Efficient and flexible sampling with blue noise properties of triangular meshes

Area of Science:

• Computer Graphics
• Computational Geometry
• Numerical Analysis

Background:

• Generating random samples on 3D mesh surfaces is crucial for simulations and rendering.
• Existing methods for Monte Carlo distributions can be inefficient or prone to errors.
• Need for flexible sampling techniques adaptable to specific constraints.

Purpose of the Study:

• To develop and evaluate efficient algorithms for random sampling on 3D mesh surfaces.
• To introduce a novel sampling scheme, Constrained Poisson-disk sampling, for polygonal meshes.
• To enable customized point distributions, including importance sampling and geometrically constrained sets.

Main Methods:

• Discussed efficient and practical generation of Monte Carlo distributions, addressing common pitfalls.
• Proposed Constrained Poisson-disk sampling, a new scheme for polygonal meshes.
• Presented two specific algorithms based on the Constrained Poisson-disk sampling approach.

Main Results:

• Demonstrated the effectiveness of the proposed Constrained Poisson-disk sampling for generating diverse point distributions.
• Provided an in-depth analysis of the frequency characteristics and performance of the developed algorithms.
• Showcased the adaptability of the method for customized sampling needs.

Conclusions:

• The Constrained Poisson-disk sampling offers an efficient and flexible solution for generating random samples on 3D meshes.
• The proposed algorithms provide practical tools for creating customized point sets, enhancing applications in computer graphics and beyond.
• This work advances the state-of-the-art in mesh sampling techniques.