Showing papers on "Polygon published in 2006"

Spectral surface quadrangulation

Abstract: Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of this work has focused on triangular remeshing, yet quadrilateral meshes are preferred for many surface PDE problems, especially fluid dynamics, and are best suited for defining Catmull-Clark subdivision surfaces. We describe a fundamentally new approach to the quadrangulation of manifold polygon meshes using Laplacian eigenfunctions, the natural harmonics of the surface. These surface functions distribute their extrema evenly across a mesh, which connect via gradient flow into a quadrangular base mesh. An iterative relaxation algorithm simultaneously refines this initial complex to produce a globally smooth parameterization of the surface. From this, we can construct a well-shaped quadrilateral mesh with very few extraordinary vertices. The quality of this mesh relies on the initial choice of eigenfunction, for which we describe algorithms and hueristics to efficiently and effectively select the harmonic most appropriate for the intended application.

System and method of three-dimensional image capture and modeling

Abstract: System and method for constructing a 3D model of an object based on a series of silhouette and texture map images. In the exemplary embodiment an object is placed on a rotating turntable and a camera, which is stationary, captures images of the object as it rotates on the turntable. In one pass, the system captures a number of photographic images that will be processed into image silhouettes. In a second pass, the system gathers texture data. After a calibration procedure (used to determine the camera's focal length and the turntable's axis of rotation), a silhouette processing module determines a set of two-dimensional polygon shapes (silhouette contour polygons) that describe the contours of the object. The system uses the silhouette contour polygons to create a 3D polygonal mesh model of the object. The system determines the shape of the 3D model analytically by finding the areas of intersection between the edges of the model faces and the edges of the silhouette contour polygons. The system creates an initial, (rough) model of the 3D object from one of the silhouette contour polygons, then executes an overlaying procedure to process each of the remaining silhouette contour polygons. In the overlaying process, the system processes the silhouette contour polygons collected from each silhouette image, projecting each face of the (rough) 3D model onto the image plane of the silhouette contour polygons. The overlaying of each face of the (rough) 3D model onto the 2D plane of the silhouette contour polygons enables the present invention to determine those areas that are extraneous and should be removed from the (rough) 3D model. As the system processes the silhouette contour polygons in each image it removes the extraneous spaces from the initial object model and creates new faces to patch “holes.” The polygonal mesh model, once completed, can be transformed into a triangulated mesh model. In a subsequent step, the system uses a deterministic procedure to map texture from the texture images onto the triangles of the 3D mesh model, locating that area in the various texture map images that is “best” for each mesh triangle.

Mean value coordinates for arbitrary planar polygons

Abstract: Barycentric coordinates for triangles are commonly used in computer graphics, geometric modeling, and other computational sciences because they provide a convenient way to linearly interpolate the data that is given at the corners of a triangle. The concept of barycentric coordinates can also be extended in several ways to convex polygons with more than three vertices, but most of these constructions break down when used in the nonconvex setting. Mean value coordinates offer a choice that is not limited to convex configurations, and we show that they are in fact well-defined for arbitrary planar polygons without self-intersections. Besides their many other important properties, these coordinate functions are smooth and allow an efficient and robust implementation. They are particularly useful for interpolating data that is given at the vertices of the polygons and we present several examples of their application to common problems in computer graphics and geometric modeling.

Delaunay Triangulation Based Surface Reconstruction

Abstract: The surfaces considered in surface reconstruction are 2-manifolds that might have boundaries and are embedded in some Euclidean space R. In the surface reconstruction problem we are given only a finite sample P ⊂ R of an unknown surface S. The task is to compute a model of S from P . This model is referred to as the reconstruction of S from P . It is generally represented as a triangulated surface that can be directly used by downstream computer programs for further processing. The reconstruction should match the original surface in terms of geometric and topological properties. In general surface reconstruction is an ill-posed problem since there are several triangulated surfaces that might fulfill these criteria. Note, that this is in contrast to the curve reconstruction problem where the optimal reconstruction is a polygon that connects the sample points in exactly the same way as they are connected along the original curve. The difficulty of meeting geometric or topological criteria depends on properties of the sample and on properties of the sampled surface. In particular, sparsity, redundancy, noisiness of the sample or non-smoothness and boundaries of the surface make surface reconstruction a challenging problem.

Monitoring environmental boundaries with a robotic sensor network

Abstract: In this paper we propose and analyze an algorithm to monitor an environmental boundary with mobile sensors. The objective is to optimally approximate the boundary with a polygon. The mobile sensors rely only on sensed local information to position some interpolation points and define an approximating polygon. We design an algorithm that distributes the vertices of the approximating polygon uniformly along the boundary. The notion of uniform placement relies on a metric inspired by known results on approximation of convex bodies. The algorithm is provably convergent for static boundaries and also for slowly-moving boundaries because of certain input-to-state stability properties.

Capacitive touch sense device having polygonal shaped sensor elements

Abstract: A touch sensor pad having polygon shaped sensor elements of five or more sides is described.

Streaming and interactive visualization of filled polygon data in a geographic information system

Abstract: Interactive geographic information systems (GIS) and techniques are disclosed that provide users with a greater degree of flexibility, utility, and information. A markup language is provided that facilitates communication between servers and clients of the interactive GIS, which enables a number of GIS features, such as network links (time-based and/or view-dependent dynamic data layers), ground overlays, screen overlays, placemarks, 3D models, and stylized GIS elements, such as geometry, icons, description balloons, polygons, and labels in the viewer by which the user sees the target area. Also, “virtual tours” of user-defined paths in the context of distributed geospatial visualization is enabled. Streaming and interactive visualization of filled polygon data are also enabled thereby allowing buildings and other such features to be provided in 3D. Also, techniques for enabling ambiguous search requests in a GIS are provided.

3D SLAM using planar segments

Abstract: This paper presents an improved feature-based 3D SLAM approach for a mobile robot equipped with a rotating laser scanner. The features are represented using the SPmodel, with associated planar segment information based on decimated polygon sets. An Extended Kalman Filter is used to build a three-dimensional map of the environment and track the robot's pose. As shown, the resulting maps are highly detailed, useful for higher-level robotic tasks and small in size.

Mapcurves: a quantitative method for comparing categorical maps

Abstract: We present Mapcurves, a quantitative goodness-of-fit (GOF) method that unambiguously shows the degree of spatial concordance between two or more categorical maps. Mapcurves graphically and quantitatively evaluate the degree of fit among any number of maps and quantify a GOF for each polygon, as well as the entire map. The Mapcurve method indicates a perfect fit even if all polygons in one map are comprised of unique sets of the polygons in another map, if the coincidence among map categories is absolute. It is not necessary to interpret (or even know) legend descriptors for the categories in the maps to be compared, since the degree of fit in the spatial overlay alone forms the basis for the comparison. This feature makes Mapcurves ideal for comparing maps derived from remotely sensed images. A translation table is provided for the categories in each map as an output. Since the comparison is category-based rather than cell-based, the GOF is resolution-independent. Mapcurves can be applied either to entire map categories or to individual raster patches or vector polygons. Mapcurves also have applications for quantifying the spatial uncertainty of particular map features.

Caging Polygons with Two and Three Fingers.

Abstract: We present algorithms for computing all placements of two and three fingers that cage a given polygonal object with n edges in the plane. A polygon is caged when it is impossible to take the polygon to infinity without penetrating one of the fingers. Using a classification into squeezing and stretching cagings, we provide an algorithm that reports all caging placements of two disc fingers in O(n 2logn) time. Our result extends and improves a recent solution for point fingers. In addition, we construct a data structure requiring O(n 2) storage that can answer in O(logn) whether two fingers in a query placement cage the polygon. We also study caging with three point fingers. Given the placements of two so-called base fingers, we report all placements of the third finger so that the three fingers jointly cage the polygon. Using the fact that the boundary of the set of placements for the third finger consists of equilibrium grasps, we present an algorithm that reports all placements of the third finger in O(n 6log2 n) deterministic time and O(n 6logn(loglogn)3) expected time. Our results extend previous solutions that only apply to convex polygons.

Task-driven Support Polygon Reshaping for Humanoids

Abstract: In this paper we address a task-driven motion generation method that allows a humanoid robot to make whole-body motions including support polygon reshaping to achieve the given tasks In the proposed method, generalized inverse kinematics (IK) is employed with floating-base to generate humanoid whole-body motions that enable the robot to accomplish the tasks according to given priorities During the motion, several criteria such as manipulability or end-effector position error are tracked If the desired task cannot be done because of those criteria, a geometric planner for support polygon is activated Then the whole-body motion is computed again always using the generalized IK solver including stepping motion that realizes the deformed support polygon by using dynamic walking pattern generator This method provides a way to perform tasks that could not be done without changing the humanoid's support state We have verified the proposed framework through simulations and experiments using humanoid robot HRP-2

Pattern based map comparisons

Abstract: Map comparison techniques based on a pixel-by-pixel comparison are useful for many purposes, but fail to reveal important aspects of map similarities and differences. In contrast, pattern based map comparison techniques address the question of structural similarity, although with these approaches the comparison problem becomes open ended, since there is an unlimited number of ways to characterise a pattern. Two types of pattern based technique are used here to analyse the test sets of maps. The first, a fuzzy polygon based matching technique, focuses on the meso-scale aspects of pattern. It is based on the areal intersection of land use polygons on the two maps being compared. The areal intersection, areal complement, and polygon size values are fuzzified into an appropriate set of categories, a set of fuzzy inference rules is applied to derive memberships in local matching categories, and finally the local matching category memberships are defuzzified to yield local matching values for each land use polygon on the reference map. The second approach, fractal analysis, captures macro-scale or global qualities of the maps. Two measures are calculated here: the radial dimension and the cluster size—frequency dimension. The polygon matching approach provides only limited insight when applied to the case of the map set representing differences in classification. It proves much more effective when applied to the problem of change detection, revealing areas where the pattern has changed and giving local measures of the degree of change. The approach is particularly useful in the case where there is a considerable degree of random change at the pixel level, as changes in the underlying pattern are extracted from the noise, while pixel based approaches largely detect the noise.

Systems and methods for generating user specified information from a map

Abstract: An embodiment relates generally to a method of generating user-specified information. The method includes receiving a plurality of points selected on a map to form a first continuous line having one or more vertices. The method also includes generating a closed polygon having a plurality of edges, where at least one edge forms a second continuous line substantially parallel to and spaced apart at a distance from the first continuous line. The method also includes determining a plurality of coordinate pairs each associated with a point on the plurality of edges of the closed polygon and retrieving user specified information for an area enclosed by the plurality of coordinate pairs.

Correcting Pyramidal Error of Polygon Scanner In Scanning Beam Display Systems

Abstract: Scanning beam display systems using fluorescent screens and various servo feedback control mechanisms to control display imaging qualities, including techniques and mechanism for measuring and correcting pyramidal errors of a polygon scanner.

Computing the Fréchet distance between simple polygons in polynomial time

Abstract: We present the first polynomial-time algorithm for computing the Frechet for a non-trivial class of surfaces: simple polygons. For this, we show that it suffices to consider homeomorphisms that map an arbitrary triangulation of one polygon to the other polygon such that diagonals of the triangulation are mapped to shortest paths in the other polygon.

Exact and efficient construction of planar Minkowski sums using the convolution method

Abstract: The Minkowski sum of two sets A,B ∈ Rd, denoted A ⊕ B, is defined as {a+b|a ∈ A,b ∈ B}. We describe an efficient and robust implementation for the construction of Minkowski sums of polygons in R2 using the convolution of the polygon boundaries. This method allows for faster computation of the sum of non-convex polygons in comparison with the widely-used methods for Minkowski-sum computation that decompose the input polygons into convex sub-polygons and compute the union of the pairwise sums of these convex sub-polygon. Partially supported by the IST Programme of the EU as a Shared-cost RTD (FET Open) Project under Contract No IST-006413 (ACS - Algorithms for Complex Shapes), and by the Hermann Minkowski-Minerva Center for Geometry at Tel Aviv University.

Modeling and computing ternary projective relations between regions

Abstract: Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(nlogn) time

Polygon‐based contact resolution for superquadrics

Abstract: The representation of discrete objects in the discrete element modelling is a fundamental issue, which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems. Disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency, but they are unable to provide resistance to rolling motion. For this reason, some non-circular/spherical objects, such as polygons/polyhedrons, superquadrics, or the clustering of disks/spheres to form irregular shapes, are introduced. When superquadrics are used as discrete elements, the bottleneck of contact resolution is associated with the searching for intersections of two non-linear functions, which is a very expensive operation and may sometimes fail in finding the solution. In this work, an efficient and robust algorithm is proposed for contact resolution of 2D superquadrics, in which any superquadric is approximated with a convex polygon through adaptive sampling; then by clipping two polygons, an efficient linear algorithm is performed to search for intersections and overlap area of the polygons; the contact forces and directions are determined by employing a newly established corner/corner contact model. It is important to highlight that the proposed methodology can also be extended to general non-circular discrete object cases. The performance of the algorithm is demonstrated via numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.

Distribution and origin of patterned ground on Mullins Valley debris-covered glacier, Antarctica: the roles of ice flow and sublimation

Abstract: We map polygonally patterned ground formed in sublimation tills that overlie debris-covered glaciers in Mullins Valley and central Beacon Valley, in southern Victoria Land, Antarctica, and distinguish five morphological zones. Where the Mullins Valley debris-covered glacier debouches into Beacon Valley, polygonal patterning transitions from radial (orthogonal) intersections to non-oriented (hexagonal) intersections, providing a time-series of polygon evolution within a single microclimate. We offer the following model for polygon formation and evolution in the Mullins Valley system. Near-vertical cracks that ultimately outline polygons are produced by thermal contraction in the glacier ice. Some of these cracks may initially be oriented radial to maximum surface velocities by pre-existing structural stresses and material weaknesses in the glacier ice. In areas of relatively rapid flow, polygons are oriented down-valley forming an overall fan pattern radial to maximum ice velocity. As glacier flow moves the cracks down-valley, minor variations in flow rate deform polygons, giving rise to deformed radial polygons. Non-oriented (largely hexagonal) polygons commonly form in regions of stagnant and/or near-stagnant ice. We propose that orientation and morphology of contraction-crack polygons in sublimation tills can thus be used as an indicator of rates of subsurface ice flow.

An extraction method of environmental surface profile using planar end-effectors

Abstract: It is very important for robots working in unknown environment to recognize surface profile of the environment. This paper presents an extraction method of environmental surface profile based on environmental modes. Contact condition between a planar end-effector and the environment is also determined by using active motion which is named "groping motion" of the end-effector. The extraction method utilizes discrete Fourier transform (DFT) matrices as matrices transforming into environmental modes. The proposed method can be applied to a planar end-effector whose shape is an arbitrary polygon. Moreover, a compliance controller for attitude of a planar end-effector with 3 supporting points is proposed to realize stable contact motion with unknown environment. The validity of the proposed method is shown by the experimental results

Contour approximation in sensor networks

Abstract: We propose a distributed scheme called Adaptive-Group-Merge for sensor networks that, given a parameter k, approximates a geometric shape by a k-vertex polygon. The algorithm is well suited to the distributed computing architecture of sensor networks, and we prove that its approximation quality is within a constant factor of the optimal. We also show through simulation that our scheme outperforms several other alternatives in preserving important shape features, and achieves approximation quality almost as good as the optimal, centralized scheme. Because many applications of sensor networks involve observations and monitoring of physical phenomena, the ability to represent complex geometric shapes faithfully but using small memory is vital in many settings.

Producing joint polygons,cutting joint blocks and finding key blocks for general free surfaces

Abstract: This paper describes a process of cutting blocks from statistically generated finite joint polygons in 3D space.If the ratio of joint length divided by joint spacing is less than 10,the rock mass is likely connected.If this joint length ratio is greater than 10,the rock is likely to be blocky.An algorithm is also presented for finding all removable blocks along any given moving direction.The rock mass boundary can be any excavated and natural free surfaces.The algorithm works for both joint sets and for any joint system where each joint has its own direction.This is an application of polygon cutting code DC of 3D DDA.

Finding large sticks and potatoes in polygons

Abstract: We study a class of optimization problems in polygons that seek to compute the "largest" subset of a prescribed type, e.g., a longest line segment ("stick") or a maximum-area triangle or convex body ("potato"). Exact polynomial-time algorithms are known for some of these problems, but their time bounds are high (e.g., O(n7) for the largest convex polygon in a simple n-gon). We devise efficient approximation algorithms for these problems. In particular, we give near-linear time algorithms for a (1 - ∈)-approximation of the biggest stick, an O(1)-approximation of the maximum-area convex body, and a (1 - ∈)-approximation of the maximum-area fat triangle or rectangle. In addition, we give efficient methods for computing large ellipses inside a polygon (whose vertices are a dense sampling of a closed smooth curve). Our algorithms include both deterministic and randomized methods, one of which has been implemented (for computing large area ellipses in a well sampled closed smooth curve).

Maximizing Visibility in Nonconvex Polygons: Nonsmooth Analysis and Gradient Algorithm Design

Abstract: This paper presents a motion control algorithm for a planar mobile observer such as a mobile robot equipped with an omnidirectional camera. We propose a nonsmooth gradient algorithm for the problem of maximizing the area of the region visible to the observer in a non-self-intersecting nonconvex polygon. First, we show that the visible area is almost everywhere a locally Lipschitz function of the observer location. Second, we provide a novel version of the LaSalle invariance principle for discontinuous vector fields and Lyapunov functions with a finite number of discontinuities. Finally, we establish the asymptotic convergence properties of the nonsmooth gradient algorithm and illustrate numerically its performance.

Fingerprint Matching Using Minutia Polygons

Abstract: Fingerprint distortion changes both the geometric position and orientation of minutiae, and leads to difficulties in establishing a match among multiple impressions acquired from the same finger In this paper, minutia polygons are used to match distorted fingerprints. A minutia polygon describes not only the minutia type and orientation but also the minutia shape. This allows the minutia polygon to be bigger than the conventional tolerance box without losing matching accuracy. In other words, a minutia polygon has a higher ability to tolerate distortion. Furthermore, the proposed matching method employs an improved distortion model using a multi-quadric basis function with parameters. Adjustable parameters make this model more suitable for fingerprint distortion. Experimental results show the proposed method is two times faster and more accurate (especially, on fingerprints with heavy distortion) than the method by A.M.Bazen and S.H.Gerez (2003)

Determination of areas on the plane, sphere and ellipsoid

Abstract: This paper shortly reviews various methods to determine the area of a closed polygon on the plane, sphere and ellipsoid. A new method is derived for calculating the area of a geodetic polygon, i.e. a polygon on the ellipsoid limited by sections of geodesics. By a recursive procedure the area can be determined to any desired order of the eccentricity of the ellipsoid. Finally we also present a direct method for numerical integration of the area under the geodesic.