A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

Chapter 1

Analytical Geometry

Olga Sorkine-Hornung and Daniel Cohen-Or

When dealing with geometric problems, we typically deal with 2D

and 3D objects. These objects are represented mathematically in

the computer. Therefore, the basic requirement is to have a good

grasp of the mathematical entities that represent the objects, and

be familiar with the tools that enable their manipulation. The

basic geometric elements are linear (points, lines, planes), and the

typical queries and manipulations we encounter in common geo-

metric applications include distances, transformations, projections

and so on.

All these manipulations require performing computations