Showing papers on "Polygon published in 2001"

A developer's survey of polygonal simplification algorithms

Abstract: Polygonal models currently dominate interactive computer graphics. This is chiefly because of their mathematical simplicity: polygonal models lend themselves to simple, regular rendering algorithms that embed well in hardware, which has in turn led to widely available polygon rendering accelerators for every platform. Unfortunately, the complexity of these models, which is measured by the number of polygons, seems to grow faster than the ability of our graphics hardware to render them interactively. Put another way, the number of polygons we want always seems to exceed the number of polygons we can afford. Polygonal simplification techniques offer one solution for developers grappling with complex models. These methods simplify the polygonal geometry of small, distant, or otherwise unimportant portions of the model, seeking to reduce the rendering cost without a significant loss in the scene's visual content. The article surveys polygonal simplification algorithms, identifies the issues in picking an algorithm, relates the strengths and weaknesses of different approaches, and describes several published algorithms.

Tools for 3D-object retrieval: Karhunen-Loeve transform and spherical harmonics

Abstract: We present tools for 3D object retrieval in which a model, a polygonal mesh, serves as a query and similar objects are retrieved from a collection of 3D objects. Algorithms proceed first by a normalization step (pose estimation) in which models are transformed into a canonical coordinate frame. Second, feature vectors are extracted and compared with those derived from normalized models in the search space. Using a metric in the feature vector space nearest neighbors are computed and ranked. Objects thus retrieved are displayed for inspection, selection, and processing. For the pose estimation we introduce a modified Karhunen-Loeve transform that takes into account not only vertices or polygon centroids from the 3D models but all points in the polygons of the objects. Some feature vectors can be regarded as samples of functions on the 2-sphere. We use Fourier expansions of these functions as uniform representations allowing embedded multi-resolution feature vectors. Our implementation demonstrates and visualizes these tools.

The point in polygon problem for arbitrary polygons

Abstract: A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even–odd ruleand the winding number, the former leading to ray-crossing, the latter to angle summationalgorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algorithm for determining the winding number. Then we examine how to accelerate this algorithm and how to handle special cases. Furthermore we compare these algorithms with those found in literature and discuss the results.  2001 Elsevier Science B.V. All rights reserved.

Inapproximability Results for Guarding Polygons and Terrains

Abstract: Past research on art gallery problems has concentrated almost exclusively on bounds on the numbers of guards needed in the worst case in various settings. On the complexity side, fewer results are available. For instance, it has long been known that placing a smallest number of guards for a given input polygon is NP -hard. In this paper we initiate the study of the approximability of several types of art gallery problems.

Hierarchical fuzzy pattern matching for the regional comparison of land use maps

Abstract: The evaluation of the spatial similarities and land use change between two raster maps is traditionally based on pixel-by-pixel comparison techniques. However, a pixel-by-pixel comparison can register a small displacement in pixels as land use disagreement even though the land use patterns may be essentially the same. The techniques of unique polygons mapping and hierarchical fuzzy pattern matching, where the maps are compared on both a local and global level, are combined to provide a more robust alternative approach. Local matchings determine the degree of containment of each unique polygon in the template map in terms of fuzzy areal intersections. Formally, the local agreement values are based on polygon property containments and are calculated from a fuzzy logical Max-Min compositional algorithm. A global agreement value is derived by the fuzzy summation of the local matchings. The uses of these basic methods are discussed and further refinements and modelling possibilities are outlined.

Image processing device, image processing method and recording medium

Abstract: In an image processing device composed such that it can display a prescribed object whilst changing the shape of the object. Furthermore, the image processing device includes a first memory for recording information for first polygons which form the object; a second memory for recording information for second polygons that form the object and are linked to the first polygons; and when the shape of the object is changed, the shapes of the second polygons are changed such that no gaps are produced between the first polygons and the second polygons. Using computer graphics in a video game it is possible to achieve a more realistic object representation, wherein joint regions move in a natural manner.

Detailed Shape Representation with Parallax Mapping

Abstract: Although texture mapping is a common technique for adding apparent surface detail to 3-D objects, it lacks the capability to represent the motion parallax effect. So the mesh to which it is applied limits its realism. In this paper, we propose Parallax Mapping, a simple method to motion parallax effects on a polygon. This method has very fast per-pixel shape representation and can be performed in real-time with current hardware.

Sub-pixel land cover mapping for per-field classification

Abstract: A method was developed to transform a soft land cover classification into hard land cover classes at the sub-pixel scale for subsequent per-field classification. First, image pixels were segmented using vector boundaries. Second, the pixel segments (ranked by area) were labelled with a land cover class (ranked by class typicality). Third, a hard per-field classification was generated by examining each polygon (representing a land cover parcel, or field) in its entirety (by grouping the fragments of the polygon contained within different image pixels) and assigning to it the modal land cover class. The accuracy of this technique was considerably higher than that of both a corresponding hard per-pixel classification and a perfield classification based on hard per-pixel classified imagery.

Cutting and stitching: converting sets of polygons to manifold surfaces

Abstract: Many real-world polygonal surfaces contain topological singularities that represent a challenge for processes such as simplification, compression, and smoothing. We present an algorithm that removes singularities from nonmanifold sets of polygons to create manifold (optionally oriented) polygonal surfaces. We identify singular vertices and edges, multiply singular vertices, and cut through singular edges. In an optional stitching operation, we maintain the surface as a manifold while joining boundary edges. We present two different edge stitching strategies, called pinching and snapping. Our algorithm manipulates the surface topology and ignores physical coordinates. Except for the optional stitching, the algorithm has a linear complexity and requires no floating point operations. In addition to introducing new algorithms, we expose the complexity (and pitfalls) associated with stitching. Finally, several real-world examples are studied.

Visibility-Based Pursuit-Evasion in a Polygonal Region by a Searcher

Abstract: We consider the most basic visibility-based pursuit-evasion problem defined as follows: Given a polygonal region, a searcher with 360° vision, and an unpredictable intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In this paper, we present simple necessary and sufficient conditions for a polygon to be searchable, which settles a decade-old open problem raised in [13]. We also show that every searchable polygon is also searchable by a searcher with two flashlights (that is, two ray visions). This implies, combined with the previous work [7], that there is an O(n2)-time algorithm for constructing a search path for an n-sided polygon.

Hybrid simplification: combining multi-resolution polygon and point rendering

Abstract: Multi-resolution hierarchies of polygons and more recently of points are familiar and useful tools for achieving interactive rendering rates. We present an algorithm for tightly integrating the two into a single hierarchical data structure. The trade-off between rendering portions of a model with points or with polygons is made automatically. Our approach to this problem is to apply a bottom-up simplification process involving not only polygon simplification operations, but point replacement and point simplification operations as well. Given one or more surface meshes, our algorithm produces a hybrid hierarchy comprising both polygon and point primitives. This hierarchy may be optimized according to the relative performance characteristics of these primitive types on the intended rendering platform. We also provide a range of aggressiveness for performing point replacement operations. The most conservative approach produces a hierarchy that is better than a purely polygonal hierarchy in some places, and roughly equal in others. A less conservative approach can trade reduced complexity at the far viewing ranges for some increased complexity at the near viewing ranges. We demonstrate our approach on a number of input models, achieving primitive counts that are 1.3 to 4.7 times smaller than those of triangle-only simplification.

System for identifying clusters in scatter plots using smoothed polygons with optimal boundaries

Abstract: An apparatus and method for identifying clusters in two-dimensional data by generating a two-dimensional histogram characterized by a grid of bins, determining a density estimate based on the bins, and identifying at least one cluster in the data. A smoothed density estimate is generated using a Gaussian kernel estimator algorithm. Clusters are identified by locating peaks and valleys in the density estimate (e.g., by comparing slope of adjacent bins). Boundaries (e.g., polygons) around clusters are identified using bins after bins are identified as being associated with a cluster. Boundaries can be simplified (e.g., by reducing the number of vertices in a polygon) to facilitate data manipulation.

Hardware support for non-photorealistic rendering

Abstract: Special features such as ridges, valleys and silhouettes, of a polygonal scene are usually displayed by explicitly identifying and then rendering `edges' for the corresponding geometry. The candidate edges are identified using the connectivity information, which requires preprocessing of the data. We present a non-obvious but surprisingly simple to implement technique to render such features without connectivity information or preprocessing. At the hardware level, based only on the vertices of a given flat polygon, we introduce new polygons, with appropriate color, shape and orientation, so that they eventually appear as special features.

Method and system for high performance computer-generated virtual environments

Abstract: A computer system and computer-implemented method for rendering images in real-time with a three-dimensional appearance. Using a database including at least one pair of texture maps uses as a stereo pair behind a portal to simulate a scene. An input database can be processed to generate a processed database by performing texture mapping to replace at least one portion of the input data representing a view (or object) by data indicative of a pair of texture maps and an associated polygon or polygons. One of the texture maps represents the view (object) from a left-eye viewpoint; the other represents the view (object) from a right-eye viewpoint. In some embodiments, to generate the texture map pairs, the input database analyzed to produce the images. In other embodiments the images are from photographs or other sources.

FIST: Fast Industrial-Strength Triangulation of Polygons

Abstract: We discuss a triangulation algorithm that is based on repeatedly clipping ears of a polygon. The main focus of our work was on designing and engineering an algorithm that is (1) completely reliable, (2) easy to implement, and (3) fast in practice. The algorithm was implemented in ANSI C, based on floating-point arithmetic. Due to a series of heuristics that get applied as a back-up for the standard ear-clipping process if the code detects deficiencies in the input polygon, our triangulation code can handle any type of polygonal input data, be it simple or not. Based on our implementation we report on different strategies (geometric hashing, bounding-volume trees) for speeding up the ear-clipping process in practice. The code has been tuned accordingly, and cpu-time statistics document that it tends to be faster than other popular triangulation codes. All engineering details that ensure the reliability and efficiency of the triangulation code are described in full detail. We also report experimental data on how different strategies for avoiding sliver triangles affect the cpu-time consumption of the algorithm. Our code, named FIST as an acronym for fast industrial-strength triangulation, forms the core of a package for triangulating the faces of three-dimensional polyhedra, and it has been successfully incorporated into several industrial graphics packages, including an implementation for Java 3D by Sun Microsystems.

Incremental and hierarchical Hilbert order edge equation polygon rasterizatione

Abstract: A rasterization algorithm must efficiently generate pixel fragments from geometric descriptions of primitives. In order to accomplish per-pixel shading, shading parameters must also be interpolated across the primitive in a perspective-correct manner. If some of these parameters are to be interpreted in later stages of the pipeline directly or indirectly as texture coordinates, then translating spatial and parametric coherence into temporal coherence will improve texture cache performance. Finally, if framebuffer access is also organized around cached blocks, then organizing rasterization so fragments are generated in block-sequential order will maximize framebuffer cache performance. Hilbert-order rasterization accomplishes these goals, and also permits efficient incremental evaluation of edge and interpolation equations.

Texture information assignment method, object extraction method, three-dimensional model generating method, and apparatus thereof

Abstract: The present method represents a three-dimensional shape model by polygons according to a plurality of object images information picked up by rotating a real object for every arbitrary angle to assign texture information on each polygon from object image information having the largest projection area of the relevant polygon. In order to improve the color continuity between adjacent polygons, the object image information having correspondence between a polygon of interest and an adjacent polygon thereof is selected so as to be the object image information approximating the shooting position and the shooting direction. An alternative method divides an object image into a plurality of regions, obtains difference between an object image and a background image in region level, outputs a mean value of the absolute value of difference in the region level, and detects the region having the mean value of absolute values of difference equal to or greater than a threshold value as the object portion. Another further method obtains a plurality of object images by shooting only a background of an object of interest and by shooting the object of interest during each rotation. A silhouette image is generated by carrying out a difference process between the object image and the background image. A voting process is carried out on the voxel space on the basis of the silhouette image. A polygon is generated according to the three-dimensional shape obtained by the voting process. The texture obtained from the object image is mapped to the polygon.

Destination input method in navigation system and navigation system

Abstract: When specifying a Point of Interest (POI) as a destination in a navigation system, a relation between a POI and associated POIs is defined as a parentage. Detailed information such as polygon data, address, position, etc., is stored for a POI, and if the POI is a parent, a list of the child POIs or polygon data thereof also is stored. In setting a destination, the navigation system: (1) displays the detailed information and the polygon of the parent, and when a parent POI is selected from the POI list, (2) displays a list of the child POIs or polygons of the child POIs as requested, and (3) specifies a child POI from the list of the child POIs or the polygons of the child POIs to input a destination.

Method and apparatus for determining bins to be updated for polygons, including lines

Abstract: Embodiments of the present invention provide a method and apparatus for determining the zones that a polygon overlaps to minimize the bins that are updated during binning and reduce the number of polygons to be set up in the render phase. The polygons supported include, but are not limited to, points, lines, triangles and rectangles. Each zone has associated with it a batch buffer to which data is written back for the polygons that overlap that zone. This data includes the setting up of state and the indices for those polygons. Since the zones that a polygon overlaps is precisely determined, the data written back is minimized and the polygons to be set up during the render phase is optimally reduced.

Volume-preserving interpolation of a smooth surface from polygon-related data

Abstract: The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties. In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular grid is extended to surface representations based on an irregular triangular network (TIN).

System and method for performing flood zone certifications

Abstract: After FEMA flood maps are scanned and converted to raster maps on a computer system, they are georeferenced. The georeferenced raster maps are stored on the system. Map inset polygons are surrounded by a virtual bounding box and a determination is made whether each grid rectangle intersects any bounding box. For each such intersection, the relevant inset polygon is traced to determine if it actually intersects the grid rectangle. If there is such intersection, the inset polygon is added to a list attached to the grid rectangle. At the end of the process, the list for each grid rectangle identifies each inset polygon intersected thereby. When an address of a property subject to a flood zone determination is entered into the system and geocoded, the grid rectangle containing the address is immediately called up. If only one inset polygon is on the list, it is used to make the flood determination. If more than one inset polygon is on the list, the various polygons are examined to determine which one is appropriate for making the flood determination, which is then made.

Antialiasing method and apparatus for video applications

Abstract: A method for antialiasing a video graphic A sample point is defined within eachpixel and a determination made if the sample point lies within the polygon (404) or outside of the polygon If the sample point lies within the polygon, the color of the edge pixel (408) is set to the color of the polygon If the sample point lies outside of the polygon, the color of the edge pixel is set to the color of the background The color of the pixel is stored in a frame buffer with the percent value that lies in the space associated with the sample point and in association with an indication that the sample point lies within the polygon or outside of the polygon

Method and system for communicating location in a cellular wireless system

Abstract: A method and system for communicating location information in a cellular wireless system. Each sector in a coverage area is characterized by a polygon of influence with respect to the other sectors. The polygon of influence is then used as a basis to characterize the scope or position of the sector and, particularly, the location of a mobile station that is operating in the sector. A location-based-service provider can then use that polygon of influence based location information to facilitate providing a location-based service.

Critical area computation for missing material defects in VLSI circuits

Abstract: We address the problem of computing critical area for missing material defects in a circuit layout. The extraction of critical area is the main computational problem in very large scale integration yield prediction. Missing material defects cause open circuits and are classified into breaks and via blocks. Our approach is based on the L/sub /spl infin// medial axis of polygons and the weighted L/sub /spl infin// Voronoi diagram of segments. We also introduce the min-max Voronoi diagram of rectangles, a combinatorial structure of independent interest. The critical area problem for breaks and via blocks is reduced to variations of weighted L/sub /spl infin// Voronoi diagram of segments. Plane sweep algorithms to compute the appropriate Voronoi diagrams for each case are presented. As a result, the critical area for breaks and via blocks on a single layer can be computed accurately in one pass of the layout. The time complexity is O(n log n) in the case of breaks and O((n+K)log n) in the case of via blocks, where n is the size of the input and K is upper-bounded by the number of interacting vias (in practice K is small). The critical area computation assumes square defects and reflects all possible defect sizes following the D(r)=r/sub 0//sup 2//r/sup 3/ defect size distribution. The method is presented for rectilinear layouts.

A computational approach for the analysis of changes in polygon distributions

Abstract: This paper develops a computational method for analyzing changes in polygon distributions. Unmovable polygons that change discontinuously without explicit functional linkage information are discussed. Six types of primitive events are used to describe the change: 1) generation, 2) disappearance, 3) expansion, 4) shrinkage, 5) union, and 6) division. The change of polygon distributions is decomposed into a combination of these events. A computational procedure for deducing a set of events from polygon distributions of two times is proposed. The method is applied to the analysis of the spatial competition between the major and small chains of convenience stores in Tokyo, Japan. Some empirical findings are shown.