03/26/2002
15-462 Graphics I
11
Rays and Parametric Surfaces
•Ray in
parametric form
–Origin
p0 = [x0 y0
z0 1]T
–Direction
d = [xd yd zd
0]t
–Assume
d normalized (xd2 + yd2 + zd2 = 1)
–Ray p(t)
= p0 + d t for t > 0
•Surface
in parametric form
–Point
q = g(u, v), possible bounds on u, v
–Solve p
+ d t = g(u, v)
–Three
equations in three unknowns (t, u, v)