Improving the Watertightness of Parametric Surface/Surface Intersection

The parametric surface/surface intersection (SSI) computation serves as a fundamental component in geometric modelling kernels for computer-aided design (CAD) systems. The geometric fidelity of intersection curves—particularly whether the computed intersection loci in the two parametric domains (mathematical equation-curves) under the two surface maps agree with the true intersection curve in the modelling space—determines the watertightness of the surface trimming. Despite abundant research and industrial developments for SSI algorithms, ensuring the watertightness of the intersection remains challenging, which directly impacts the stability and reliability of the modelling systems.<br> In this paper, we present a practical algorithm for computing parametric SSI with gap control between the maps in the modelling space of the two mathematical equation-curves. We first analyse the topology of the two mathematical equation-curves by solving lower-dimensional systems of equations and build a graph in each domain representing the topology. Then we refine the graphs through adaptive edge subdivision and construct initial approximation of mathematical equation-curves by interpolation. A constrained optimization framework incorporating distance and tangential information is employed to improve accuracy and minimize gaps. We demonstrate the effectiveness of our algorithm through extensive experiments and comparisons with the intersection package in the open source software OCCT and the commercial engine ACIS.

Computer Graphics Forum. 2025: e70298.