Free-form surfaces have been widely used in aerospace, automotive and other fields. Due to its complex geometry, free-form surface inspection is generally conducted by touch-trigger or measuring probe-based Coordinate Measurement Machines or On-machine Measurement. Sampling strategy plays a decisive role in improving both measurement accuracy and efficiency, which is determined by sample size and distribution of sample points. However, it is difficult to simultaneously take the surface curvature, sampling density and approximation error into account, considering the complexity of surface geometry. In this paper, triangle mesh simplification is innovatively adopted in sampling planning to achieve multi-geometric constraints. As triangle mesh has outstanding advantages in representing the surface features, strong stability and is easy to modify its structure, free-form surface is converted to a dense triangle mesh. Triangle mesh simplification is implemented by iteratively contracting triangle edges. An improved quadric error metric is established to decide contraction order and optimal target vertices under discrete curvature constraint. Sampling density is controlled by limiting the triangle edge length. Detailed adaptive sampling algorithm under multi-geometric constraints is then developed. Both simulation and experiment are conducted to validate feasibility and robustness of the proposed method. The results are compared with uniform sampling and existing adaptive sampling strategy to show that the proposed method can prominently reduce sampling error when sample size is small.

自由曲面已经广泛用于航空航天，汽车和其他领域。由于其复杂的几何形状，自由形式的表面检查通常通过接触式触发或基于测头的坐标测量机或在机测量进行。采样策略在提高测量精度和效率方面起着决定性的作用，这取决于采样大小和采样点的分布。但是，考虑到表面几何形状的复杂性，很难同时考虑表面曲率，采样密度和近似误差。本文在采样规划中创新地采用了三角形网格简化方法，以实现多几何约束。由于三角形网格物体在表示表面特征方面具有突出的优势，稳定性强且易于修改其结构，自由曲面转换为密集的三角形网格。三角形网格的简化是通过迭代收缩三角形边缘来实现的。建立了改进的二次误差度量来确定离散曲率约束下的收缩顺序和最佳目标顶点。采样密度是通过限制三角形边缘的长度来控制的。然后，开发了在多几何约束下的详细自适应采样算法。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。三角形网格的简化是通过迭代收缩三角形边缘来实现的。建立了改进的二次误差度量来确定离散曲率约束下的收缩顺序和最佳目标顶点。采样密度是通过限制三角形边缘的长度来控制的。然后，开发了在多几何约束下的详细自适应采样算法。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。三角形网格的简化是通过迭代收缩三角形边缘来实现的。建立了改进的二次误差度量来确定离散曲率约束下的收缩顺序和最佳目标顶点。采样密度是通过限制三角形边缘的长度来控制的。然后，开发了在多几何约束下的详细自适应采样算法。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。建立了改进的二次误差度量来确定离散曲率约束下的收缩顺序和最佳目标顶点。采样密度是通过限制三角形边缘的长度来控制的。然后，开发了在多几何约束下的详细自适应采样算法。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。建立了改进的二次误差度量来确定离散曲率约束下的收缩顺序和最佳目标顶点。采样密度是通过限制三角形边缘的长度来控制的。然后，开发了在多几何约束下的详细自适应采样算法。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。通过仿真和实验验证了该方法的可行性和鲁棒性。将结果与均匀采样和现有的自适应采样策略进行比较，结果表明，该方法可以在样本量较小时显着减少采样误差。