Trimmed Spline Surfaces with Accurate Boundary Control

We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of standard CAD/CAM systems and the associated file exchange formats. Our construction is based on the appropriate blend of a base surface, which traces out the intended global shape, and a series of reparametrized ribbons, which dominate the shape near the boundary.