pjm@calmasd.GE.COM (Pierre Malraison) (11/18/88)
Levin's work on quadrics provides nice ways of getting
exact solutions for q-q intersection curves in terms
of square roots of lowish degree polynomials.
The torus, alas, is not a quadric.... but it is pretty simple
algebraically. It seems similar methods ought to work to represent t-q
and torus-torus intersections.
Any obscure references or suggestions welcomed. Public domain
ideas only please. E-mail to me appreciated.
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These opinions are solely mine and in no way reflect those of my employer.
Pierre Malraison @ GE/Calma R&D, Geometric Modeling Group, San Diego
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These opinions are solely mine and in no way reflect those of my employer.
Pierre Malraison @ GE/Calma R&D, Geometric Modeling Group, San Diego
...{ucbvax|decvax}!sdcsvax!calmasd!pjm pjm@calmasd.GE.COMjbn@glacier.STANFORD.EDU (John B. Nagle) (11/20/88)
In article <149@calmasd.GE.COM> pjm@calmasd.UUCP (Pierre Malraison) writes: >Levin's work on quadrics provides nice ways of getting >exact solutions for q-q intersection curves in terms >of square roots of lowish degree polynomials. Reference, please. Can this work be extended to deformed superquadrics, along the lines of Pentland's Supersketch system? I spent some time trying to determine whether two deformed superquadrics intersected, and after about a month was able to reduce it to a messy quadratic programming problem but could get no further. Then I found out that one of Barr's students at UCLA was trying to solve the problem by using enclosing polyhedra. This, too, is messy. Is there a cleaner solution? John Nagle
usenet@cps3xx.UUCP (Usenet file owner) (11/22/88)
In article <17855@glacier.STANFORD.EDU> jbn@glacier.UUCP (John B. Nagle) writes: >In article <149@calmasd.GE.COM> pjm@calmasd.UUCP (Pierre Malraison) writes: >>Levin's work on quadrics provides nice ways of getting >>exact solutions for q-q intersection curves in terms >>of square roots of lowish degree polynomials. > > Reference, please. > 1. Levin, J., ``Mathematical Methods for Determining the Intersections of Quadric Surfaces'', CGIP 11, pp. 73-87, 1979. -- also -- 2. Sarraga, R., ``Algebraic Methods for Intersections of Quadric Surfaces in GMSOLID'', CVGIP 22, pp. 222-238, 1983. -- and maybe -- 3. Farouki, R., ``The Characterization of Parametric Surface Sections'', CVGIP 33, pp. 209-236, 1986. 4. Koparkar, P. and S. Mudur, ``Computational Techniques for Processing Parametric Surfaces'', CVGIP 28, 303-322. -- 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."