Image synthesis using classical optics Raytracing Image synthesis using classical optics

Raytracing Create 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 Raytracing Simplest 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 rays from eye screen

Rays A 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) = 0 Then 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 Quadrics Cylinders, 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 Calculation So… we know where the ray hits the surface But what does the surface look like? Need to compute lighting at the point of intersection

Local Lighting Calculation Can use 3-term lighting calculation local illumination Raytracing allows us to do global illumination shadows reflected and refracted light

Shadow Rays Decide if a point is in shadow or not based on new ray intersection test Cast ray from intersection point towards light source If intersection found, point is in shadow Otherwise, not in shadow

Raytracing Tree Resolving a ray intersection can result in multiple additional rays Ray intersection Transmitted rays Shadow ray Reflected rays

Reflected Rays Recursive 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 Intersections Majority of work in raytracer in computing intersections Simple-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 supreme But, 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