ritter@versatc.UUCP (Jack Ritter) (08/26/88)
(I had to re-send this; sorry)
On page 299 of Procedural Elements for Computer Graphics, the following
general quadric surface locus is stated:
Q(x,y,z) = a1*x**2 + a2*y**2 + a3*z**2 + b1*yz + b2*xz + b3*xy +
+ c1*x + c2*y + c3*z + d =0.
The text implies that this locus can be translated into a primed coord sys
where x & y =0. The alleged transformation is the one which rotates the ray
of interest into the z axis (ie 2 rotations).
QUESTION 1: Is there a general analytic solution to this? Can you analytically
"rotate" the coefficients to get the new prime coefficients?
If not, I would settle for subsets of Q defined by having some
of the coefficients = 0, but more than spheres & cones!
I didnt see this locus mentioned in Ref 1-1 (Math. Elem. for Comp. Graphics).
QUESTION 2: Is there an analytic solution for the normal N(x,y,z) ?
QUESTION 3: Are there analytic solutions for arc length along one dimension?
Thanks
--
Jack Ritter, Software Engineer
Versatec, 2805 Bowers Avenue, Santa Clara, Calif 95051
Mail Stop 1-7 (408)982-4332
UUCP: {pyramid,ubvax!vsi1}!versatc!jack