reddy@silma.com (Reddy) (03/19/91)
Does anybody out there know a better way to approximate partial derivatives
(specifically normal - du X dv) on parametric surface S(u,v) at a degenerate point. At
the degenerate point S(u0,v0) either du=0 or dv=0 or du=dv=0.
You could offset parameter u0 or v0 by small value (epsilon) and evaluate the surface,
but that is not what I want.
Any references would be appreciated.
Thanks
Reddy
e_mail - reddy@silma.comspencer@eecs.umich.edu (Spencer W. Thomas) (03/19/91)
In article <1991Mar18.213610.18736@silma.com> reddy@silma.com (Reddy) writes:
Does anybody out there know a better way to approximate partial derivatives
(specifically normal - du X dv) on parametric surface S(u,v) at a degenerate point. At
the degenerate point S(u0,v0) either du=0 or dv=0 or du=dv=0.
Assuming the tangent plane exists, then if dS/du is 0, use (d^2 S)/du^2,
(or the lowest n such that (d^n S)/du^n is non-zero).
At a point such that dS/du is parallel to dS/dv, you need to evaluate
a directional derivative in another direction. If you choose the vector
(u,v)=(1,1) then you can just evaluate (d S(u,u))/du. Again, assuming
the tangent plane exists, this should not be parallel to dS/du
(although I'm sure I could come up with a pathological case where it
was, and a higher-order derivative was required.)
--
=Spencer W. Thomas EECS Dept, U of Michigan, Ann Arbor, MI 48109
spencer@eecs.umich.edu 313-936-2616 (8-6 E[SD]T M-F)