【源码】基于标准B样条的样条曲线曲面定义、计算及可视化样条工具箱

该样条工具箱提供了基于节点向量的一般定义、B样条基函数的阶数及其系数定义样条曲线和曲面的可能性。

This Spline toolbox provides the possibility to define spline curves and surfaces according to the common definition with knot vectors, the order of the B-spline basis functions and their coefficients.

样条曲线对象可以通过多种方式进行求值、区分和可视化，如曲面网格点的快速求值或各种曲率的计算。

The Spline objects can be evaluated, differentiated and visualized in multiple fashions, e.g. fast evaluation at grid points for surfaces or the calculation of all sorts of curvatures.

由于评估是基于Horner方案在不同多项式段上的应用，因此甚至可以连续扩展函数并在域中不包含的点上进行评估。

As the evaluation is based on the application of Horner’s scheme on the different polynomial segments, it is even possible to extend the functions continuously and evaluate at points that are not contained in the domain.

此外，该工具箱允许计算给定函数值对的样条逼近，无论是曲线还是曲面。

Furthermore, this toolbox allows the calculation of spline approximants for given pairs of function values, in both cases of curves and surfaces.

它们可以通过考虑额外的插值和平滑条件来扩展。

They can be extended by considering additional interpolation and smoothing conditions.

所有功能的详细描述及结合的几个例子，可以在文档中找到。

A detailed description of all functionalities, combined with several examples, can be found in the documentation.

此工具箱仅为研究项目中的应用程序创建，因此只有在定义样条曲线时才能正确处理错误。

This toolbox was only created for the application in a research project, so errors are only handled properly during the definition of a spline.

任何其他误差通常源于维数不匹配，例如通过手动操作特性，或未正确定义节点向量/系数。

Any other error is often originated in mismatching dimensions, e.g. by manual manipulation of properties, or not correctly defined knots vectors/coefficients.

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