In generative, constraint-based design, users graphically select shape elements of design instances in order to specify shape operations that have generic intent. We discuss techniques for naming algorithmically and generically the identified geometric instance, and report on our experience with implementing these techniques. In a companion paper, we give algorithms for matching the names when editing designs.

Let C1,…, Cn and C′1,…, C′n be two collections of equal disks in the plane, with centers c1,…, cn and c′1,…, c′n. According to a well-known conjecture of Klee and Wagon (1991), if |ci − cj| ≥ |c′i − c′j| for all i, j, then Area(∩i Ci) ≤ Area(∩i C′i). We prove this statement in the special case when there is a continuous contraction of {c1,…, cn} onto {c′1,…, c′n}.

A clamper is composed of two opposing parallel edges with variable distance between them. We present a model that describes when the edges of the clamper and some edges of a polygon produce a clamp on the polygon. Using this model, we show that a fairly large class of polygons can be clamped.