The Similarity Comparison Algorithm of Free-Form Surfaces with Single Curvature Feature

This paper studies the shape similarity evaluation of free-form surfaces expressed by B-spline with single curvature feature and proposes a similarity evaluation algorithm based on curvature feature. Firstly, we calculate the normal vector direction of the two surfaces compared, and use it as the Z axis, so that the two surfaces are aligned on the Z axis. Then, the two surfaces are cut with planes that all perpendicular to the Z axis, and the intersection sets of two surfaces are obtained respectively. Finally, we design the similarity algorithm of plane curves to realize the similarity comparison of corresponding curves in the two sets of intersection, and which is used as the basis for evaluating the similarity between two surfaces. The algorithm transforms the problem of similarity comparison between 3D surfaces into two dimensional space by plane cutting method, and reduces the complexity of the problem effectively. The algorithm only needs to align one coordinate axis in the process of posture adjustment, so it is easy to implement. In order to test the effect of the algorithm, simulation experiments on different type of single curvature feature B-spline surfaces are carried out. The results show that the proposed similarity comparison algorithm of free-form surfaces is feasible and effective. 研究具有单一曲率特征的B样条表达的自由曲面形状相似性评价问题，提出了一种基于曲率特征的相似性评价算法。首先计算相比较的2个曲面上各点法向矢量和，并将该和矢量作为 Z 轴，使2个曲面 Z 轴对齐；然后用垂直于 Z 轴的平面分别截切两曲面，得到2个曲面各自的截交线集合；最后，设计了平面曲线相似性比较算法，实现2个截交线集合中对应曲线的相似性比较，并以此作为评价2个曲面相似性的依据。算法通过平面截切的方法将三维空间的曲面相似性比较问题转化到二维空间来实现，有效地降低了问题的复杂度。算法在姿态调整中仅需对齐一个坐标轴，简单易行。为检验算法的效果，分别对不同类型单一曲率特征B样条曲面进行仿真实验，结果表明，提出的自由曲面相似性比较算法可行有效。