TABLE OF CONTENTS Traditional geometry, plane and solid or even analytic does not tell us how to create even the most simple shapes we see all around us in both the natural world and the made one. The methods of constructive solid geometry (CSG) gives us a way to describe complicated solid shapes as combinations of simpler solid shapes. This makes it an important tool for computer graphics and geometric modeling. CSG uses Boolean operators to construct a procedural model of a complex solid. This model, or rather the data describing the model, is stored in the mathematical form of a binary tree, where the leaf nodes are simple shapes, or primitives, sized and positioned in space, and each branch node is a Boolean operator: union, difference, or intersection.
This chapter discusses set theory, Boolean algebra, halfspaces, binary trees, solids, and special operators called regularized Boolean operators, set- membership classification, the Boolean model and how to construct it using those operators, primitives, and boundary evaluation.
Recall that a set is a collection of objects, called elements or members of the set (see Section 7.2). Examples of a set may be mathematical, as in the set of all even numbers; geometric, as in the set of points on a line segment; logical, as in all nonempty sets; or almost any specifiable collection of things, as in all white crows.
A set containing all of the elements of all of the sets in a...
