Describing data, obtained by various instruments, with an analytic function is one of the tasks that people often face in a wide variety of applications such as virtual reality, CAD design, reverse engineering, data visualization, medical imaging, and cultural relic restoration and so on. Moreover, non-uniform B-spline is an extensively-used tool for interpolation which is an effective means of describing data. In this paper, according to the geometric features reflected in the data points, a method for calculating the tangent vectors at the corresponding data points is proposed for reference. And based on the constraints on tangent vectors (calculated by the proposed reference method, can also be given beforehand) and control points, non-dominated sorting genetic algorithms-II, namely NSGA-II, is adopted for adaptive B-spline curve interpolation without knowing nodes and knots in advance. The resulting interpolation curve approximates the given tangent vectors and the data polyline, and it is more natural-looking, in general than those obtained by other methods. In addition, the new method works well in a higher degree. Testing results on the feasibility and universal applicability of the new method are also included.

描述通过各种仪器获得的具有分析功能的数据是人们在诸如虚拟现实，CAD设计，逆向工程，数据可视化，医学成像和文物修复等广泛应用中经常面临的任务之一。上。此外，非均匀B样条是广泛使用的插值工具，是描述数据的有效手段。本文针对数据点所反映的几何特征，提出一种计算相应数据点处切向量的方法，以供参考。根据切线向量（通过参考方法计算得出，也可以事先给出）和控制点的约束条件，采用非支配排序遗传算法-II，即NSGA-II，在不事先知道节点和结的情况下，采用B样条进行自适应B样条曲线插值。所得的插值曲线近似于给定的切向量和数据折线，通常看起来比通过其他方法获得的更自然。此外，新方法在更高的程度上效果很好。还包括有关新方法的可行性和普遍适用性的测试结果。