,y) by looking-up a corresponding cflash x,y value for each flash in the table and summing together the corresponding cflash x,y values. The present invention may be used in a method for determining correction steps to which a design layout is to be subjected during wafer proximity correction.

Newton polygons and formal groups: Conjectures by Manin and Grothendieck.

Abstract: We consider p-divisible groups (also called Barsotti-Tate groups) in characteristic p, their deformations, and we draw some conclusions. For such a group we can define its Newton polygon (abbreviated NP). This is invariant under isogeny. For an abelian variety (in characteristic p) the Newton polygon of its p-divisible group is "symmetric". In 1963 Manin conjectured that conversely any symmetric Newton polygon is "algebroid"; i.e., it is the Newton polygon of an abelian variety. This conjecture was shown to be true and was proved with the help of the "HondaSerre-Tate theory". We give another proof in Section 5. Grothendieck showed that Newton polygons "go up" under specialization: no point of the Newton polygon of a closed fiber in a family is below the Newton polygon of the generic fiber. In 1970 Grothendieck conjectured the converse: any pair of comparable Newton polygons appear for the generic and special fiber of a family. This was extended by Koblitz in 1975 to a conjecture about a sequence of comparable Newton polygons. In Section 6 we show these conjectures to be true. These results are obtained by deforming the most special abelian varieties or p-divisible groups we can think of. In describing deformations we use the theory of displays; this was proposed by Mumford, and has been developed in [17], [18], and recently elaborated in [32] and [33]; also see [11], [31]. Having described a deformation we like to read off the Newton polygon of the generic fiber. In most cases it is difficult to determine the Newton polygon from the matrix defined by F on a basis for the (deformed) Dieudonne module. In general I have no procedure to do this (e.g. in case we deform away from a formal group where the Dieudonne module is not generated by one element). However in the special case we consider here, a(Go) = 1, a noncommutative version of the theorem of Cayley-Hamilton ("every matrix satisfies its own

Interactive Vegetation Rendering with Slicing and Blending

Abstract: Detailed and interactive 3D rendering of vegetation is one of the challenges of traditional polygon-oriented computer graphics, due to large geometric complexity even of simple plants. In this paper we introduce a simplified image-based rendering approach based solely on alpha-blended textured polygons. The simplification is based on the limitations of human perception of complex geometry. Our approach renders dozens of detailed trees in real-time with off-the-shelf hardware, while providing significantly improved image quality over existing real-time techniques. The method is based on using ordinary mesh-based rendering for the solid parts of a tree, its trunk and limbs. The sparse parts of a tree, its twigs and leaves, are instead represented with a set of slices, an imagebased representation. A slice is a planar layer, represented with an ordinary alpha or color-keyed texture; a set of parallel slices is a slicing. Rendering from an arbitrary viewpoint in a 360 degree circle around the center of a tree is achieved by blending between the nearest two slicings. In our implementation, only 6 slicings with 5 slices each are sufficient to visualize a tree for a moving or stationary observer with the perceptually similar quality as the original model.

Accurate estimation of the cost of spatial selections

Abstract: Optimizing queries that involve operations on spatial data requires estimating the selectivity and cost of these operations. In this paper, we focus on estimating the cost of spatial selections, or window queries, where the query windows and data objects are general polygons. Cost estimation techniques previously proposed in the literature only handle rectangular query windows over rectangular data objects, thus ignoring the very significant cost of exact geometry comparison (the refinement step in a "filter and refine" query processing strategy). The cost of the exact geometry comparison depends on the selectivity of the filtering step and the average number of vertices in the candidate objects identified by this step. In this paper, we introduce a new type of histogram for spatial data that captures the complexity and size of the spatial objects as well as their location. Capturing these attributes makes this type of histogram useful for accurate estimation, as we experimentally demonstrate. We also investigate sampling-based estimation approaches. Sampling can yield better selectivity estimates than histograms for polygon data, but at the high cost of performing exact geometry comparisons for all the sampled objects.

Tiled polygon traversal using half-plane edge functions

Abstract: Existing techniques for traversing a polygon generate fragments one (or more) rows or columns at a time. (A fragment is all the information needed to paint one pixel of the polygon.) This order is non-optimal for many operations. For example, most frame buffers are tiled into rectangular pages, and there is a cost associated with accessing a different page. Pixel processing is more efficient if all fragments of a polygon on one page are generated before any fragments on a different page. Similarly, texture caches have reduced miss rates if fragments are generated in tiles (and even tiles of tiles) whose size depends upon the cache organization.We describe a polygon traversal algorithm that generates fragments in a tiled fashion. That is, it generates all fragments of a polygon within a rectangle (tile) before generating any fragments in another rectangle. For a single level of tiling, our algorithm requires one additional saved context (the values of all interpolator accumulators, such as Z depth, Red, Green, Blue, etc.) over a traditional traversal algorithm based upon half-plane edge functions. An additional level of tiling requires another saved context for the special case of rectangle copies, or three more for the general case. We describe how to use this algorithm to generate fragments in an optimal order for several common scenarios.

Accelerating time-varying hardware volume rendering using TSP trees and color-based error metrics

Abstract: This paper describes a new hardware volume rendering algorithm for time-varying data. The algorithm uses the Time-Space Partitioning (TSP) tree data structure to identify regions within the data that have spatial or temporal coherence. By using this coherence, the rendering algorithm can improve performance when the volume data are larger than the texture memory capacity by decreasing the amount of textures required. This coherence can also allow improved speed by appropriately rendering flat-shaded polygons instead of textured polygons, and by not rendering transparent regions. To reduce the polygonization overhead caused by the use of the hierarchical data structure, we use a fast incremental polygon slicing algorithm. The paper also introduces new color-based error metrics, which more accurately identify coherent regions compared to the earlier scalar-based metrics. By showing experimental results from runs using different data sets and error metrics, we demonstrate that the new methods give substantial improvements in volume rendering performance.

Perceptual Issues in Substituting Texture for Geometry

Abstract: An important goal in interactive computer graphics is to allow the user to interact dynamically with three-dimensional objects. The computing resources required to represent, transmit and display a three dimensional object depends on the number of polygons used to represent it. Many geometric simplification algorithms have been developed to represent the geometry with as few polygons as possible, without substantially changing the appearance of the rendered object. A popular method for achieving geometric simplification is to replace fine scale geometric detail with texture images mapped onto the simplified geometry. However the effectiveness of replacing geometry with texture has not been explored experimentally. In this paper we describe a visual experiment in which we examine the perceived quality of various representations of textured, geometric objects, viewed under direct and oblique illumination. We used a pair of simple large scale objects with different fine-scale geometric detail. For each object we generated many representations, varying the resources allocated to geometry and texture. The experimental results show that while replacing geometry with texture can be very effective, in some cases the addition of texture does not improve perceived quality, and can sometimes reduce the perceived quality.

Method and apparatus for providing a vertex cache

Abstract: A method for caching data defining vertices of a polygon to be displayed by an input/output display device including the steps of providing an index by a vertex for which data is to be cached, storing data defining attributes of a polygon at a vertex in a cache under the index provided, issuing a command signifying a polygon to be manipulated by indicating indices of the vertices of the polygon for which data is cached.

A positivity property of the Satake isomorphism

Abstract: Let G be an unramified reductive group over a local field. We consider the matrix describing the Satake isomorphism in terms of the natural bases of the source and the target. We prove that all coefficients of this matrix which are not obviously zero are in fact positive numbers. The result is then applied to an existence problem of F-crystals which is a partial converse to Mazur's theorem relating the Hodge polygon and the Newton polygon.

Searching a polygonal room with one door by a 1-searcher

Abstract: The 1-searcher is a mobile guard whose visibility is limited to a ray emanating from his position, where the direction of the ray can be changed continuously with bounded angular rotation speed. Given a polygonal region with a specified boundary point d, is it possible for a 1-searcher to eventually see a mobile intruder that is arbitrarily faster than the searcher within , before the intruder reaches d? We decide this question in O (n log n)-time for an n-sided polygon. Our main result is a simple characterization of the class of polygons (with a boundary point d) that admits such a search strategy. We also present a simple O(n2)-time algorithm for constructing a search schedule, if one exists. Finally, we compare the search capability of a 1-searcher with that of two guards.

Color image forming device

Abstract: An intermediate belt made of an endless belt is provided by 45 degrees inclined horizontally and looped over two rollers at both its ends, and four photosensitive drums are provided in contact with the top surface of this intermediate belt A reflection mirror is provided over each photosensitive drum, and a single polygon mirror is provided on almost the same level as these reflection mirrors The polygon mirror is provided on the side of the reflection mirror of which optical path to the corresponding photosensitive drum is the longest so that the optical path lengths from the polygon mirror to the respective photosensitive drums are equal to each other

Image processing apparatus

Abstract: In a controller, a three-dimensional shape defined by at least one polygon is set on the basis of a signal from an input unit, and in a three-dimensional rendering unit, a three-dimensional image corresponding to the three-dimensional shape is rendered on the basis of a vertex of the polygon forming the three-dimensional shape, a pixel value at the vertex, and the like. The three-dimensional image is outputted as a key signal to a mixing unit for mixing images. Thus, various key signals are generated at high speed.

Method and apparatus for reducing three-dimensional shape data

Abstract: A method and apparatus for reducing three-dimensional shape data, includes calculating estimation values for portions to be deformed by converging two or more vertices of a polygon model, and reducing the number of data for the polygon model by converging two or more vertices of the polygon model when the estimation values are equal to or below the predetermined permissible value. Estimation values for surfaces to be deformed by shrinking edges or surfaces are calculated based on distances between the respective surfaces and all the original vertices involved in the surface deformation. Before each data reduction, the portion having been involved in all the previous data reductions is defined as a reduction prohibition area, and a succeeding data reduction is applied to a portion other than the reduction prohibition area.

On the Structure of Multiple Translational Tilings by Polygonal Regions

Abstract: We consider polygons with the following ``pairing property'': for each edge of the polygon there is precisely one other edge parallel to it. We study the problem of when such a polygon K tiles multiply the plane when translated at the locations Λ , where Λ is a multiset in the plane. The pairing property of K makes this question particularly amenable to Fourier analysis. As a first application of our approach we establish a necessary and sufficient condition for K to tile with a given lattice Λ . (This was first found by Bolle for the case of convex polygons—notice that all convex polygons that tile, necessarily have the pairing property and, therefore, our theorems apply to them.) Our main result is a proof that a large class of such polygons tile multiply only quasi-periodically, which for us means that Λ must be a finite union of translated two-dimensional lattices in the plane. For the particular case of convex polygons we show that all convex polygons which are not parallelograms tile multiply only quasi-periodically, if at all.

A novel approach in the determination of visible surfaces in 3D vector geometries for ray-optical wave propagation modelling

Abstract: Image theory as a ray-tracing method is a well known but cumbersome tool for propagation modelling. A promising way to enhance its efficiency is a prior reduction of complexity of the scenario under consideration. Only the visible surfaces from the receiver and transmitter locations are potential ray interceptors. Thus, only they have to be subject to the imaging algorithm. The determination of the visible surfaces is discussed. The proposed algorithm is based on a successive dimensional reduction of the problem. In the first step the whole 3D scenario is projected perspectively in several 2D planes. The spatial information is hereby preserved. The resulting 2D polygons, which represent the surfaces, are tested for overlap. This is efficiently done by applying a sweep-line algorithm. With the knowledge of the relative surface positions a graph theory based polygon subtraction is applied to determine the visible surfaces. An inverse projection into 3D space yields the actual visible 3D polygons.

On Simple Polygonalizations with Optimal Area

Abstract: We discuss the problem of finding a simple polygonalization for a given set of vertices P that has optimal area. We show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P and prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given vertex set, resulting in a proof of NP-completeness for the corresponding area optimization problems. This answers a generalization of a question stated by Suri in 1989. Finally, we turn to higher dimensions, where we prove that, for 1 \(\leq\)kd , 2 \(\leq\)d , it is NP-hard to determine the smallest possible total volume of the k -dimensional faces of a d -dimensional simple nondegenerate polyhedron with a given vertex set, answering a generalization of a question stated by O'Rourke in 1980.