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Polygon

About: Polygon is a research topic. Over the lifetime, 12552 publications have been published within this topic receiving 173923 citations. The topic is also known as: 2-polytope.


Papers
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Proceedings ArticleDOI
01 Nov 1990
TL;DR: A method is presented that approximates tetrahedral volume cells with hardware renderable transparent triangles that produces results which are visually similar to more exact methods for scalar volume rendering, but is faster and has smaller memory requirements.
Abstract: One method of directly rendering a three-dimensional volume of scalar data is to project each cell in a volume onto the screen. Rasterizing a volume cell is more complex than rasterizing a polygon. A method is presented that approximates tetrahedral volume cells with hardware renderable transparent triangles. This method produces results which are visually similar to more exact methods for scalar volume rendering, but is faster and has smaller memory requirements. The method is best suited for display of smoothly-changing data.

468 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of determining the minimum number of vertex guards that can see an n -wall simply connected art gallery is shown to be NP-hard, and it can be modified to show that the problems of finding edge guards and point guards in a simply connected polygonal region are also NP-Hard.
Abstract: We study the computational complexity of the art gallery problem originally posed by Klee, and its variations. Specifically, the problem of determining the minimum number of vertex guards that can see an n -wall simply connected art gallery is shown to be NP-hard. The proof can be modified to show that the problems of determining the minimum number of edge guards and the minimum number of point guards in a simply connected polygonal region are also NP-hard. As a byproduct, the problem of decomposing a simple polygon into a minimum number of star-shaped polygons such that their union is the original polygon is also shown to be NP-hard.

441 citations

Journal ArticleDOI
TL;DR: It is shown that any polygonal part can be oriented without sensors by giving anO[n2 logn) algorithm for finding the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull.
Abstract: In manufacturing it is often necessary to orient parts prior to packing or assembly. We say that a planar part ispolygonal if its convex hull is a polygon. We consider the following problem: given a list ofn vertices describing a polygonal part whose initial orientation is unknown, find the shortest sequence of mechanical gripper actions that is guaranteed to orient the part up to symmetry in its convex hull. We show that such a sequence exists for any polygonal part by giving anO[n 2 logn) algorithm for finding the sequence. Since the gripper actions do not require feedback, this result implies that any polygonal part can be orientedwithout sensors.

439 citations

OtherDOI
Henri Gouraud1
01 Jul 1998
TL;DR: 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 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 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.

437 citations

Journal ArticleDOI
TL;DR: In this paper, conforming finite elements on polygonal meshes are developed, and a particular contribution is the use of mesh-free (natural-neighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons.
Abstract: SUMMARY In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to construct different trial and test approximations on polygonal elements. A particular and notable contribution is the use of meshfree (natural-neighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons. This numerical formulation enables the construction of conforming approximation on n-gons (n 3), and hence extends the potential applications of finite elements to convex polygons of arbitrary order. Numerical experiments on second-order elliptic boundary-value problems are presented to demonstrate the accuracy and convergence of the proposed method. Copyright 2004 John Wiley & Sons, Ltd.

429 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20226
2021319
2020443
2019420
2018419
2017438