Path: utzoo!utgpu!watmath!clyde!att!rutgers!mailrus!eecae!cps3xx!usenet From: usenet@cps3xx.UUCP (Usenet file owner) Newsgroups: comp.graphics Subject: Re: Superquadrics Keywords: superquadrics Message-ID: <1245@cps3xx.UUCP> Date: 6 Dec 88 14:37:14 GMT References: <3270@entire.UUCP> <1665@hp-sdd.HP.COM> <1988Nov16.234857.2372@cs.rochester.edu> <1679@hp-sdd.HP.COM> <146@terminus.Morgan.COM> Reply-To: flynn@pixel.cps.msu.edu (Patrick J. Flynn) Distribution: na Organization: Pattern Rec. & Img. Processing Lab, CS, Mich. State U. Lines: 36 In article <146@terminus.Morgan.COM> chuck@Morgan.COM () writes: >Could someone explain the nature of superquadrics along with mathematical >representations and interpretations. I am especially interested in >rendering techniques. I have heard that there are a number of articles >around but no one wants to provide a specific reference. Thanks. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Shame on them. A point on a `basic' superquadric surface is given as follows. Let eta and omega be latitude and longitude parameters (angles), respectively; C(eta), S(eta), C(omega), S(omega) are the sine and cosine of eta and omega, epsilon1 and epsilon2 are the `shape' parameters of the SQ. Then a point on the SQ is given by x(eta,omega)= (C(eta)**epsilon1)*(C(omega)**epsilon2) y(eta,omega)= (C(eta)**epsilon1)*(S(omega)**epsilon2) z(eta,omega)= S(eta)**epsilon1 Vary eta between -pi/2 and pi/2, and omega between -pi and pi, and you sweep out a closed surface. Therefore, SQs are volumetric primitives. You can build other shapes by bending, twisting, and tapering the basic form. Some references: Barr, Superquadrics and angle-preserving transformations, IEEE CG&A 1, 1-20. Pentland, Perceptual Organization and the Representation of Natural Form, Artificial Intell. J. 28, 293-331. Bacjsy and Solina, Three Dimensional Object Repreentation Revisited, Proc. 1st Int. Conf. on Computer Vision (ICCV-87), London, 231-240. Boult and Gross, Recovery of superquadrics from depth information, Proc. 1987 Workshop on Spatial Reasioning and Multisensor Fusion, St. Charles, IL, 128-137. These, and the references in them, should be a decent introduction. Pentland's paper is the best of the four (IMHO). -- Patrick Flynn, Dept. of Computer Science, Michigan State University flynn@cpsvax.cps.msu.edu flynn@eecae.UUCP FLYNN@MSUEGR.BITNET "First we break 'em in half.... then we mash 'em to a pulp."