# Assignment 1: Summary of Problem from Chapter 8 Arrangements and Duality Supersampling and Ray Tracing

##### February 3, 2000

• Summary
• Glossary
• Bibliography
• Time assessment

## Summary

An important topic in computer graphics today is the generation of 3-dimensional scenes. A technique that helps to do this is ray tracing.

A synthesis of what is involved in ray tracing:
We are given a 3-dimensional scene, a light source, and a view point. To
render this scene of the screen, we must determine which object is visible to every pixel on the screen. We must also find out the intensity of light emitted from the object in the direction of the view point at the particular point which the pixel 'sees'. We must now take into account how much light that point is receiving from the light source, either directly or via reflection off other objects.

A problem is that a pixel is not a point, but a small square area. Most of the time, the pixel is completely covered by one object. On the borders the pixel may see more than one object. We could assume falsely that the whole pixel was covered, but this would give a jaggedy looking image. We can improve this by taking into account the percentage of hit or miss, and adjust the intensity of the pixel with this information. If more than one object is visible inside the pixel, we could mix the object intensities.

To incorporate all the different pixel intensities into the ray tracing scheme, we shoot more than one ray per pixel. Distributing these rays uniformly again gives us problems because the eye perceives regularity easily. A random pattern improves on this, but we still want the sample points to be distributed so that the number of hits is close to the percentage of covered area.

## Glossary

render - generating an image
pixel - extremely small dot on screen that displays color attributes
intensity - brightness

## Bibliography

• McGill College Computational Geometry Bibliography
• The Geometry Center
• Directory of Computational Geometry Software
• Los Alamos e-print archive

## Time Assessment

This assignment took me 2.5 hours to complete.

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