Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells

The following sections are included:

• Basic Geometry of Local Packings and Local Cells

  • Associated spherical configurations and polyhedrons of (Σ, {h_j})

  • Geometric correlations between spherical configurations and associated polyhedrons

    • The correlation between and T(Σ)

    • The basic geometry of T(Σ, {h_j})

    • The relationships between T(Σ) and T(Σ, {h_j}) (resp. and )

    • The peripheral part and its rectilinear slabs

  • Basic strategies of volume estimation of local cells

    • The separation of a local cell into its core part and its peripheral part

    • The subdivision of the peripheral part into rectilinear slabs

    • Spherical configuration and a basic volume formula of T(Σ), the basic strategy for the estimation of the core part

• Technique of Volume Estimation of the Core Part

  • The volume function of tangent subpolyhedron

    • A basic volume formula

    • A volume formula of T(Σ)

      • A gradient formula of vol T(Σ)

    • Two basic lemmas of volume estimation

    • Some direct applications

• Volume Estimation of a Rectilinear Slab

  • The local geometry surrounding a given neighbor of

  • Lower bound volume estimates of rectilinear slabs

• Volume Estimation of Local Cells