Packing volumes by spheres

Area of Science:

• Computational geometry
• Geometric algorithms
• Data visualization

Background:

• Sphere packing is a fundamental problem in geometry and computer science.
• Existing methods like Blum's transform have limitations in data reduction.
• Efficiently representing complex volumes requires advanced packing techniques.

Purpose of the Study:

• To present a new algorithm for packing spheres within arbitrary volumes.
• To improve data reduction compared to existing sphere packing methods.
• To enable the derivation of a hierarchy of intrinsic volume properties.

Main Methods:

• Developing an algorithm that fits only tangential spheres of variable radii.
• Generating a graph representation where nodes are sphere centers and arcs connect tangent spheres.
• Analyzing computational complexity, time, and error considerations.

Main Results:

• The algorithm achieves larger data reduction than Blum's transform.
• Variable radii spheres allow for a hierarchy of intrinsic volume properties.
• The output is a graph detailing sphere center positions and tangent connections.

Conclusions:

• The proposed sphere packing algorithm offers enhanced data reduction for arbitrary volumes.
• The variable radii approach provides a multi-scale analysis of volume properties.
• The resulting graph structure is valuable for geometric analysis and visualization.