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# Topic: Superellipse

 superellipse Superellipses have a form partway between an ellipse and a rounded rectangle (or, if a = b, partway between a circle and a rounded square). The Danish poet and architect Piet Hein decided that the superellipse with n = 5/2 and a/b = 6/5 is the most pleasing the eye. The surface of revolution of a superellipse is a superellipsoid, one special form of which has been nicknamed the superegg. www.daviddarling.info /encyclopedia/S/superellipse.html   (187 words)

 SuperEllipse and SuperEllipsoid This is the form most easily employed to draw a superellipse, the angle ø is varied from 0 to 2pi in suitably small steps, a line is drawn to each subsequent value of ø. Note that the superellipse always passes through the same points at ø = 0, pi/2, pi, 3pi/2 and so it is possible to have different values of n in each quadrant. The superellipse is name given to a family of shapes formed from the spherical product of two superquadratric curves. astronomy.swin.edu.au /~pbourke/surfaces/superellipse   (537 words)

 [No title] The cross-section is actually described by a superellipse where shearx defines the amount of shear applied to the light cone direction.} default {0} } parameter float sheary { range {0 4} subtype slider description {one of many controls for shaping the light cross-section. The cross-section is actually described by a superellipse where width defines the dimensions of the barn door opening. The cross-section is actually described by a superellipse where height defines the dimensions of the barn door opening. www.renderman.org /RMR/Shaders/TLShaders/l_uber.slim   (1430 words)

 Denmark.dk: Official website - Denmark - The superellipse   (Site not responding. Last check: 2007-11-05) His superellipse was to solve the double contrast between the circle and the square and that of the ellipse and the rectangle. The solution was the application of the superellipse to both square and roundabout at the new Sergels Torg. Later on the superellipse has been used in Canada, France, Japan, the US and Mexico in connection with the solution of as different constructions as residential areas and sports centres for example the Olympic Stadium in Mexico City. www.denmark.dk /portal/page?_pageid=374,899055&_dad=portal&_schema=PORTAL   (325 words)

 BBC - h2g2 - The Superellipse Superellipses are the family of curves that lie between ellipses and rectangles (or circles and squares if the axes are equal). He hit on the superellipse with an exponent of 2.5 as ideal to fit the needs of the developers. This Danish article appears to be a translation of Martin Gardner's Superellipse article, but with the bonus of a photo of part of Sergel's Torg, and some supereggs. www.bbc.co.uk /dna/h2g2/A1053884   (1254 words)

 Superellipse and a good coordinate system Text - Physics Forums Library If A is different than B but still n =1, the coordinate system is similar but it involves also hyperbolic sine and cosine and one family of curves is the generic ellipse and the other family is the generic hyperbola and they are perpendicular to each other, like it happens in the polar coordinates. But instead of ellipses I have a particular kind of superellipses in which n is positive integer (see previous equation). Notice that when you change superellipse, A,B change as well, like in polar coordinate system, when you move from a circle to another one r changes. www.physicsforums.com /archive/index.php/t-115796.html   (463 words)

 Equal-Distance Sampling of Superellipse Models - Pilu, Fisher (ResearchIndex) Abstract: Superellipses are parametric models that can be used for representing two dimensional object parts or aspects of 3-D parts. Equal-distance sampling of superellipse model contours is however important for rendering and in cases in which a cost function needs to be estimated for data fitting or parameter estimation, such as in model-based optimisation. 12 The superellipse: a curve that lies between the ellipse and.. citeseer.ist.psu.edu /pilu95equaldistance.html   (474 words)

 Tutorial - Superellipse He then defined the Superellipse as any curve satisfying the last equation with n greater than 2. Especially he choose n = 2.5 for the actual problem, because he found that with this value the curve was looking especially pleasing for the eye. Just to mention a few, the Superellipse was used in the design of the Olympic Stadium in Mexico City. www.oberonplace.com /products/plotter/tutor/lesson2.htm   (1124 words)

 Superellipse -- from Wolfram MathWorld A superellipse is a curve with Cartesian equation The area of a superellipse is given by Gielis (2003) has considered the further generalization of the superellipse given in polar coordinates by mathworld.wolfram.com /Superellipse.html   (402 words)

 Piet Hein - Superellipse Civilized man is surrounded on all sides, indoors and out, by a subtle, seldom-noticed conflict between two ancient ways of shaping things: the orthogonal and the round. Moreover, such curves could be nested to give a strong feeling of harmony and parallelism between the concentric ovals. When the entire center is finally completed - perhaps in 1967 - it is expected to be one of the great tourist attractions (certainly for mathematicians!) of Sweden. io.uwinnipeg.ca /~estrauss/PietHein/superellipse.html   (841 words)

 Piet Hein   (Site not responding. Last check: 2007-11-05) This became the superellipse which solved the double contrast between the circle and the square and that of the ellipse and the rectangle. This harmonic geometrical figure was first used on a large scale in connection with the solution to a town planning problem in Stockholm. Within furniture design the superellipse also became the solution to various problems - especially in relation to Piet Hein's design for table tops the superellipse became popular. www.thetouch.com.sg /designers/PietHein/page1   (86 words)

 DesignMatcher.com, Finding your favourite Design It is possible to make a formula for the superellipse but the construction can be characterized as a crossing between a rectangle and an ordinary ellipse (see formulas of both). The Superellipse has the formula of a modified ellipse (math freaks): x/an + y/bn = 1 with the exponent n = 2 1/2. Parameter a and b are in the Superellipse hald the lenght and the width of the Superellipse. www.designmatcher.com /nl/gallery_detail.php?galleryID=893   (703 words)

 [No title]   (Site not responding. Last check: 2007-11-05) % % Input, real R1, R2, the "radius" of the superellipse % in the major and minor axis directions. % % Input, real PSI, the angle that the major axis of the % superellipse makes with the X axis. A value of 0.0 means that the % major and minor axes of the superellipse will be the X and Y % coordinate axes. www.csit.fsu.edu /~burkardt/m_src/geometry/super_ellipse_points_2d.m   (263 words)

 Landscape of Round Holes: August 2005 C. This is Piet Hein's superellipse, with his recommended ratio of 6/5 and roundness of 2.5. The superellipse hit all the right criteria for the design, not too square, not too round, could be of any length, any width, it was nestable, and subtle differences from a rectangle with the corners rounded off gave it a simple beauty. If a superellipse is revolved around the major axis a superellipsoid is formed, also called a superegg. landscape.typepad.com /landscape_of_round_holes/2005/08   (5004 words)

 perplexus.info :: Geometry : Square the Circle If n is greater than 2, then this is a "superellipse" (if a = b, then this is a supercircle). The latter value differs from (pi+4)/2 at just about the number of places that the approximation to pi differs from pi, showing the discrepancy is due to the coarseness of the Riemann increment. It is peculiar, as this is surely the correct answer, that Martin Gardner's "Mathematical Carnival", in the addendum to chapter 18 on Piet Hein's Superellipse, states "Norton Black, using a computer, determined that the value is a trifle greater than 3.17." Perhaps a slip of the finger from the 6 key to the 7 key? perplexus.info /show.php?pid=2066&cid=18412   (365 words)

 environment help   (Site not responding. Last check: 2007-11-05) %./superellipse -r 400 400 -b 2.0 -a 1.5 > ellipse_command.txt %./superellipse -r 400 400 -b 1.0 -a 1.5 >> ellipse_command.txt %./superellipse -r 400 400 -b 1.0 -a 1.5 www-users.itlabs.umn.edu /classes/Fall-2004/csci5107/pipes.htm   (252 words)

 DesignAddict Forums   (Site not responding. Last check: 2007-11-05) Fritz Hansen hproduces the table in maple...anyway all of this you can find by going to the designaddict links under "history" Bruno Matthson is wrongly identified as danish, but than again in Swedisch history it is not the first time that his birthplace Varnamo was considered Danish by the danes. I have forgotten the small and elegant formula, but they are easy to construct in the same way as gardeners draw regular ellipses: (with a loop of a constant length and two centers) for a superellipse you add two extra centers to form a square or a regular rectangle. Depending on the exess length of your loop you will have a superellipse that is closer to the square (short) or closer to a circle (long). www.designaddict.com /design_addict/forums/index.cfm/fuseaction/thread_show_one/thread_id/31/index.cfm   (626 words)

 Math Trek: A Geometric Superformula, Science News Online, May 3, 2003   (Site not responding. Last check: 2007-11-05) These shapes, he contends, are useful for modeling natural structures and providing insight into why certain forms grow as they do. The result, which he dubs the superformula, is a generalization of the superellipse formula to encompass many more shapes: Additional information about superellipses is available at http://mathworld.wolfram.com/Superellipse.html. www.sciencenews.org /articles/20030503/mathtrek.asp   (679 words)

 Piet Hein   (Site not responding. Last check: 2007-11-05) Because of his longing for his native country he designed a Great Bear candelabra in steel wire which reminded him of the night sky in Denmark. In a three-dimensional version the superellipse became the super egg which has been used for for instance the Stress Egg. The Stress Egg is produced in stainless steel and comes with small suede pouch. www.thetouch.com.sg /collections/piethein/page1   (104 words)

 Piet Heins Superellipse I 1968 producerede man et designbord med superellipse som bordflade. Nedenfor har jeg tegnet en superellipse med netop dette forhold mellem a og b, dvs. Efter Piet Heins opfindelse dukkede superellipser op mange steder. www.matematiksider.dk /piethein.html   (2346 words)

 Search ScienceWorld A superellipse is a curve with Cartesian equation x/a^r+y/b^r==1, first discussed in 1818 by Lamé. A superellipse may be described parametrically bySuperellipses with a==b are also known as Lamé curves or Lamé ovals. The restriction to r>2 is sometimes also made. scienceworld.wolfram.com /search/index.cgi?as_q=Biological+symmetry   (104 words)

 Comments on 21158 | MetaFilter In the design world, he is most famous for the SuperEllipse, a figure that rivals Buckminster Fuller's geodesics in ingenuity, an aesthetic balance between a circle and a square, and a mathematical figure which has been used to design a square in Stockholm. From the SuperEllipse, you can get the SuperEgg, a strange solid which will unexpectedly balance on one end and has been mistaken for an alien artifact. I believe there's a font based on superellipses. www.metafilter.com /comments.mefi/21158   (497 words)

 Fitting Superellipses   (Site not responding. Last check: 2007-11-05) In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the nonlinear nature of the problem. In addition, we describe various alternative error of fit (EOF) measures that can be applied by most superellipse fitting methods. Citation:  Paul L. Rosin, "Fitting Superellipses," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22,  no. 7,  pp. csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tp/&toc=comp/trans/tp/2000/07/i7toc.xml&DOI=10.1109/34.865190   (408 words)

 CS 4810 Computer Graphics -- Assignment 5   (Site not responding. Last check: 2007-11-05) Try to make your code as flexible as possible, i.e, try not to hardcode coordinates. Add the ability to draw one additional type of shape, such as an arch, meander or superellipse. Check with the instructor if you want to draw different shapes instead of one of these. www.cs.rockhurst.edu /~cigas/CS4810/hw05.html   (382 words)

 Superellipse and a good coordinate system The following code was used to generate this LaTeX image: This is a parametric representation of the superellipse, not a coordinate system. To find a tangent vector to some superellipse given by fixed www.physicsforums.com /showthread.php?p=970773#post970773   (610 words)

 LBasicFr - Trucs et Astuces - Andy Amaya   (Site not responding. Last check: 2007-11-05) La Sub SuperEllipse vous permet de creer des formes tels que des rectangles, diamands, triangles, pentagones, hexagones, heptagones, ellipse, cercles, et bien d'autre avec une seule formule, changez les parametres et vous changez de forme. '** hauteur - est le rayon sur l'axe y de SuperEllipse ** SuperEllipse centerX, centerY, wide, high, exponent, numSegments, penSize, rotAngle lbasic.atomysk.com /trucs/andyamaya/index.htm   (1183 words)

 all-new super different but similar and kinda familiar blog: Funxion SUPERELLIPSE� all-new super different but similar and kinda familiar blog: Funxion SUPERELLIPSE� In 1959 Stockholm city planners tried to find a new and better shape to their old city square, Sergels Torg. When they asked Piet Hein to give it a try, he came up with the SUPERELLIPSE?." www.psylux.com /blog/2002/10/funxion-superellipse.html   (106 words)

 He invented a poetic form, a board game and a 3D puzzle as well as helping in Vi... He invented the grook, the game Hex and the Soma cube (which I’d never heard of until now). He is supposed to have suggested a superellipse-shaped table for the Vietnam peace talks, and the superellipse was used in the design of the Azteca stadium in Mexico City. I came across this while looking up the puzzle called the Bedlam Cube. www.funtrivia.com /ask.cfm?action=details&qnid=60738   (228 words)

 Geometry and Pattern in Nature 1: Exploring the shapes of diatom frustules with Johan Gielis' Superformula. ², where r=radius) with that for a superellipse. A superellipse is a specific type of mathematical curve that produces a number of different shapes, for example, astroids, circles and diamonds, depending on the power the sine and cosine terms are raised to. For a more detailed explanation and mathematical equations, please see: www.microscopy-uk.org.uk /mag/artapr04/cbdiatom2.html   (1114 words)

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