1. Image synthesis using classical optics
Raytracing
Image synthesis using classical optics

2. 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

5. 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

6. Raytracing
rays from eye
screen

7. 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

8. 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

9. Ray Intersection

10. 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

11. 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

12. 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

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

14. 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

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

16. 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

18. 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

19. 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