TAPESTRY: The Art of Representation and Abstraction
Derivative Geometry: Math with Geometry, Boolean Operations
Boolean Operations: Arithmetic with Shapes
An English mathematician named George Boole lent his name to both the binary number system used by computers (numbers represented as 0's and 1's) and to a certain operations, called Boolean Operations, which can be performed on "sets". You may have encountered these in the form of Venn diagrams similar to the two shown on this page. They are often featured in geometry courses. They are also part of logic or rhetoric. They help us understand statements such as "Which classmates are MALE and OVER 20 years old" as compared to "Which classmates are MALE or OVER 20 years old". The terms "and" and "or" in the two sentences are known as "boolean operators". They combine two distinct tests "age>20" and "gender=male" go identify a set of individuals. Whoopie.
![[A Boolean Difference]](graphics.invis/bool-diff.gif)
When it get's interesting is when you change the context of the questions. For instance, given two closed geometrical shapes, A & B, we could create new objects by identifying points in space which are "in A and B", "in A or B", "in A but not B" (illustrated at right) and so on. Such combinations amount to adding a shape to or subtracting a shape from another shape. That kind of description comes pretty close to how designers descibe the mental processes they use to generate designs. Perhaps for this reason, designers frequently utilize boolean operations in the process of formulating shapes.
![[A Boolean Union]](graphics.invis/bool-union.gif)
There are a number of different Boolean operations, which we might think of as merging, subtracting, and so on. The figure above illustrates a difference operation, while the one at left illustrates a union operation. The existence of topological data (hence, the ability to tell the "insides" of one shape from another) enables a program to perform generalized boolean operations. Some programs (notably, Modelshop), perform a "pseudo-boolean" operation involving holes in extruded forms, but some investigation will usually reveal them to be quite limited.
Last updated: April, 2014
