An Introduction to Ray Tracing

CS 288

10/27/1998

Vic Baker

What is Ray Tracing?

“Ray Tracing” determines the visibility of surfaces by tracing imaginary rays of light from the viewer’s eye to the objects in the scene

Ray Tracing evolved from an algorithm used to simulate trajectories of ballistic projectiles and nuclear particles

Ray Tracing Algorithm

Select center of projection and window on viewplane

for (each scan line in image) {

for (each pixel in scan line) {

determine ray from center of projection through pixel;

for (each object in scene) {

if ( object is intersected and is closest thus far )

record intersection and object name;

}

set pixel’s color to that at closest object intersection;

}

}

Why Speed Up Ray Tracing?

Depending on the output size of a ray traced image, as well as the complexity of the scene itself, it is not uncommon for a ray traced image to take minutes or days to render!!!!

A 1024x1024 image requires that 1 million pixels be calculated!!!!!

Why Speed Up Ray Tracing?

Since ray tracing calculates every pixel’s color, a picture of size 512 x 512 contains 262144 pixels that require a color which is dependent on its distance from the COP, your eye.

A 1024x768 image has 786432 pixels to calculate independently!

A Minimal Ray Tracing Program

In an attempt to investigate how computationally demanding rendering a 3D scene is, I will demonstrate a minimal ray tracing program known as Minray.

The History of Minray.c

Paul Heckbert (CMU, Pixar) issued a challenge to the graphics community to write the smallest ray tracing program possible.

Minray is the result of taking the best portions of the best entries and combining them into a ray tracer

Minray hierarchy chartP ip e lin e fo r M in ray.c

vcom b vd ot

vu n it() vcom b ()

vd o t vcom b

in te rsec t vd o t vcom b vu n it

trace()

m a in ()

Frequency chart for a 32x32 image

0

20000

40000

60000

80000

100000

120000

140000

vdotvcombvunitintersecttracemain

vdot()

Calculates the dot product for two vectors Each call to vdot requires 113 clock cycles That’s 120978 * 113 = 13,670,514 clock cycles

for a 32x32 image

vcomb()

Vcomb adds two vectors Each call to vcomb requires 155 clock

cycles That’s 155 * 99408 = 15,408,240 clock

cycles for a 32x32 image

vunit()

Normalizes vectors Makes calls to vdot and vcomb Costs 331 clock cycles to execute That’s 331 * 15946 = 5,278,126 clock

cycles

intersect()

Determines if a ray intersects an object Requires vdot() and vcomb() Costs 2547 clock cycles Total cost for a 32x32 image is 9011 * 2547

= 22,951,017 clock cycles

trace()

Keeps track of nearest intersection of object and maps color to pixel

Costs 141 * 5998 = 845,718 clock cycles for a 32x32 image

How can we speed ray tracing up? By using loop unrolling, straight-lining

code, as well as using macros instead of function calls, you can drastically reduce overhead

What’s out there?

A good ray tracing program is the POV-Ray.

Let’s see some examples...