Physically-Based Mesh Generation for Confined 3D Point Clouds Using Flexible Foil Models

TL;DR

This work addresses generating high-quality, closed-surface meshes from confined 3D point clouds by simulating a flexible foil constrained by fixed vertices. It couples elasticity-based forces with a pressure-driven contraction and uses adaptive snapping to fixed vertices under a damping regime, all evolved with explicit-Euler integration; the updates follow $v_{t+1}=v_t+Delta t * a_t$, $x_{t+1}=x_t+Delta t * v_{t+1}$, $a_t=f_t/m$. The contributions include a physics-grounded mathematical formulation (elastic, pressure, damping), a complete implementation pipeline (Fibonacci lattice initialization, convex hull meshing, snapping, smoothing, refinement), and stability-guided evaluation demonstrating smooth convergence and mesh quality under constraints. The results show a stable, structured evolution that preserves boundary constraints while improving uniformity, offering a practical pathway for applications in engineering, biomedical modeling, and computer graphics.

Abstract

We propose a method for constructing high-quality, closed-surface meshes from confined 3D point clouds via a physically-based simulation of flexible foils under spatial constraints. The approach integrates dynamic elasticity, pressure-driven deformation, and adaptive snapping to fixed vertices, providing a robust framework for realistic and physically accurate mesh creation. Applications in computer graphics and computational geometry are discussed.

Figures (4)

• Figure 1: (Left) Fixed vertices and guiding lines. (Right) Sphere and initial mesh definition.
• Figure 2: Mesh evolution after 10 and 20 iterations, showing initial contraction and alignment.
• Figure 3: Refinement and stabilization of the flexible foil mesh at iterations 40 and 55.
• Figure 4: (Left) Maximal displacement of mesh points. (Right) Evolution of nearest-neighbor distances.