Constraint-Based Design of Faired Parametric Curves
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This chapter demonstrates techniques to allow relations on parametric curves in a variational design system. Constraints on the curves, which are normally represented as constrained nonlinear optimization problems, are reduced to systems of nonlinear equations (using the necessary conditions of the Non-Linear Programming). Additional degrees of freedom are constrained through fairing the curve and the resulting NLP is also reduced to its necessary conditions. Although the solution set of the necessary conditions contains the optimum, it contains many other solutions as well. The COAST design consistency algorithm introduced in Chapter 14 is extended to handle consistency when constraints take the form of relations between objects. Examples are given for elementary curves and for an apparel design system.
KeywordsGeometric Design Distance Constraint Nonlinear Optimization Problem Consistent Solution Composite Object
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