Optical scanning instruments require sampling and reconstruction with high accuracy and low computational cost. T-splines have recently been developed that allow significant reductions in the number of control parameters by overcoming some of the topological constraints of B-splines and NURBS. As a subset of T-splines, analysis-suitable T-splines (ASTS) show promise due to the linear independence and partition of unity of their basis functions. In this paper, a computationally efficient ASTS fitting algorithm for freeform surface reconstruction is proposed. This algorithm starts with adaptive construction of an initial analysis-suitable T-mesh according to the distribution of high-curvature feature points. A local refinement and local optimisation algorithm of the analysis-suitable T-mesh is then iteratively performed until a preset accuracy condition is satisfied. Our experimental results show that the proposed ASTS fitting can produce over 50% root-mean-square reconstruction error reduction compared to NURBS fitting, with the same number of control parameters. The computing efficiency of the proposed algorithm is equivalent to or higher than that for simple T-spline fitting. Fast derivative analysis of the ASTS has also been carried out, where two automatic intelligent sampling design methods have been developed, namely element area sampling and element curvature sampling. Up to 50% reconstruction error reduction is observed when compared to uniform and statistically optimised sampling designs. With the novel reconstruction and compatible intelligent sampling design techniques, freeform surface measurement accuracy and efficiency could be effectively improved using coordinate measuring machines.

光学扫描仪器需要高精度和低计算量的采样和重构。最近已经开发出T样条，通过克服B样条和NURBS的某些拓扑约束，可以显着减少控制参数的数量。作为T样条的子集，适合分析的T样条（ASTS）由于其基本函数的线性独立性和统一性而显示出希望。本文提出了一种用于自由曲面重构的高效计算的ASTS拟合算法。该算法首先根据高曲率特征点的分布自适应构造适合初始分析的T网格。然后迭代执行适合分析的T网格的局部优化和局部优化算法，直到满足预设的精度条件为止。我们的实验结果表明，与NURBS拟合相比，在控制参数数量相同的情况下，拟议的ASTS拟合可以减少50％以上的均方根重构误差。所提算法的计算效率等于或高于简单T样条拟合的效率。还进行了ASTS的快速导数分析，开发了两种自动智能采样设计方法，即元素面积采样和元素曲率采样。与统一且经过统计优化的采样设计相比，可减少多达50％的重建误差。