论文标题
四面体花键的尺寸的下限
A lower bound for the dimension of tetrahedral splines in large degree
论文作者
论文摘要
我们得出了一个公式，该公式是四面体分区上三面键的尺寸的下限，该分区的尺寸在很大程度上与订单$ r $不断差异。尽管该公式在低度中可能无法在样条空间的尺寸上成为一个下限，但我们在Alfeld和Schumaker考虑的几个示例中说明，如果顶点位置是通用的，则我们的公式可能会在很大程度上给出足够大的样条空间的确切尺寸。相比之下，对于频率不断差异的花键$ r> 1 $，在这些示例中，文献中的每个下限都与样条空间的维度有很大程度的分歧。我们使用交换和同源代数得出结合。
We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order $r$ in large enough degree. While this formula may fail to be a lower bound on the dimension of the spline space in low degree, we illustrate in several examples considered by Alfeld and Schumaker that our formula may give the exact dimension of the spline space in large enough degree if vertex positions are generic. In contrast, for splines continuously differentiable of order $r>1$, every lower bound in the literature diverges (often significantly) in large degree from the dimension of the spline space in these examples. We derive the bound using commutative and homological algebra.
