03/26/2002
15-462 Graphics I
12
Rays and Implicit 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
•Implicit surface
–Given by f(q) = 0
–Consists of all points q such
that f(q) = 0
–Substitute ray equation for q: f(p0 + d t) = 0
–Solve for t (univariate root
finding)
–Closed form (if possible) or numerical
approximation