Raytracing

Image synthesis using classical optics

RaytracingCreate an image by following the paths

of rays through a scene“Backward raytracing": traces rays out

of the light sources out into the world“Forward raytracing": traces rays out

from the eye (camera) and out into the world and eventually back to the light sources

Forward RaytracingSimplest form (raycasting):

for each pixel on the screen, send a ray out into the world

determine the first surface hit by the ray perform a lighting calculation at that

surface point set the color of the pixel according to the

result of the lighting calculation

Raytracing

screen rays from eye

RaysA ray is a half-line – it has only one end It can be written

p = o + t*d, t in (0,∞)

p is position (vector)o is the origin (vector)d is direction (vector)t is the parameter

Ray Intersection Key computation: intersection of ray with

objects Typically produced by solving an equation:

p = f(t)Say the object is defined by an implicit surface,

g(x,y,z) = 0Then g(f(t)) = 0

Smallest value of t means first intersection

Ray Intersection

Ray-Sphere Intersection Implicit equation of sphere:

(x-xc)2 + (y-yc)2 + (z-zc)2 – R2 = 0 Or, (p-pc)•(p-pc) – R2 = 0

Say ray is given by p(t) = e + t*d

Then(d • d)t2 + 2d•(e - c)t + (e – c)•(e – c) – R2 = 0

Other QuadricsCylinders, ellipsoids, paraboloids,

hyperboloids: all have the property that they are algebraic surfaces of degree 2, aka quadrics

The intersection calculation can be done analytically using the quadratic equation

Lighting CalculationSo… we know where the ray hits the

surfaceBut what does the surface look like?Need to compute lighting at the point of

intersection

Local Lighting CalculationCan use 3-term lighting calculation

local illumination

Raytracing allows us to do global illumination shadows reflected and refracted light

Shadow RaysDecide if a point is in shadow or not

based on new ray intersection testCast ray from intersection point towards

light source If intersection found, point is in shadowOtherwise, not in shadow

Raytracing TreeResolving a ray intersection can result in multiple additional rays

Transmitted rays

Ray intersection

Reflected rays

Shadow ray

Reflected RaysRecursive call to raycast:

ray’s color is (1-c) times the color computed at the surface, plus c times the color computed by a new ray heading out of the surface in the reflected direction

May cast multiple reflected rays at slightly different directions

Need to terminate the recursion: maximum depth minimum energy carried by the ray

Accelerating IntersectionsMajority of work in raytracer in

computing intersectionsSimple-minded method: compute

intersections with every object in scene, take smallest parameter

Need to speed this up bounding geometry spatial partitioning

Raytracing vs Z-Buffer Initial intersection test is the hard part

Z-buffer still supremeBut, all kinds of effects with same code

transparency, reflection, shadows, caustics in Z-buffer, bizarre stack of methods

"Embarrassingly parallel": well suited to GPU from process viewpoint – but, recursion not possible on cards