CS 435 Autumn 1997 --- Introduction to Interactive Graphics

Simple Ray Tracing Guide

Viewing

The simplest ray tracer does hidden surface removal, lighting, and shadows.
To simplify things further, you can trace the scene in a restricted world (eye) space by requiring the viewer to be at the origin, looking down the negative Z-axis

To calculate the field of view, assume that your rays go from

X: -tan(theta) to tan(theta)

Y: -ratio*tan(theta) to ratio*tan(theta), where

ratio = (Vyt - Vyb)/(Vxr - Vxl)

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General Algorithm Outline

• Read in scene information and object information
• Initialize color table (using ct_gen)
• Calculate viewing parameters and area to raytrace
• For Y = -ratio*tan(theta) to ratio*tan(theta)
  • Initialize color_buffer to background color
  • For X = -tan(theta) to tan(theta)
    • For each object in the scene
      • Test to see if ray intersects each object and
        save t value of this intersection and object number if this is the closest one so far.
    • Shoot shadow ray for this pixel for the closest object
      Shadow ray origin = Intersection point
      Shadow ray direction = light - Intersection point
    • Shoot reflection ray for this pixel for the closest object
      Reflection ray origin = Intersection point
      Reflection ray direction = 2*N*(N.E) - E
    • Calculate the illumination and color of this object based on
      the illumination model, shadow information, and reflection color.
      I suggest adding Ir*ks*.5 for the reflected color.
    • color_buffer[x] = color from above
  • Write color_buffer to screen or file (using write_buffer cmd)

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Ray Intersection

For this lab, you need to calculate the intersection of a parametric semi-infinite ray with a sphere:

Let the ray be R(t) = O + D*t

Rx = O.x + t * D.x

Ry = O.y + t * D.y

Rx = O.z + t * D.z
where O is the origin of the ray,
D is the direction of the ray, and
t > 0 traces out the ray.
If we have a sphere centered at (cx,cy,cz) with radius r, then the points on the sphere satisfy

(x -cx)² + (y -cy)² + (z -cz)²= r²
To solve this, we put the ray's Rx, Ry, Rz into the sphere equation and solve for t.

(O.X + D.x * t - cx)² + (O.y + D.y * t - cy)² + (O.z + D.z * t - cz)² = r²
or At² + Bt + C = 0
with:

A = D.x² + D.y² + D.z²

B = 2 * (D.x * (O.x - cx) + D.y * (O.y - cy) + D.z * (O.z - cz))

C = (O.x - cx)² + (O.y- cy)² + (O.z - cz)² - r²
So, the quadratic equation can be used to solve for the t's. If no real roots exist, then there is no intersection.
Choose the smallest t for the closest point..

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Color Calculation:

Use the edge library calls ct_gen and write_buffer to create the color table and to write the scanline information for the image. See the sample program "scan_sample.c" in the class area for examples of how to use these functions.

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David S. Ebert
December 1998