Delaunay triangulation part of sphere
cfdman
i have been trying to come up with a resolution to a problem i am
having but so far i cannot come up with a solution and i am hoping
someone here has an idea i can try.
Problem:
suppose i have a sphere or part of a sphere so it is periodic in one
direction and has either one or two poles. suppose that the sphere is
periodic in U and the parameter runs from 0 to 360.
next, suppose i have a set of curves which are on the surface of the
sphere such that they form a closed set in physical space but the
curves can cross the periodic seam and also either use one of the
poles or the pole is interior to the set of curves.
i next discretize the curves and project each of the points onto the
sphere to obtain U,V coordinates so that i can then eventually use a
2D Delaunay triangle mesher and then evaluate the mesh into physical
space.
the problem is that when i project each of the discrete points onto
the sphere they do not form a closed set in parametric space.
rotating the sphere to remove the singularity out of the closed set of
curves is out of the question because i want this to work on any
arbitrary singular, periodic surfaces. so i was wondering if anyone
has any ideas on how to make this work; is there some alternate
parametrization i can use such that the point projection would be
closed and properly oriented in UV space?
thanks
Dave Eberly
news:df7264e9-6973-4a1f...@j14g2000yqm.googlegroups.com...
> i next discretize the curves and project each of the points onto the
> sphere to obtain U,V coordinates so that i can then eventually use a
> 2D Delaunay triangle mesher and then evaluate the mesh into physical
> space.
Why not just compute the convex hull of the points that were projected onto
the sphere? This gives you a triangulation directly. Your approach maps
the 3D points to 2D, triangulates in 2D, and then lifts back into 3D, which
perhaps are too many steps...
--
Dave Eberly
http://www.geometrictools.com
Kenneth Sloan
Represent your points on the sphere using X,Y,Z coordinates.
Compute the 3D Convex Hull of these points.
Trim.
If convenient, you might consider adding an extra point in the middle of
the "outside" of your patch - this might make it easier to trim (just
discard triangles from the Convex Hull which use that point as a vertex.
--
Kenneth Sloan Kennet...@gmail.com
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://KennethRSloan.com/
cfdman
> Computer and Information Sciences +1-205-932-2213
> University of Alabama at Birmingham FAX +1-205-934-5473
> Birmingham, AL 35294-1170 http://KennethRSloan.com/
thanks for these ideas but they don't apply in my case because this
mesh usually applies to multiple surfaces patches such as those
imported from a CAD file or locally constructed and there must be
point to point congruency of points at the boundaries. also, this
parametrization is necessary in order to verify trims and spatial
relationships between trims such as containment, self-intersections or
trim to trim intersections.