Ray Tracing

Ray Tracing Highly realistic Considerable computation time

Ray Tracing prp

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

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 }

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)

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

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

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

Ray Tracing

Ray Tracing

Ray Tracing

Ray Tracing