PIMesh: An automatic point cloud and unstructured mesh generation algorithm for meshless methods and finite element...

Area of Science:

• Computational geometry
• Scientific computing
• Computer-aided design

Background:

• Generating high-quality point clouds and unstructured meshes is crucial for various computational applications.
• Existing methods often require significant user intervention and struggle with complex geometries.
• The need for automated, robust, and versatile mesh generation tools is persistent.

Purpose of the Study:

• To present a novel algorithm, the particle injection mesh generator (PIMesh), for automated generation of point clouds and unstructured meshes.
• To demonstrate PIMesh's capability to handle domains of arbitrary shapes with minimal user input.
• To showcase PIMesh's adaptability for diverse applications, including meshless and finite element methods, computer graphics, and surgical simulation.

Main Methods:

• The PIMesh algorithm treats the domain as an "airtight container" where particles are injected and move based on pseudo-molecular dynamics (PMD).
• Particles interact via repulsive forces and a velocity-dependent drag force, distributing themselves evenly within the domain.
• A Delaunay triangulation algorithm connects the resulting point cloud to form an unstructured mesh.

Main Results:

• PIMesh successfully generates optimized point clouds and high-quality unstructured meshes for 2D and 3D domains of any shape.
• The algorithm requires minimal to no user intervention and allows for control over mesh grading.
• Demonstrated effectiveness on various domains, including complex scanned objects like bones.

Conclusions:

• PIMesh offers a robust, easy-to-implement, and automated solution for point cloud and mesh generation.
• The algorithm's versatility makes it suitable for a wide range of computational applications.
• PIMesh represents a significant advancement in simplifying and optimizing mesh generation processes.