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Showing papers on "Polygon published in 1982"


Proceedings ArticleDOI
03 Nov 1982
TL;DR: It is proved that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3.
Abstract: Let P be a simple polygon with N vertices, each being assigned a weight ∈ {0,1}, and let C, the weight of P, be the added weight of all vertices. We prove that it is possible, in O(N) time, to find two vertices a,b in P, such that the segment ab lies entirely inside the polygon P and partitions it into two polygons, each with a weight not exceeding 2C/3. This computation assumes that all the vertices have been sorted along some axis, which can be done in O(Nlog N) time. We use this result to derive a number of efficient divide-and-conquer algorithms for: 1. Triangulating an N-gon in O(Nlog N) time. 2. Decomposing an N-gon into (few) convex pieces in O(Nlog N) time. 3. Given an O(Nlog N) preprocessing, computing the shortest distance between two arbitrary points inside an N-gon (i.e., the internal distance), in O(N) time. 4. Computing the longest internal path in an N-gon in O(N2) time. In all cases, the algorithms achieve significant improvements over previously known methods, either by displaying better performance or by gaining in simplicity. In particular, the best algorithms for Problems 2,3,4, known so far, performed respectively in O(N2), O(N2), and O(N4) time.

294 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that the minimax approximation that minimizes the maximum distance between the given points and the approximated line is the best approximation for the problem, and a method is presented for obtaining the minimumax approximated lines from the given N points in time proportional to N ∗ log N. From the obtained lines a polygon is then found using another algorithm.

163 citations


Journal ArticleDOI
TL;DR: An algorithm is presented that computes the intersection of two convex polygons in linear time, fundamentally different from the only known linear algorithms for this problem, due to Shamos and to Hoey.

133 citations


Journal ArticleDOI
TL;DR: It is shown that the frequently used algorithm for finding the convex hull of a simple polygon in linear running time does in fact work for a family of simple polygons known as weakly externally visible polygons.

107 citations


Journal ArticleDOI
TL;DR: An efficient algorithm for the solution of linear equations arising in a finite element method for the Dirichlet problem and the cost is proportional to N2log2N (N=1/h) where the cost of solving the capacitance matrix equations is N log2N on regular grids and N3/2log 2N on irregular ones.
Abstract: An efficient algorithm for the solution of linear equations arising in a finite element method for the Dirichlet problem is given. The cost of the algorithm is proportional toN 2log2 N (N=1/h) where the cost of solving the capacitance matrix equations isNlog2 N on regular grids andN 3/2log2 N on irregular ones.

106 citations


Patent
22 Jun 1982
TL;DR: An electro-optical light scanning system using a modulated laser illumination source directed upon a multifaceted rotating polygonal mirror or polygon is described in this paper, where the mirrored facets reflect the impinging light toward a moving photoreceptor and forms a raster of scan lines as the photoreceiver moves.
Abstract: An electro-optical light scanning system using a modulated laser illumination source directed upon a multifaceted rotating polygonal mirror or polygon. The mirrored facets reflect the impinging light toward a moving photoreceptor and forms a raster of scan lines as the photoreceptor moves. The system incorporates sensing optics and closed loop electronics for correcting inaccuracies in the position of the reflected light resulting from defects in the angular relationship between the plane of the facets and that of the rotating axis of the polygon as well as those errors due to inherent angular misalignment between each of the facets of the rotating polygon. The invention also encompasses amplitude modulation for varying the intensity of the laser illumination in conjunction with the acousto-optical modulation for maintaining a constant level illumination and/or for varying the spot size.

70 citations


Patent
18 Jan 1982
TL;DR: In this article, a method for filling polygons displayed by a color CRT monitor of a raster graphic system is described, in which a graphic controller produces control signals which control the mode of operation of the system, two of which are a fast polygon write, or fast-fill write, mode and a fast-polygon display, or display fastfill, mode.
Abstract: Method and apparatus for filling polygons displayed by a color CRT monitor of a raster graphic system. A graphic controller produces control signals which control the mode of operation of the system, two of which are a fast polygon write, or fast-fill write, mode and a fast polygon display, or display fast-fill, mode. When the system is in the fast polygon write mode, the graphic controller reads fast-fill toggle bits from a frame memory of boundary pixels defining initial and terminal pixels of each fill element. The fast-fill toggle bits of boundary pixels are set if the toggle bit read from memory was not set and, if set, it will reset it. In the fast polygon display mode, the system senses the initial boundary pixel of each fill element by its fast-fill toggle bit being set and applies the color address of the initial boundary pixel to a color look-up memory until the terminal pixel of the fill element is read from the memory. Thereafter, the color address of each pixel of a horizontal scan line is applied to the color look-up memory in synchronization with the raster scan until another initial boundary pixel of another fill element is sensed, etc., or until the end of the horizontal scan line is reached.

67 citations


Patent
18 Feb 1982
TL;DR: In this paper, the authors present a real-time graphics system using logic-enhanced pixels within an image buffer, permitting parallel (simultaneous) calculations at every pixel, which is a relatively inexpensive raster-scan type graphics system capable of real time operation.
Abstract: The present invention provides a relatively inexpensive raster-scan type graphics system capable of real time operation, utilizing logic-enhanced pixels within an image buffer, permitting parallel (simultaneous) calculations at every pixel. A typical implementation would be as custom VLSI chips. In the sequence of most general applications, each polygon is operated upon in sequence, and the image is built up as the polygons are processed without the necessity of sorting. With respect to each successive polygon, the following operations are effected: (1) all pixels within the polygon are identified; (2) the respective pixels which would be visible to the observer, that is, not obstructed by some previously processed polygon, are determined; and (3) the proper color intensities for each visible pixel are determined.

60 citations


Henri Gouraud1
01 Jan 1982
TL;DR: In this paper, a procedure for computing shaded pictures of curved surfaces is presented, where the surface is approximated by small polygons in order to solve easily the hidden-parts problem, but the shading of each polygon is computed so that the discontinuities of shade are eliminated across the surface and a smooth appearance is obtained.
Abstract: A procedure for computing shaded pictures of curved surfaces is presented. The surface is approximated by small polygons in order to solve easily the hidden-parts problem, but the shading of each polygon is computed so that the discontinuities of shade are eliminated across the surface and a smooth appearance is obtained. In order to achieve speed efficiency, the technique developed by Watkins is used which makes possible a hardware implementation of this algorithm.

60 citations


Journal ArticleDOI
TL;DR: Two general O(n) algorithms for solving the problem of determining the inclusion of a point in volume-enclosing polyhedra (shapes) in 3D space by reducing the 3D case into the solvable 2D case are presented.

49 citations


Proceedings Article
18 Aug 1982
TL;DR: An algorithm is presented which efficiently finds good collision-free paths for convex polygonal bodies through space littered with obstacle polygons by characterizing the volume swept by a body as it is translated and rotated as a generalized cone.
Abstract: Free space is represented as a union of (possibly overlapping) generalized cones. An algorithm is presented which efficiently finds good collision free paths for convex polygonal bodies through space littered with obstacle polygons. The paths arc good in the sense that the distance of closest approach to an obstacle over the path is usually far from minimal over the class of topologically equivalent collision free paths. The algorithm is based on characterizing the volume swept by a body as it is translated and rotated as a generalized cone and determining under what conditions one generalized cone is a subset of another.

Book ChapterDOI
01 Jan 1982
TL;DR: The main objective of the work was to develop an automated digitizing system capable of handling specially-prepared DoE polygon maps.
Abstract: A system has been set up which automatically interprets the binary pixel representation of an image on the basis of a predefined model. The model is that the image contains only a network of polygons with each polygon being labelled by a digit code written within its boundary, and the end point of the interpretive process is the generation of the feature-coded vector representation of each polygon boundary. The main components of the system are a raster-to- vector conversion module, a database module, a symbol extraction and classification module and a polygon recognition module. All but the last module are of more general applicability, and at present the other modules are being used in a system which is being developed for the automatic interpretation of engineering drawings. The main objective of the work was to develop an automated digitizing system capable of handling specially-prepared DoE polygon maps.

Journal ArticleDOI
TL;DR: In this paper, a method of moments surface patch model for polygon plates is presented and three methods for segmenting polygonal plates are considered, including full surface testing and point matching, as it affects the efficiency and generality of the solution.
Abstract: A method of moments surface patch model for polygon plates is presented. Three methods for segmenting polygon plates are considered. Also, the choice between full surface testing and point matching is discussed as it affects the efficiency and generality of the solution. Numerical results are compared with measurements and independent calculations for polygonal plates of three different shapes, including a wire to plant junction.

ReportDOI
01 Mar 1982
TL;DR: This paper shows that a class of series-parallel networks, for which only exponentially complex algorithms were previously known, can be analyzed in polynomial time and introduces a new reliability-preserving graph reduction of general applicability and produces a linear-time algorithm for computing the reliability of any graph with an underlying series- parallel structure.
Abstract: : Analysis of network reliability is of major importance in computer, communication and power networks. Even the simplest models lead to computational problems which are NP-hard for general networks, although polynomial-time algorithms do exist for certain network configurations such as 'ladders' and 'wheels' and for some series-parallel structures such as the well-known 'two-terminal' series-parallel networks. In this paper, we show that a class of series-parallel networks, for which only exponentially complex algorithms were previously known, can be analyzed in polynomial time. In doing this, we introduce a new reliability-preserving graph reduction of general applicability and produce a linear-time algorithm for computing the reliability of any graph with an underlying series-parallel structure.

Journal ArticleDOI
TL;DR: An algorithm for determining visible lines or visible surfaces in polygonal form, at object resolution, is presented, which is useful for smooth shaded or textured images, as well as for the creation of shadows.
Abstract: An algorithm for determining visible lines or visible surfaces in polygonal form, at object resolution, is presented. The original scene must consist of non-intersecting planar polygons. The procedure relies on image coherence, since the sampling is dependent on the complexity of the image. The reconstruction method is based on an elaborate data structure, which allows the polygonal output to be easily obtained. The polygonal output is useful for smooth shaded or textured images, as well as the for creation of shadows.

Patent
30 Jun 1982
TL;DR: In this paper, an articulated structure for wheelchairs for the handicapped is presented, consisting of two lateral symmetric systems, each comprising a deformable quadrilateral 17, a second deformable quadrurilateral 26, a trilateral polygon 34, an elastic member 38 and a handling unit 41.
Abstract: Assistance for the handicapped. The device is made in the form of an articulated structure 12 comprising two lateral symmetric systems 13 each comprising a first deformable quadrilateral 17, a second deformable quadrilateral 26, a trilateral polygon 34, an elastic member 38 and a handling unit 41. Application to wheelchairs for the handicapped.

Journal ArticleDOI
TL;DR: It is shown that Pavlidis's method for decomposing a polygon into (possibly overlapping) convex pieces can be viewed as simplifying a Boolean switching function expressed in disjunctive normal form, suggesting that the search for a minimal polygon decomposition can be organized along the same lines used to find a minimal prime implicant cover for a Boolean expression.

Journal ArticleDOI
TL;DR: In this article, the local behavior of root loci around zeros and poles is investigated by relating the Newton diagrams which arise in the local analysis to the McMillan structure of the open-loop system.
Abstract: The local behaviour of root loci around zeros and poles is investigated. This is done by relating the Newton diagrams which arise in the local analysis to the McMillan structure of the open-loop system, by means of what we shall call the McMillan polygon. This geometric construct serves to clarify the precise relationship between the McMillan structure, the principal structure, and the branching patterns of the root loci. In addition, several rules are obtained which are useful in the construction of the root loci of multivariable control systems.

Patent
16 Jan 1982
TL;DR: In this article, the authors proposed to increase the speed of feed to enhance the finished surface roughness and the efficiency of cutting by a metal cutting throw-away chip by forming each cutting edge in the vicinity of the apex of an imaginary polygon to have a radius of curvature which is larger than the radius of a circle inscribed in the polygon.
Abstract: PURPOSE:To increase the speed of feed to aim at enhancing the finished surface roughness and the efficiency of cutting by a metal cutting throw-away chip, by forming each cutting edge in the vicinity of the apex of an imaginary polygon to have a radius of curvature which is larger than the radius of a circle inscribed in the imaginary polygon CONSTITUTION:The radius R of curvature of each curved cutting edge 5 of a triangular chip 3a is set larger than the radius (r) of a circle 2 which is inscribed in an imarginary triangle 1a that indicated the contour of the triangular chip 3a, and as well the mid-point of the cutting edge 6 is contacted to the inscribed circle 2 while ends of each curved cutting edge 5 are joined with the ends of the adjacent curved cutting edges 5 within the imaginary triangle 1a Since the finished surface roughness is proportional to the square of feed and as well inversely proportional to eight times as large as the radius R of curvature of the curved cutting edge, the larger the radiaus R of curvature the less the finished surface roughness may be made without the feed speed being decreased With this arrangement, the efficiency of cutting may be enhanced by increasing the radius R

Journal ArticleDOI
TL;DR: A family of convex polygons is described for which Snyder and Tang's algorithm fails and it is pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in O(n) time.
Abstract: Recently, Snyder and Tang [1] proposed an algorithm for finding the diameter of a convex polygon. In this note a family of convex polygons is described for which their algorithm fails. It is also pointed out that the diameter of an arbitrary simple n-vertex polygon can be computed in O(n) time.

Journal ArticleDOI
G. Cybenko1
TL;DR: In this article, it was shown that the zeros of the predictor polynomial determined by a finite-data least-squares linear prediction problem lie inside an irregular polygon contained in the unit circle of the complex plane.
Abstract: This work shows that the zeros of the predictor polynomial determined by a finite-data least-squares linear prediction problem lie inside an irregular polygon contained in the unit circle of the complex plane. The polygon is independent of the data, only depending on the length of the data and the order of the predictor. The results are an analytic statement of the resolution limitations of spectral estimates based on finite-data least-squares linear predictors.

Journal ArticleDOI
TL;DR: A method is described for subdivision of an arbitrary polygon into triangular elements by construction of a boundary-matching superposition mesh to form interior elements followed by a procedure to connect the interior to the boundary.
Abstract: A method is described for subdivision of an arbitrary polygon into triangular elements. The method involves construction of a boundary-matching superposition mesh to form interior elements followed by a procedure to connect the interior to the boundary.

Patent
19 Jan 1982
TL;DR: In this article, a self-locking sling of the type comprising a strap folded and sewn into the shape of a clover-leaf is described, with the number of tips being equal to that of the loops of said clover leaf.
Abstract: Self-locking sling of the type comprising a strap folded and sewn into the shape of a clover-leaf (1), characterized by a second strap or ribbon, folded and sewn into a star-shaped polygon (2), the number of tips (5) of which being equal to that of the loops (4) of said clover-leaf (1).

Journal ArticleDOI
TL;DR: The dominant large-N classical solution for the one-plaquette (one-polygon) model is obtained in this article, where the level spacing ω (singlet and adjoint) is the angular frequency of the classical abelian analogue (here a pendulum) in its first Bohr orbit.

Patent
29 Sep 1982
TL;DR: A polygon box tool as mentioned in this paper can be used for turning a hexagon shape on the outside diameter of the workpiece while simultaneously turning flats on a smaller diameter in front of the hexagon contour.
Abstract: A polygon box tool for use with different machine tools by which a cutting and boring operation may be performed simultaneously. The polygon box tool may be used for turning a hexagon shape on the outside diameter of the workpiece while simultaneously turning flats on a smaller diameter in front of the hexagon contour.

Journal ArticleDOI
TL;DR: This correspondence presents a procedure to recognize handprinted alphanumeric characters written on a graphic tablet using several statistical classifiers and a recursive learning procedure in the statistical classifier.
Abstract: This correspondence presents a procedure to recognize handprinted alphanumeric characters written on a graphic tablet. After preprocessing, the input character is segmented into a polygon using a simple segmentation procedure. A feature vector is formed by the parameters which describe the segments of the polygon. Classification is done in two steps, the first one based on structural information extracted from the feature vector and the second based on statistical decision rule using parameters of the segments. A recursive learning procedure is introduced in the statistical classifier. The evaluation includes the measurement of recognition rates using several statistical classifiers, the validity test on the hypothesis concerning the distribution of feature vectors and the possibility of further simplification using principal axis analysis. Databases were created and used for the evaluation.

Journal ArticleDOI
TL;DR: In this article, an efficient programmable procedure is given for evaluating the integral of the bivariate normal distribution (IBND) over an arbitrary polygon, where the class of arbitrary polygons includes simple polygons, limit elements, and self-intersecting polygons.
Abstract: An efficient programmable procedure is given for evaluating the integral of the bivariate normal distribution (IBND) over an arbitrary polygon $\Pi $ The class of arbitrary polygons includes the subclasses: simple polygons, limit elements of sequences of uniformly bounded N-sided simple polygons with the same orientation, and self-intersecting (SI) polygons For a given element $\Pi $ defined by N ordered points in the plane, the subclass need not be specified The method evaluates the IBND over N exterior angular regions $A_1 ,A_2 , \cdots ,A_N $ of $\Pi $ to determine the IBND for $\Pi $ If $\Pi $ is SI, a quantity called the “winding number” of $\Pi $ is introduced which is given by the sum of the angular measures of the $A_i (i = 1,2 \cdots ,N)$ divided by $2\pi $ A detailed numerical example, using a Fortran IV program, with approximately 9-decimal-digit accuracy is included

Patent
04 Mar 1982
TL;DR: In this article, a double endless band assembly for the continuous prodn. of foamed plastics composite elements comprises bands each made from a series of plates driven and guided around polygonal wheels.
Abstract: A double endless band assembly for the continuous prodn. of foamed plastics composite elements comprises bands each made from a series of plates driven and guided around polygonal wheels. A constant speed drive (13) for the polygonal wheels (8) transmits the motion to the polygonal wheels in such a manner that the endless band (6) moves at virtually uniform speed. Pref. each polygonal drive wheel (8) has keyed to it, a polygonal driven wheel (10) possessing the same number of sides; each corner of this polygon has a chain tooth (11) which can be engaged by the teeth (12) of a finely divided drive chain (12) driven by a constant-speed, circular wheel (13). The fine divisions of the chain (tK) constitute a whole number fraction of one side of the driven polygon (10). With this arrangement, a polygon possessing a comparatively small number of fairly large sides, and consequently continuous bands composed of large plates, can be used since the drive cancels out the 'polygon' effect.

01 Jan 1982
TL;DR: A method is presented for converting polygons coded in raster data structures into conventional vector structures to allow the output of scanner-based data collection systems to be input directly to conventional geographic information systems.
Abstract: A method is presented for converting polygons coded in raster data structures into conventional vector structures to allow the output of scanner-based data collection systems to be input directly to conventional geographic information systems. The method relies on topological principles to (1) uniquely label each polygon in the image and produce an output image in which each pixel is described by the label of the polygon to which it belongs; (2) create line segment components of polygon boundaries, with nodes labeled and the two adjacent polygons identified; and (3) traverse the polygon boundaries by connecting the appropriate adjacent line segments. The conversion capability makes it possible to design systems which automatically convert to the data structure most appropriate for a particular application.