Raytracing and Global IlluminationIntro. to Computer Graphics, CS180, Fall 2008 UC Santa Barbara

Rasterization vs. Raytracing

Rasterize:

- Project polygons onto picture plane- Efficient hardware. OpenGL, DirectX

Raytrace:

- Cast light rays into scene through picture plane.

project cast

Inverse View Matrix

- Compute ray directions using Inverse Projection and Camera matrix

- Loop over all pixels in image. Start with 3D ray extending from camera

p = Cam Cam Proj p’(x,y)

p’(x,y) = clip ( P V M p(x,y,z) ) = Proj View p

T R-1 -1 -1

p

p -1

Inverse Projection Matrix

- Where else have we see the Inverse Projection Matrix?

- Just draw a line from the origin to the pixel (x, y)

p

x

y

Ray-Sphere Intersection

r

p(t) = R + t R t > 0 Ray definition

p: (x – xc) + (y – yc) + (z – zc) = r Sphere definition2 2 2 20 dir

Solve for p:

p

0R

dirR

A t + B t + C = 02A = Rx + Ry + RzB = 2 * (Rx (Rx0–Sx) + Ry (Ry0-Sy) + Rz(Rz0-Sz) )C = (Rx0–Sx) + (Ry0–Sy) + (Rz0–Sz)

2 2 2

2 2 2

- What do we do when we hit an object?

- Warn lighting model. Trace rays to each light source, and also new terms for reflected and trasmitted light

Raytracing – Illumination Model

First application of Raytracing:

Rene Descarte, Geometry of Rainbows, 1641

- Rainbows are caused by refraction of light in a spherical water dropplet- Proved that rainbows always occur at 42 degs between viewer & sun

Raytracing - History

Turner WhittedAn improved illumination model for shaded displayCommunications of the ACM, v.23 n.6, p.343-349, June 1980

ABSTRACT To accurately render a two-dimensional image of a three-dimensional scene, global illumination information that affects the intensity of each pixel of the image must be known at the time the intensity is calculated. In a simplified form, this information is stored in atree of “rays” extending from the viewer to the first surface encountered and from there to other surfaces and to the light sources. Consideration of all of these factors allows the shader to accurately simulate true reflection, shadows, and refraction, as well as the effects simulated by conventional shaders.

Monte Carlo Raytracing

- Multiple rays per pixel = Anti-aliasing- Multiple rays per light = Soft shadows- Multiple rays per reflect = Diffuse reflections - Multiple rays per frame = Motion blur

What might be some limitations of raytracing?

What might be some limitations of raytracing?

1. Performance

2. Light propagation - no caustics

3. Memory – All geometry must fit in memory

10 million rays, simple scene

Solution: Acceleration structures: k-d Tree, Octree

Monsters, Inc. (Pixar) 13 hours per single frame,most of that is spent raytracing individual hairs of fur.

Acceleration:

k-d Tree Special case of BSP Tree.. Axis-aligned BSP Tree

Geometry is inserted in tree.

Rays traversethrough it.

Daniel Horn, Jeremy Sugerman, Mike Houston, Pat Hanrahan“Interactive k-D Tree GPU Raytracing”, 2007

GPU Raytracing

18x

8x

4x

16.3 million rays/sec

CPU (AMD 2.4ghz) 2.4 fpsGPU (ATI X1900): 14.2 fpsPS3 (Cell Proc): 20.0 fps

Free source code