Ray TracingRay Tracing

Ray Tracing

Highly realistic

Considerable computation time

Ray Tracing

prp

Ray Tracing

ambient light: ka Iadiffuse light: kd (N.L)

specular light: ks (H.N)ns

specular reflection direction:

R = u-(2u.N)N

T = [(i/r) cos i - cos r] N - (i/r)L

cos r = √1 - (i/r)2 (1-cos2 i )

T

reflected light

i

incoming ray(viewing direction V = -u)

r

R

L

N

H

u

shadow ray

i

r

Ray Tracing

main() {Select prpfor (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 objectif (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 termfor (each light) Sray = ray to light from point if (N.L>0)

compute how much light is blocked by opaque andtransparent surfaces, and use to scale diffuse andspecular terms before adding term to color

if (depth < maxdepth) if (object is reflective)

Rray = ray in reflection direction from pointRcolor = Trace (Rray, depth+1)scale Rcolor by specular coeff. and add to color

if (object is transparent)Tray = ray in refraction direction from pointif (total internal reflection does not occur) Tcolor = Trace (Tray, depth+1) scale Tcolor by transmission coeff. and add to

colorreturn color

}

Ray TracingRay equation

P = P0 + s.u

P: any point along the rayP0: initial position vectors: 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.

prp

ray path

P0

x

y

z

u

Ppix

Ray Tracing

Ray Tracing

Ray Tracing

Ray Tracing