Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


Steven
Posts:
4
Registered:
6/30/12


Re: line surface intersection
Posted:
Jan 20, 2014 10:22 AM


Hi,
I've been working on this problem for a couple of days  and have a solution below which achieves the correct result.
However I'm looking to make this much more efficient in order to use in animation.
I'd be grateful for any pointers!
Thanks Steven
"John D'Errico" <woodchips@rochester.rr.com> wrote in message <ighcj0$n28$1@fred.mathworks.com>... > "Peter Schreiber" <schreiber.peter15@gmail.com> wrote in message <igh7cl$ph8$1@fred.mathworks.com>... > > Hi guys, > > I'm trying to find the line surface intersection in following program. For now I can > > assume that there is one and only one such intersection possible. The code works > > but I was wondering if anyone has any ideas improving the speed/performance. > > Is there something that can be vectorized or are there any other ways to improve > > speed? > > > > Ugh. Personally, that code looks like it runs like a dog > with two legs. I would completely rewrite it. > > The idea is to rotate the surface so that the line becomes > a coordinate axis. This makes the intersection a far more > trivial one. Then, identify those simplexes which MAY > possibly intersect the axis in question using either a > circumsphere or a bounding box. (I don't recall which > I used.) Now just test each potential simplex more > accurately. > > I've got some code that I can give out to compute this > intersection of a general line with any nmanifold. A surface > would qualify if you have a triangulation for it, and that > triangulation is trivial to generate for z(x,y). If there are > multiple points of intersection, all of them are generated. > A quick check shows that the code I wrote generates the > point of closest approach if the line fails to intersect the > manifold at all. > > You can do a large fraction of this in a vectorized form. > > John



