1. Ray Tracing

2. Ray Tracing
Highly realistic
Considerable computation time

3. Ray Tracing
prp

4. Ray Tracing R3 T3 T2 R2 R4 R1 T1 T4 R1 T1 R2 T2 R4 T4
prp R3 T3

5. Ray Tracing Algorithm main() {
Select prp
for (each scan line)
for (each pixel in scan line)
determine ray from prp through pixel
pixel = Trace (ray, 1) }
Trace (ray, depth)
determine closest intersection of ray with an object
if (object hit)
compute normal at intersection
return Shade( closest object hit, ray, intersection, normal, depth)
else
return background_value
Shade ( object, ray, point, normal, depth) {
color = ambient term
for (each light)
Sray = ray to light from point
if (N.L>0)
compute how much light is blocked by opaque and
transparent surfaces,
use it to scale diffuse and specular terms and
add term to color
if (depth < maxdepth)
if (object is reflective)
Rray = ray in reflection direction from point
Rcolor = Trace (Rray, depth+1)
scale Rcolor by specular coeff. and add to color
if (object is transparent)
Tray = ray in refraction direction from point
if (total internal reflection does not occur)
Tcolor = Trace (Tray, depth+1)
scale Tcolor by transmission coeff. and
add to color
return color }

6. Ray Tracing ambient light: ka Ia diffuse light: kd (N.L)
specular light: ks (H.N)ns
specular reflection direction:
R = u-(2u.N)N
T = [(hi/hr) cos qi - cos qr] N - (hi/hr)L
cos qr = √1 - (hi/hr)2 (1-cos2 qi )
reflected light R L
shadow ray T qr N qi hr H hi u
incoming ray
(viewing direction V = -u)

7. Ray Tracing Ray equation u = ------------------ | Ppix – Pprp |
P = P0 + s.u
P: any point along the ray
P0: initial position vector
s: distance of P to P0
u: unit direction vector
Ppix – Pprp
u =
| Ppix – Pprp |
Initially P0 is Ppix or prp.
Update P0 and u at each intersection point on the ray with a surface. y
ray path u P0
Ppix x
prp z

8. Ray Tracing P: intersection point of the sphere along the ray
Pc: center of sphere
r: radius of sphere
|P - Pc |2 – r2 = 0
|P0 + s.u - Pc |2 – r2 = 0
s = u.P  (u.P)2 - |P|2+r2
where P = Pc – P0
If discriminant < 0
ray does not intersect sphere
Otherwise
calculate P using P = P0 + s.u P r P0 x y z u Pc

9. Ray Tracing If the ray does not intersect the sphere,
eliminate the polyhedra
Otherwise
do the following:
Identify front faces using: u.N<0
For each face that satisfies u.N<0:
- Solve plane equation:
N.P = -D
N.(P0 + s.u) = -D
 s = - (D+N.P)
N.u
- Perform inside-outside test to check if the intersection is inside the polygon P0 x y z u Pc u
Infinite plane

10. Ray Tracing

11. Ray Tracing

12. Ray Tracing

13. Ray Tracing