The Scale Method for Blending Operations in Functionally-Based Constructive Geometry

This paper presents a scale method for developing high dimensional scale functions to blend implicitly defined objects. Scale functions are differentiable on the entire domain except the origin, provide blending range control, and behave like Min/Max operators everywhere, so even a successive composition of blending operations containing overlapped blending regions can be generated smoothly. Because the scale method is a generalized method, implicit or parametric curves, such as cubic Bezier curves, rational conic curves, and implicit conics and hyper-ellipsoids, can be used to develop scale functions. As a result, it can enhance the flexibility of generating the implicitly blending surfaces in Ricci’s constructive geometry, soft objects modeling, and implicit sweep objects.