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.

当测量具有不同几何形状的表面时，自动设计采样点和采样位置的数量对于实现自主制造至关重要。均匀采样已广泛用于简单的几何测量，例如平面和球体。但是，缺乏适用于复杂自由曲面的适当采样技术，尤其是那些具有稀疏地形特征（例如切削刃和其他高曲率特征）的曲面。提出了一种提高效率的稀疏曲面无失真智能采样重建方法。在这种方法中，首先应用局部精炼的T样条逼近，将曲面映射到简化的T样条空间。然后将平移不变的空间采样方法和相应的重构方法应用于表面测量。这种采样策略提供了一种经济高效的采样设计，并保证了表面重建，而不会在T样条空间中造成信息丢失。理论论证和案例研究表明，与从宏观到纳米尺度的稀疏表面测量相比，这种采样策略可以在精度或效率上提高多达一个数量级。