doug@eris (Doug Merritt) (04/05/88)
A few years ago I read a paper by a guy at Stanford who came up with an interesting model that allowed two way transformations: model => rendered image, and digitized image => model. It was based on "superquadrics"; his paper did not adequately define these. Can someone explain "superquadrics", or give an easily accesible reference that does? Doug Merritt doug@mica.berkeley.edu (ucbvax!mica!doug) or ucbvax!unisoft!certes!doug
trainor@lanai.cs.ucla.edu (Vulture of Light) (04/06/88)
In article <8340@agate.BERKELEY.EDU> doug@mica.berkeley.edu (Doug Merritt) writes: >A few years ago I read a paper by a guy at Stanford who came up >with an interesting model that allowed two way transformations: >model => rendered image, and digitized image => model. It was >based on "superquadrics"; his paper did not adequately define these. > >Can someone explain "superquadrics", or give an easily accesible reference >that does? Just for the other people, this is a computer vision system whose model of the world is comprised of superquadrics, akin to earlier systems that used, say, generalized cylinders. Superquadrics are fun, easy, and are a generalization of quadric surfaces. All you do is fiddle with exponents in the equations! To illustrate the concept, take a circle: _ [ ] [ 1 ] X = [ cos (theta) ] = [ cos (theta) ] [ ] [ 1 ] [ sin (theta) ] [ sin (theta) ] And to make it "super" just paramaterize the exponent: _ [ r ] X = [ cos (theta) ] [ r ] [ sin (theta) ] Play with "r" and you get all sorts of cool shapes. Now just do this with the quadrics (too messy in ascii...). If you want to find out more I suggest reading: Barr, A.H. ``Superquadrics and Angle-Preserving Transformations,'' IEEE Computer Graphics and Applications, Vol. 1, No. 1, 1981.
turk@mit-amt.MEDIA.MIT.EDU (Matthew Turk) (04/06/88)
In article <10919@shemp.CS.UCLA.EDU>, trainor@lanai.cs.ucla.edu (Vulture of Light) writes: > In article <8340@agate.BERKELEY.EDU> doug@mica.berkeley.edu (Doug Merritt) writes: > >A few years ago I read a paper by a guy at Stanford who came up > >with an interesting model that allowed two way transformations: > >model => rendered image, and digitized image => model. It was > >based on "superquadrics"; his paper did not adequately define these. > > > >Can someone explain "superquadrics", or give an easily accesible reference > >that does? > > Just for the other people, this is a computer vision system whose model > of the world is comprised of superquadrics, akin to earlier systems > that used, say, generalized cylinders. > > [...] > > ... I suggest reading: > > Barr, A.H. ``Superquadrics and Angle-Preserving Transformations,'' > IEEE Computer Graphics and Applications, Vol. 1, No. 1, 1981. Alex Pentland (now at the MIT Media Lab) is the person mentioned by Doug Merritt. He developed a 3-D modeling system called "SuperSketch" which uses superquadrics as its primitives. SuperSketch allows a user to quickly model a wide range of natural and man-made shapes in a way that captures the intuitive "part structure" of the object. This is the "model => rendered image" part. The "digitized image => model" transformation is described for range data in a paper by Pentland and Bob Bolles (see reference below). I believe superquadrics were invented by Peit Hein, a Danish designer. They are a superset of CSG modeling primitives. -> Barr, A. H. (above) -> Gardiner, M. "The superellipse: a curve that lies between the ellipse and the rectangle", Sci. Am., Sept 1985. -> Pentland, A. "Perceptual organization and the representation of natural form", Artificial Intelligence, May 1986. -> Pentland and Bolles, "Learning and recognition in natural environments", (don't know if this is published yet...) Hope this helps... Matthew
chuck@Morgan.COM (chuck) (12/03/88)
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. Chuck Ocheret Morgan Stanley & Co., Inc. 1251 Ave of the Americas, NY, NY 10020 (212)704-4474 chuck@morgan.com
usenet@cps3xx.UUCP (Usenet file owner) (12/06/88)
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."
prem@geomag.fsu.edu (Prem Subrahmanyam) (01/12/90)
I have been doing a lot of work with DBW_Render lately (honors thesis),
and have acquired DBW 2.0 from the present keeper and author (Bill
Baldridge). One of the new shapes that it supports is called a
superquadric. Now, I've attempted to look up info in IEEE CG&A about
them and found out that the first issue ever to come out had an article
about these, however, our library does not have this issue. So, can
anyone point out another source for info about these (the full equation
used for them, and how to do a ray-superquadric intersection (complete
with normal calculation for a given point))? Thanks in advance......
---Prem Subrahmanyamflynn@pixel.cps.msu.edu (Patrick J. Flynn) (01/12/90)
In article <438@fsu.scri.fsu.edu> prem@geomag.gly.fsu.edu (Prem Subrahmanyam) writes: > One of the new shapes that [DBW_render] supports is called a > superquadric. Now, I've attempted to look up info in IEEE CG&A about > them and found out that the first issue ever to come out had an article > about these, however, our library does not have this issue. So, can > anyone point out another source for info about these (the full equation > used for them, and how to do a ray-superquadric intersection (complete > with normal calculation for a given point))? Thanks in advance...... The computer vision community has been using superquadrics for representation for a few years. Alexander Pentland developed a solid modeler (SuperSketch) around them, and recent papers have dealt with fitting them to 3D data. Parametric form for a point on a superquad.: Let c(e,x) = (cos x)^e s(e,x) = (sin x)^e (x(u,v),y(u,v),z(u,v)) = ( c(e1,u)*c(e2,v) , c(e1,u)*s(e2,v), s(e1,u) ) u and v are parameters of latitude and longitude. The parameters e1 and e2 control the shape of the primitive obtained when you sweep u and v over the sphere. The normal can be obtained by differentiation. Ref: Pentland, A.P., Perceptual Organization and the Representation of Natural Form, Art. Intell. J. 28: 293-331, 5/86. Fitting problems have been attacked by Ruzena Bajcsy and colleagues at U. Pennsylvania, Terry Boult and Students at Columbia, and others. If you're interested, check out Proceedings of the first and second Int. Confs. on Computer Vision (IEEE), the AAAI workshop on Spatial Reasoning and Multisensor Fusion (1987), and the recent IEEE workshop on 3D scene interpretation. -- Patrick Flynn, CS, Mich. State U., flynn@cps.msu.edu
wrf@mab.ecse.rpi.edu (Wm Randolph Franklin) (01/17/90)
In article <438@fsu.scri.fsu.edu> prem@geomag.gly.fsu.edu (Prem Subrahmanyam) writes: > > I have been doing a lot of work with DBW_Render lately (honors thesis), > and have acquired DBW 2.0 from the present keeper and author (Bill > Baldridge). One of the new shapes that it supports is called a > superquadric. Now, I've attempted to look up info in IEEE CG&A about > them and found out that the first issue ever to come out had an article > about these, however, our library does not have this issue. So, can > anyone point out another source for info about these (the full equation > used for them, and how to do a ray-superquadric intersection (complete > with normal calculation for a given point))? Thanks in advance...... > ---Prem Subrahmanyam 1. You have a bad library since this is a standard journal. They should get the back copies that are missing. 2. You might contact the author, Al Barr, then at RPI but now at Caltech, for the paper. An old address is barr@cit-vax.ARPA or @csvax.caltech.edu. 3. There was a second paper a little later on superquadrics in IEEE CGA by Barr and me. I'll send you a copy if you give me your address. 4. Al has probably had other papers on them; he researches and publishes a lot. There might have been a Siggraph tutorial. -- Wm. Randolph Franklin Internet: wrf@ecse.rpi.edu (or @cs.rpi.edu) Bitnet: Wrfrankl@Rpitsmts Telephone: (518) 276-6077; Telex: 6716050 RPI TROU; Fax: (518) 276-6261 Paper: ECSE Dept., 6026 JEC, Rensselaer Polytechnic Inst, Troy NY, 12180
<MASOUDA@QUCDN.QueensU.CA> (09/14/90)
Hello !
I would appreciate if anybody would send me some informations about a software
that can be used to plot the superquadrics.
Thanks.