Robustly blending surfaces via spherical parametrization

Abstract

In various embodiments of the present invention, a blending engine blends multiple surfaces included in a three-dimensional (3D) model of an object. First, the blending engine trims off portions of the surfaces that are targeted for blending at trimming curves to generate trimmed surfaces. The blending engine then constructs a single parametric blending surface via a unified parametrization for the trimming curves. Notably, to achieve the unified parametrization, the blending engine performs one or more spherical parametrization operations that generate parametrized curves based on the trimming curves and a fundamental sphere. After constructing the parametric blending surface based on the parametrized curves, the blending engine joins the parametric blending surface to the trimmed surfaces to produce a final, smooth intersection between the surfaces. Advantageously, because the blending engine creates a single parametric blending surface, the blending engine can blend arbitrary pipe surfaces and is compatible with computer-aided design modeling subsystems.