Trimmed Spline Surfaces with Accurate Boundary Control

TL;DR

This paper presents ABC-surfaces, a novel method for constructing watertight, smooth multi-patch NURBS surfaces with precise boundary control, addressing key limitations in standard CAD/CAM systems.

Contribution

It introduces a new class of trimmed NURBS surfaces with accurate boundary control, combining base surfaces and reparametrized ribbons for improved shape and boundary management.

Findings

Enables construction of watertight multi-patch surfaces.

Achieves smoothness up to G^2 continuity.

Improves boundary accuracy in CAD models.

Abstract

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.