Disk Density Tuning of a Maximal Random Packing.

Area of Science:

• Computational geometry
• Materials science
• Computer graphics

Background:

• Maximal random packing is crucial for various applications, including mesh generation and material modeling.
• Existing methods for tuning disk density can alter disk radii or sizing functions, limiting flexibility.
• Achieving specific spatial densities while maintaining packing properties is a significant challenge.

Purpose of the Study:

• To introduce a novel algorithmic framework for tuning the spatial density of disks in maximal random packings.
• To enable user-defined density adjustments (denser or sparser) without altering disk radii or sizing functions.
• To maintain conflict-free arrangements, coverage maximality, and blue noise properties.

Main Methods:

• Iterative relocation, injection, and ejection of disks using three local operations.
• Starting from an existing maximal random packing, such as Maximal Poisson-disk Sampling (MPS).
• Maintaining minimum disk separation and maximum domain coverage distances throughout the process.

Main Results:

• Achieved user-defined spatial densities, approaching theoretical limits.
• Tuned samples remained conflict-free and retained coverage maximality.
• Blue noise randomness properties were preserved, except in extreme density cases.

Conclusions:

• The framework offers a flexible method for controlling disk packing density.
• Applications include improving mesh quality and enhancing simulations of fiber-reinforced polymers.
• The approach efficiently satisfies sizing functions with fewer points.