Constraint Methods
John R. Bourne · 2024
What is the meaning of the term constraint ? The dictionary defines a constraint as: “something that restricts, limits or regulates” ( Morris, 1981 ). In mathematical terms, “A constraint consists of a set of variables and a relation on these variables” (Giisgen, 1989) and in terms of objects, “A constraint expresses a desired relationship between one or more objects” ( Leler, 1988 ). A favorite example used to explain constraints is the representation of the Fahrenheit to centigrade conversion equation ( Abelson and Sussman, 1985 ; Leler, 1988 ): C = 5/9 (F - 32) or F = 1.8*C + 32 This simple relationship between the two variables C (centigrade) and F (Fahrenheit) can be expressed graphically as shown in Figure 10.1 . This figure illustrates propagation of information in two directions in the graph. From centigrade to Fahrenheit the constraint is shown in the gray part of each circle; in the reverse direction, the constraint is shown in white. For each case, a numerical example is given: Converting 10°C to 50°F is shown in the first case and converting 70°F to 21°C is shown in the second case. The operations specified are inverses of each other when the data flows in opposite directions. In this simple case, the meaning of constraint is simply a mathematical relationship between the variables entering a node. In more complex situations, more complicated combination functions or even symbolic computations could be used in a node.