CSCE 441 Lecture 23

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Ray Tracing

Not meant to be used in real-time

Provides rendering method with

• refraction / trasparent surfaces
• reflective surfaces
• shadows

Necessary Information

• Eye position
• Screen position and orientation
• Objects
  • Material properties
  • Reflection / refraction coefficients
  • Index of refraction
• Light sources

Recursive Ray Tracing

for each pixel,

• intersect ray from eye through pixel with all objects in scene
• find closest (positive; in front) intersection to eye
• compute lighting at intersection point
• recur for reflected and refracted rays (if necessary)

Ray Casting

Do not recur; only compute basic lighting

Shadows

Cast a virtual ray to each light source (from each intersection point on the surface)

If there is an opaque object in the way, ignore contribution from that light source.

If there is semi-transparent object, scale contribution of that source and continue to look for intersections

Note: Objects may be self-shadowing. In this case, add $\epsilon \,{\vec {n}}$ (where $n$ is the normal and $\epsilon$ is a small value) to the intersection position to make sure we are outside the object surface

Reflection

Recall from lighting lecture:

${\vec {r}}=2\left({\vec {v}}\cdot {\vec {n}}\right)\,{\vec {n}}-{\vec {v}}$

Refraction

If object is transparent, compute a ray from intersection point that travels through object.

Snell's law:

${\frac {c_{1}}{c_{2}}}={\frac {\sin {\theta _{1}}}{\sin {\theta _{2}}}}$

If we have a vector incident to a surface at angle $\theta _{1}$ from a medium with index of refraction $c_{1}$ and into a medium with indexf of refraction $c_{2}$

Geometric formula:

1. find basis ${\vec {v}}_{\perp }$ and ${\vec {v}}_{\parallel }$ with respect to normal ${\vec {n}}$.

${\begin{aligned}{\vec {r}}&=-{\vec {n}}\,\cos {\theta _{2}}+{\frac {c_{2}}{c_{1}}}\left(\left({\vec {v}}\cdot {\vec {n}}\right)\,{\vec {n}}-{\vec {v}}\right)\\{\vec {r}}&=-{\vec {n}}\,c_{1}^{-1}\,{\sqrt {\ldots }}+{\frac {c_{2}}{c_{1}}}\left(\left({\vec {v}}\cdot {\vec {n}}\right)\,{\vec {n}}-{\vec {v}}\right)\end{aligned}}$

Progress Summary

$I=I_{direct}+\gamma _{e}\,I_{reflected}+\gamma _{a}\,I_{refracted}$

Truncate recursion at a finite depth

Pruning:

• Do not recur on non-reflective or non-refractive surfaces
• Keep track of cumulation of $\gamma _{e}^{n}$ value ($\gamma _{e}$ at $n$^th level of recursion): when $\gamma _{e}^{n}\leq {\frac {1}{512}}$, do not recur any more since no color value will affect color of pixel on screen.

Optimizations

Lots of rays generated, and ray-to-surface intersections are expensive to compute.

Associate a bounding-box in 3D space with each object: if ray doesn't intersect box, then ray doesn't intersect object.

Parallel processing:

• Ray tracing is trivially parallel
• cast rays in parallel, cast reflection, refraction, and shadow rays in parallel, and join on results
• calculate ray/surface intersections independently in parallel.

Extensions

Only considers totally specular interactions

• rays either reflect perfectly or refract perfectly (not realistic)
• Ray-traced scenes don't show "color bleed" from light reflected from other surface.

Translating from Screen to Window Coordinates

Object files for HW4 defined in $[-1,1]^{3}$ space. This needs to be mapped to $[0,w-1]\times [0,h-1]$.