O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science

• Winding number
generalizes to 3D
Point in Polyhedron
• uses solid angle
(fraction of sphere surface
used by cone at point)
• Ray crossing
generalizes to 3D
• q inside P if odd
number of
crossings
• q outside P if even
number of
crossings
Running Time
(see next slide)
P
q
r
Assume each face is a triangle.
Algorithm: : POINT in POLYHEDRON (P, R, q)
Compute bounding radius R
loop forever
r 0 = random ray of length R
r=q+r
r 0
crossings = 0
for each triangle T of polyhedron P do
SegTriInt(T, q, r)
if degenerate intersection
then go back to loop
else increment crossings appropriately
if crossings odd
then q is inside P
else q is outside P
Exit
source: O’Rourke