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Contents

All The Answers

There are only a few answers for all questions in graphics; they are:

1.
coherence
2.
incremental algorithms
3.
linear interpolation
4.
triage
5.
inner and cross products
6.
matrices
7.
homogeneous coordinates

The trick, of course, is to know which answer is correct for any given problem. Learning this trick will take some time. To start here are nutshell definitions of the answers.

The first 4 answers are all related; they all relate to making graphics algorithms efficient.

Coherence:
``Things close by in time or space are frequently similar.'' This concept applies in many areas of computer science, certainly not just in graphics.
Incremental algorithms:
Follow from noticing coherent patterns. They are distinguished by the use of one (or more) old values to generate a new value.
Linear interpolation:
The basis for many incremental algorithms. When a value y changes via a linear formula: y=mx+b, a change in x by an amount $\triangle x$, results in a new value of y that is produced by adding increment $m\triangle x$ to y.
Triage:
An algorithmic concept that says: ``serve the greatest good.'' Usually, this is interpreted as ``make the common case fast.''
Inner and cross products:
These define the geometry (length, angles and orientation) of a space. More to come.
Matrices:
Points and vectors are mapped to other points and vectors via a matrix.
Homogeneous coordinates:
A useful, non-Euclidean space, in which to describe basics steps in the graphics pipeline.
If you understand these ideas you've mastered most of the ideas in computer graphics. Of course there are other things you should know.


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1998-08-31