Design by interpolation

The design of shapes by interpolation, that is, cases where the desired shape is somehow `in between´ two given shapes, is discussed. The main issues involved in design by interpolation are: (a) capturing the `nature´ (behavior) of the guiding shapes A and B; (b) attaining automatic correspondence between points (i.e., which point in shape A should be associated with which point in shape B); and (c) determining the interpolation method. New techniques for capturing the `nature´ of shapes and for determining automatic correspondence of points are presented. Examples for interpolation of polygons, curves, and surfaces are included. The possibility of future design based upon extrapolation, rather than interpolation is also discussed