Computer Aided Geometric Design ( IF 1.3 ) Pub Date : 2020-05-12 , DOI: 10.1016/j.cagd.2020.101877 Jörg Peters 1
splines over box-complexes generalize degree 3 (cubic) tensor-product splines. A box-complex is a collection of 3-dimensional boxes forming an unstructured hexahedral mesh that can include irregular points and irregular edges where the layout deviates from the tensor-product grid layout. For example, an edge shared and enclosed by five boxes is irregular. Where the mesh is locally regular, the restriction of the space to each box is a polynomial piece of the tri-cubic tensor-product spline, by default initialized as a tri-cubic. Boxes containing irregularities have their polynomials binarily split into 23 pieces to isolate the irregularity. The pieces join with matching derivatives. The derivatives are zero at irregularities, but these singularities are removable by a local change of variables. The space consists of 23 linearly independent functions per box and is refinable.
中文翻译:
精炼的三变量C 1样条曲线,用于包含不规则点和不规则边缘的箱形复杂对象。
箱形复合体上的样条曲线泛化 三次张量积样条曲线。复杂的盒子是3维盒子的集合,这些盒子形成一个非结构化的六面体网格,其中可能包括不规则点和不规则边缘,其中布局与张量积网格布局相偏离。例如,由五个框共享和包围的边是不规则的。如果网格是局部规则的,则对每个框的空间限制是多项式的 三三次张量积样条曲线,默认情况下初始化为 三立方。包含不规则性的盒子将其多项式二分为2 3件,以隔离不规则性。这些片段与匹配的派生词相连。导数在不规则处为零,但是这些奇异点可以通过局部变量变化而消除。该空间每个盒包含2 3个线性独立的函数,并且可以优化。