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Generalized Barycentric Coordinates on Irregular Polygons
 Journal of Graphics Tools
, 2002
"... In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex nsided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to raytracing. Our new equations preserve many of ..."
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Cited by 71 (5 self)
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In this paper we present an easy computation of a generalized form of barycentric coordinates for irregular, convex nsided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to raytracing. Our new equations preserve many
Shape Functions for Concave Quadrilaterals
 First Mit Conference. Massachusetts Institute of Technology, Elsevier
, 2001
"... Shape functions of convex nsided polygons can be constructed efficiently and uniquely using computer algebra. Even this does not suffice for the precise analysis of shape changes in anatomical structures where geometrical concavity is germane to biological function. Shape function generation for th ..."
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Cited by 3 (0 self)
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Shape functions of convex nsided polygons can be constructed efficiently and uniquely using computer algebra. Even this does not suffice for the precise analysis of shape changes in anatomical structures where geometrical concavity is germane to biological function. Shape function generation
Solving geometric problems with the rotating calipers
, 1983
"... Shamos [1] recently showed that the diameter of a convex nsided polygon could be computed in O(n) time using a very elegant and simple procedure which resembles rotating a set of calipers around the polygon once. In this paper we show that this simple idea can be generalized in two ways: several se ..."
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Cited by 147 (11 self)
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Shamos [1] recently showed that the diameter of a convex nsided polygon could be computed in O(n) time using a very elegant and simple procedure which resembles rotating a set of calipers around the polygon once. In this paper we show that this simple idea can be generalized in two ways: several
Construction of nsided polygonal spline element using area coordinates and Bnet method
"... Abstract In general, triangular and quadrilateral elements are commonly applied in twodimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior ..."
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behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an nsided polygonal element based on quadratic spline interpolant, denoted by PS2 ele
FourNoded Triangular Finite Elements
 First MIT Conference
, 2002
"... The limits and extents of the isoparametric formulation for a fournoded finite element are derived by transforming the parametrized shape function from ## to xy coordinates. This analytic inversion results in a quadratic equation. The coefficients of this equation dictate whether the form of the ..."
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Cited by 3 (1 self)
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functions can be constructed. In 1975 E. L. Wachspress introduced a rational polynomial formulation for finite elements which applies consistently to any convex nsided polygon; it does not apply to elements with a midside node. Combining these results, convergent shape functions and consistent strain
Orienting Polygonal Parts without Sensors
, 1992
"... In manufacturing, it is often necessary to orient parts prior to packing or assembly. We say that a planar part is polygonal if its convex hull is a polygon. We consider the following problem: given a list of n vertices describing a polygonal part whose initial orientation is unknown, find the short ..."
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Cited by 205 (41 self)
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In manufacturing, it is often necessary to orient parts prior to packing or assembly. We say that a planar part is polygonal if its convex hull is a polygon. We consider the following problem: given a list of n vertices describing a polygonal part whose initial orientation is unknown, find
Generating uniform random points in a regular nsided polygon
, 2005
"... Abstract. Consider a regular polygon with n sides. We present a method to generate points uniformly distributed inside the polygon without using inclusion/exclusion. ..."
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Cited by 1 (0 self)
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Abstract. Consider a regular polygon with n sides. We present a method to generate points uniformly distributed inside the polygon without using inclusion/exclusion.
Finding the Maximum Area Parallelogram in a Convex Polygon
 CCCG
, 2011
"... We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an nsided polygon in O(n²) time. Achieving this running time requires proving several new structural properties of the MAP, and combining t ..."
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We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an nsided polygon in O(n²) time. Achieving this running time requires proving several new structural properties of the MAP, and combining
Interpolants within convex polygons: Wachspress’ shape functions
 JOURNAL OF AEROSPACE ENGINEERING, ASCE
, 2003
"... During the 1970s, Wachspress developed shape functions for convex ngons as polynomials of n2 degree divided by the one of n3. Originated from projective geometry these interpolants are linear on the sides and can exactly reproduce arbitrary linear fields. Here an alternative derivation is prese ..."
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Cited by 16 (1 self)
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During the 1970s, Wachspress developed shape functions for convex ngons as polynomials of n2 degree divided by the one of n3. Originated from projective geometry these interpolants are linear on the sides and can exactly reproduce arbitrary linear fields. Here an alternative derivation
On The Moduli Space Of Polygons In The Euclidean Plane
 Journal of Differential Geometry
, 1994
"... . We study the topology of moduli spaces of polygons with fixed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with fixed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all polygon ..."
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Cited by 69 (7 self)
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. We study the topology of moduli spaces of polygons with fixed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with fixed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all
Results 1  10
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