Modeling by composition

Functional composition can be computed efficiently, robustly, and precisely over polynomials and piecewise polynomials represented in the Bézier and B-spline forms (DeRose et al., 1993)  [13], (Elber, 1992)  [3], (Liu and Mann, 1997)  [14]. Nevertheless, the applications of functional composition in geometric modeling have been quite limited. In this work, as a testimony to the value of functional composition, we first recall simple applications to curve–curve and curve–surface composition, and then more extensively explore the surface–surface composition (SSC) in geometric modeling. We demonstrate the great potential of functional composition using several non-trivial examples of the SSC operator, in geometric modeling applications: blending by composition, untrimming by composition, and surface distance bounds by composition.