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
, results in a new value
of y that is produced by adding increment
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.
1998-08-31