CS6620 Assignment1

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[edit] CS 6620 Assignment 1

Reference Image generated by my ray tracer

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This is a box with a pyramid of spheres on top of it. There is also a ring casting a shadow on the spheres.

This has multiple rings.

[edit] Extra Credit

Tori

I used the intersection method outlined in the Ray Tracing from the ground up book. It requires solving a quartic equation because you can have up to 4 intersection points. I borrowed code from the web for solving that.

The equation for the torus is: $\left [ ( x^2 + z^2 )^{1/2} - a \right ]^2 + y^2 - b^2$

Squaring gives the implicit equation for a generic torus

$f (x, y, z) = (x 2 + y 2 + z 2) - 2(a 2 + b 2)(x 2 + y 2 + z 2) + 4 a 2 y 2 + (a 2 - b 2) 2 = 0$

where a = swept radius and b = tube radius

You substitute the ray equation and get a 4th degree polynomial:

$c 4 t 4 + c 3 t 3 + c 2 t 2 + c 1 t + c 0 = 0$

Then you solve for $c 4, c 3, c 2, c 1, c 0$

For the normal calculation you use the gradient: $\overrightarrow{n} = \nabla f(x,y,z) = ({\partial f}/{\partial x}, {\partial f}/{\partial y}, {\partial f}/{\partial z} )$

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CS6620 Assignment1

From Dangerski

[edit] CS 6620 Assignment 1

[edit] Creative Image

[edit] Extra Credit

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