The document is a lecture on ray tracing in computer graphics, covering concepts such as ray generation, intersections, and recursive tracing. It discusses the generic ray tracer's function in determining color through ray intersections and using the Phong model for shading. Key aspects include ray-object intersection techniques and the calculation of composite color involving light sources.

1. Ray Tracing
E0 271 - Lecture 19
October 28, 2019

2. Vijay Natarajan E0 271: Computer Graphics 1
Today
» Generic ray tracer
» Ray intersections
» Reading: Angel, Chapter 11

3. Vijay Natarajan E0 271: Computer Graphics 2
What is Ray Tracing?
» Ray tracing
§ Send a ray from eye through pixel
into scene
§ Color determined by ray
intersections with the scene
» Recursive ray tracing
§ Create new rays upon intersection
§ Simulate specular reflections and
indirect illumination
[courtesy: Anders Brodersen, University of Aarhus]

4. Vijay Natarajan E0 271: Computer Graphics 3
Examples
http://www.povray.org

5. Vijay Natarajan E0 271: Computer Graphics 4
Examples
http://www.povray.org

6. Vijay Natarajan E0 271: Computer Graphics 5
Examples
http://www.povray.org

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Generic Ray Tracer
» Given camera parameters and image resolution
§ Generate rays r(i,j) from eye passing through center of pixel (i,j)
§ Call function trace (r) on each ray
§ trace (r) returns color of the pixel
» trace (r)
§ Follow ray r into scene
§ Let O be the first object it intersects, P be the point of intersection
§ If O is reflective or translucent, then compute reflected or
transmitted ray and call trace recursively
§ For each light source, apply Phong model to compute shade at
point P if light is visible from P
§ Combine colors obtained from above two steps and return the
composite color

8. Vijay Natarajan E0 271: Computer Graphics 7
How to determine
composite color?
» Ray tracing equation for a single light source L
I = ka Ia
+ visible (P,L) * (kd Id l · n + ks Is (n · h )b )
+ kr trace(P, rr)
+ kt trace(P, rt)

9. Vijay Natarajan E0 271: Computer Graphics 8
Rays
» A ray r(t), for 0 ≤ t < ∞, is defined by
its origin P and a direction u:
§ r(t) = P + tu
§ u is a unit vector or not?

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Ray Generation
» LookAt()
§ Eye, Gaze, Up
» Perspective()
§ FOV, Aspect ratio
§ Near = 1
» Image resolution
§ nx, ny

11. Vijay Natarajan E0 271: Computer Graphics 10
Ray-Object Intersection
» Ray-Sphere
§ Point of intersection
§ Normal vector
» Ray-Polygon
§ Point of intersection
» Ray-Triangle

12. Vijay Natarajan E0 271: Computer Graphics 11
Ray Intersection
» Point of intersection specified by t
» Maintain smallest value t0 (>0) for
each ray
» t0 represents intersection with
nearest object