Spring 2000

Courtney Christman

Sophomore, Class of 2002

CSC 274: Computational Geometry

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8.1: Computing the Discrepancy

A picture on a screen is made of pixels. A third-dimension scene consists of objects, a light source, and a view point. The goal is to render the scene by determining for every pixel on the screen which object is visible at that pixel, and determining the intensity of light that the object emits in the direction of the view point at that particular point.

This is done through ray tracing. Ray tracing is a way of determining the visible object at each pixel. Once the visible object is determined, one has to compute the intensity of light emitted by the object at the visible point. You must do this without forgetting to take into account how much light the point recieves from the light surce, either directly or indirectly via reflections on the other objects. However, this method has many flaws. If the light source covers 49% of the square pixel, no changes will be made to the pixel. But if the light source covers 51% of the pixel, then the entire pixel will show the effect of the light source. Also, if ther are two objects in the pixel, then the pixel will show a mixture of the object intensities.

A remedy to this problem is supersampling. Supersampling involves taking random generated sampling points. The discrepancy of the sample set with respect to the object is the difference between the percentage of hits for an object and teh percentage of pixel area where the object is visible but small. The new goal is to calculate the discrepancy of the sample set. The maximum discrepancy over all possible ways that an object can be visible inside the pixel to be small.

Discrepancy of a point is defined with respect to a class of objects. Third-dimension curved objects are make of polygonal meshes. Two-dimensional projections are of the facts of polyhedra.

1. ray tracing, Unfamiliar

2. rendering the scene, Unfamiliar

3. supersamplling, Unfamiliar

4. discrepancy of the sample set with respect to the object, Unfamiliar

5. discrepancy of the sample set, Unfamiliar

6. discrete measure, Unfamiliar

7. continuous measure, Unfamiliar

8. pixel, Familiar

The meanings of these words is clearly explained in my summary of the section.

1. ray tracing

2. supersampling

b. Relativistic Ray-Tracing

c. Basic Ray Tracer

d. Supersampling

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update = "97.11 bibrelex"

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author = "J. Arvo and D. Kirk"

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editor = "M. C. Stone"

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update = "97.11 bibrelex"

}

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series = "Computer Graphics Proceedings, Annual Conference Series"

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update = "98.07 agarwal, 98.03 agarwal"

}

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author = "J. R. Rossignac and P. Borrel"

title = "Multi-Resolution {3D} Approximations for Rendering Complex Scenes"

type = "Technical {Report}"

number = "RC 17697 (\#77951)"

institution = "IBM Research Division, T. J. Watson Research Center"

address = "Yorktown Heights, NY 10958"

year = 1992

update = "95.01 mitchell"

}

@article{rw-3drfr-80

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journal = "Comput. Graph."

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pages = "110--116"

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@inproceedings{dm-redsp-93

author = "D. Dobkin and D. Mitchell"

title = "Random-edge discrepancy of supersampling patterns"

booktitle = "Graphics Interface '93"

year = 1993

keywords = "discrepancy"

update = "97.03 schwarzkopf"

}