Ray Tracing: Shading

CS 4620 Lecture 5

• With eye ray generation and scene intersection

for 0 <= iy < ny for 0 <= ix < nx { ray = camera.getRay(ix, iy); c = scene.trace(ray, 0, +inf); image.set(ix, iy, c); } …

Scene.trace(ray, tMin, tMax) { surface, t = surfs.intersect(ray, tMin, tMax); if (surface != null) return surface.color(); else return black; }

• Compute light reﬂected toward camera • Inputs: – eye direction – light direction (for each of many lights) l n – surface normal v – surface parameters (color, shininess, …)

• Light is scattered uniformly in all directions – the surface color is the same for all viewing directions • Lambert’s cosine law

l n Q

Top face of cube Top face of In general, light per unit receives a certain 60º rotated cube area is proportional to amount of light intercepts half the light cos θ = l • n

intensity here: I

intensity r here: I/r2

intensity here: I

• Shading independent of view direction

illumination from source

l n 2 Ld = kd (I/r ) max(0, n l) Q v ·

diffuse coefﬁcient

diffusely reﬂected light

• Produces matte appearance [Foley et al.] et [Foley

Scene.trace(Ray ray, tMin, tMax) { surface, t = hit(ray, tMin, tMax); if surface is not null { point = ray.evaluate(t); normal = surface.getNormal(point); return surface.shade(ray, point, normal, light); } else return backgroundColor; } … Surface.shade(ray, point, normal, light) { v = –normalize(ray.direction); l = normalize(light.pos – point); // compute shading }

• Surface is only illuminated if nothing blocks the light – i.e. if the surface can “see” the light • With ray tracing it’s easy to check – just intersect a ray with the scene!

Surface.shade(ray, point, normal, light) { shadRay = (point, light.pos – point); if (shadRay not blocked) { v = –normalize(ray.direction); l = normalize(light.pos – point); // compute shading } return black; }

• Don’t fall victim to one of the classic blunders:

• What’s going on? – hint: at what t does the shadow ray intersect the surface you’re shading?

• Solution: shadow rays start a tiny distance from the surface

• Do this by moving the start point, or by limiting the t range

• Important to ﬁll in black shadows • Just loop over lights, add contributions • Ambient shading – black shadows are not really right – one solution: dim light at camera – alternative: add a constant “ambient” color to the shading…

shade(ray, point, normal, lights) { result = ambient; for light in lights { if (shadow ray not blocked) { result += shading contribution; } } return result; }

• Intensity depends on view direction – bright near mirror conﬁguration

l n v

• Close to mirror ⇔ half vector near normal – Measure “near” by dot product of unit vectors

h = bisector(v, l) v + l = l n h v + l A v 2 p Ls = ks (I/r ) max(0, cos ↵) = k (I/r2) max(0, n h)p s · specularly reﬂected light specular coefﬁcient Cornell CS4620 Spring 2017 • Lecture 5 © 2017 Steve Marschner • 17 Phong model—plots

• Increasing p narrows the lobe [Foley et al.] et [Foley

ks al.] et [Foley

• Shading that does not depend on anything – add constant color to account for disregarded illumination and ﬁll in black shadows

La = ka Ia

ambient coefﬁcient

• Usually include ambient, diffuse, Phong in one model

L = La + Ld + Ls = k I + k (I/r2) max(0, n l)+k (I/r2) max(0, n h)p a a d · s · • The ﬁnal result is the sum over many lights N

L = La + [(Ld)i +(Ls)i] i=1 X N L = k I + k (I /r2) max(0, n l )+ a a d i i · i i=1 X ⇥ k (I /r2) max(0, n h )p s i i · i