$C^1$ splines over box-complexes generalize $C^1$ 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 $C^1$ tri-cubic tensor-product spline, by default initialized as a $C^2$ 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.

$C^{\mathrm{1个}}$ 箱形复合体上的样条曲线泛化 $C^{\mathrm{1个}}$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$C^{\mathrm{1个}}$ 三三次张量积样条曲线，默认情况下初始化为 $C^2$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。