Distortion-Free Intelligent Sampling of Sparse Surfaces Via Locally Refined T-Spline Metamodelling

Automatic design of the number of sample points and sample locations when measuring surfaces with different geometries is of critical importance to enable autonomous manufacturing. Uniform sampling has been widely used for simple geometry measurement, e.g. planes and spheres. However, there is a lack of appropriate sampling techniques that can be applied to complex freeform surfaces, especially those with sparse topographical features, e.g. cutting edges and other high-curvature features. In this paper, a distortion-free intelligent sampling and reconstruction method with improved efficiency for sparse surfaces is proposed. In this method, a locally-refined T-spline approximation is firstly applied which maps a surface to a simplified T-spline space; then a shift-invariant space sampling method and corresponding reconstruction are applied for the surface measurement. This sampling strategy provides a cost-effective sampling design and guarantees the surface reconstruction without information loss in a T-spline space. Theoretical demonstrations and case studies show that this sampling strategy can provide up to an order of magnitude improvement in accuracy or efficiency over state-of-the-art methods, for the measurement of sparse surfaces, from macro- to nano-scales.