We discuss the properties and computation of the boundary $\mathrm{B}$ of a CHoCC (Convex Hulls of Cospherical Circles), which we define as the curved convex hull $\mathrm{H}$ ($\mathcal{C}$) of a set $\mathcal{C}$ of $n$ oriented and cospherical circles $\left\{{\mathrm{C}}_i\right\}$ that bound disjoint spherical caps of possibly different radii. The faces of $\mathrm{B}$ comprise: $n$ disks, each bounded by an input circle, $t=2n-4$ triangles, each having vertices on different circles, and $3t∕2$ developable surfaces, which we call corridors. The connectivity of $\mathrm{B}$ and the vertices of its triangles may be obtained by computing the Apollonius diagram of a flattening of the caps via a stereographic projection. As a more direct alternative, we propose a construction that works directly in 3D. The corridors are each a subset of an elliptic cone and their four vertices are coplanar. We define a beam as the convex hull of two balls (on which it is incident) and a lattice as the union of beams that are incident each on a pair of balls of a given set. We say that a lattice is clean when its beams are disjoint, unless they are incident upon the same ball. To simplify the structure of a clean lattice, one may union it with copies of the balls that are each enlarged so that it includes all intersections of its incident beams. But doing so may increase the total volume of the lattice significantly. To reduce this side-effect, we propose to replace each enlarged ball by a CHoCC and to approximate the lattice by an ACHoCC, which is an assembly of non-interfering CHoCCs for which the contact-faces are disks. We also discuss polyhedral approximations of CHoCCs and of ACHoCCs and advocate their use for processing and printing lattices.

我们讨论边界的性质和计算 $\mathrm{乙}$一个的CHoCC（Cospherical圆凸壳的），我们将其定义为弯曲凸包 $\mathrm{H}$ （$\mathcal{C}$一组） $\mathcal{C}$ 的 $ñ$定向球面圈 $\left\{{\mathrm{C}}_{\mathrm{一世}}\right\}$绑定了半径可能不相同的不相交的球形帽。的面孔$\mathrm{乙}$ 包括： $ñ$ 圆盘，每个圆盘都由一个输入圆包围，$Ť=2ñ-4$ 三角形，每个顶点在不同的圆上，以及$3Ť∕2$可展表面，我们称之为走廊。的连通性$\mathrm{乙}$三角形的顶点可以通过通过立体投影计算瓶盖变平的Apollonius图来获得。作为更直接的替代方案，我们提出了一种可直接在3D中工作的构造。走廊分别是椭圆锥的子集，并且它们的四个顶点共面。我们定义一个光束作为两个滚珠（在其上的凸包事件）和晶格作为各在一对一组给定的球是入射光束的联合。我们说格子很干净当光束不相交时，除非光束入射到同一球上。为了简化干净晶格的结构，可以将其与球的副本合并在一起，每个副本都被放大，以便包括入射光束的所有交点。但是这样做可能会大大增加晶格的总体积。为了减少这种副作用，我们提出通过CHoCC替换每个放大球，并通过以近似晶格ACHoCC，这是组件非干扰CHoCCs的量，接触面是磁盘的一个。我们还将讨论CHoCC和ACHoCC的多面体近似，并提倡将其用于处理和打印晶格。