Shape computations with NURB curves

Freeform curves are commonly used in contemporary design practices, especially with digital modeling tools. We investigate facilitating shape subtraction and addition with two-dimensional (planar) non-uniform rational basis-spline (NURB) curves with the codes and conventions of modeling while preserving the visual continuity of curved shapes. Our proposed tool, developed in a common digital modeling environment, automates the adjustment of parameters for tangential continuity of curves in shape rule applications. When the user designates a curve range to subtract from an initial shape and provides a new curved shape to add to it, the tool splits the initial shape, scales and aligns the curve to be added to fit into this range, introduces additional control points at the joining ends of the new curve to preserve continuity and redraws the new curve. We present a sample set of design variations produced using this practical approach which can be utilized as a method or become part of an automated NURB curve manipulation tool for designers.