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.