ABSTRACT
The essence of spherical subdivision is to define point distributions that meet application needs. This chapter looks at three different but interrelated measures for point distribution on a sphere: covering, packing, and volume. Each provides a metric for comparing point distributions and to know which is more even by criteria, such as minimal variation in chord/arc lengths between points, area of faces in a tessellation, or variation between adjacent face dihedral angles. Covering measures the largest diameter of n equal circles that can be placed on the surface of the sphere without overlap and how they can be arranged to achieve this maximum. Packing arranges identical spheres around points on the sphere to maximize their minimal distance. Volume maximizes the volume of an enclosing surface surrounding the points. Each of these methods provides a metric for comparing subdivisions. They are used extensively in later chapters.
