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10 items by relevance
1 Book chapter

polygon

Hansen, Vagn Lundsgaard

Danish Encyclopedia, Bind 15 — 1999, pp. 366-366

Year: 1999

Language: Danish

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2 Journal article

Isoperimetric Polygons of Maximum Width

Audet, Charles; Messine, Frédéric; Hansen, Pierre

Discrete and Computational Geometry — 2009, Volume 41, Issue 1, pp. 45-60

The value $\frac{1}{2n}\cot(\frac{\pi}{2n})$ is shown to be an upper bound on the width of any n-sided polygon with unit perimeter. This bound is reached when n is not a power of 2

Year: 2009

Language: English

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3 Journal article

Extremal problems for convex polygons

Audet, Charles; Hansen, Pierre; Messine, Frédéric

Journal of Global Optimization — 2006, Volume 38, Issue 2, pp. 163-179

Consider a convex polygon Vn with n sides, perimeter Pn, diameter Dn, area An, sum of distances between vertices Sn and width Wn. Minimizing or maximizing any of these quantities while fixing another defines 10 pairs of extremal polygon problems (one of which usually has a trivial solution

Year: 2006

Language: English

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4 Journal article

Corner universality in polygonal hydraulic jumps

Tamim, S.I.; Nichols, T.; Hansen, J. Lundbek; Bohr, T.; Bostwick, J. B.

Physical Review Fluids — 2023, Volume 8, Issue 3

Steady polygonal hydraulic jumps have a complex flow structure and are formed when a circular jump loses stability through an increase in the downstream liquid height beyond a critical value. We report the experimental observation of a universal corner shape in polygonal hydraulic jumps over a wide

Year: 2023

Language: English

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5 Journal article

Minimum-Perimeter Polygons of Digitized Silhouettes

Sklansky, Jack; Chazin, Robert L.; Hansen, Bruce J.

Ieee Transactions on Computers — 1972, Volume C-21, Issue 3, pp. 260-268

The minimum-perimeter polygon of a silhouette has been shown to be a means for recognizing convex silhouettes and for smoothing the effects of digitization in silhouettes. We describe a new method of computing the minimum-perimeter polygon (MPP) of any digitized silhouette satisfying certain

Year: 1972

Language: English

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6 Journal article

Cover Illustration: Polygonal hydraulic jumps

Ellegaard, Clive; Hansen, Adam Espe; Haaning, Anders; Hansen, Kim; Marcussen, Anders; Bohr, Tomas; et al. (2 more)

Nonlinearity — 1999, Volume 12, Issue 1, pp. 1-7

Year: 1999

Language: English

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jigo nl bpmehfdcka
7 Preprint article

Degree of Convexity and Expected Distances in Polygons

Abrahamsen, Mikkel; Fredslund-Hansen, Viktor

We present an algorithm for computing the so-called Beer-index of a polygon $P$ in $O(n^2)$ time, where $n$ is the number of corners. The polygon $P$ may have holes. The Beer-index is the probability that two points chosen independently and uniformly at random in $P$ can see each other. Given a finite set $M$ of $m$ points in a simple polygon $P$, we also show how the number of pairs in $M$ that see each other can be computed in $O(n\log n+m^{4/3}\log^\alpha m\log n)$ time, where $\alpha<1.78$ is a constant. We likewise study the problem of computing the expected geodesic distance betw...

Year: 2022

Language: Undetermined

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8 Conference paper

Fast data parallel polygon rendering

Ortega, F. A.; Hansen, C. D.; Ahrens, J. P.

IEEE — 1993, pp. 709-718

The authors describe a data parallel method for polygon rendering on a massively parallel machine. This method, based on a simple shading model, is targeted for applications which require very fast rendering for extremely large sets of polygons. Such sets are found in many scientific visualization

Year: 1993

Language: English

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9 Journal article

Generalized Swept Mid-structure for Polygonal Models

Martin, Tobias; Chen, Guoning; Musuvathy, Suraj; Cohen, Elaine; Hansen, Charles

Computer Graphics Forum — 2012, Volume 31, Issue 2pt4, pp. 805-814

Year: 2012

Language: English

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epomhialfd j kbnc g
10 Journal article

Ranking small regular polygons by area and by perimeter

Audet, Ch.; Hansen, P.; Messine, F.

Journal of Applied and Industrial Mathematics — 2009, Volume 3, Issue 1, pp. 21-27

From the pentagon onwards, the area of the regular convex polygon with n sides and unit diameter is greater for each odd number n than for the next even number n + 1. Moreover, from the heptagon onwards, the difference in areas decreases as n increases. Similar properties hold for the perimeter

Year: 2009

Language: English

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