Generalized anisotropic stratified surface sampling.

Area of Science:

• Computer Graphics
• Geometric Modeling
• Computational Geometry

Background:

• Efficiently sampling complex surfaces is crucial for rendering and simulation.
• Existing methods often lack user control over sampling density and anisotropy.
• Achieving high-quality, low-artifact sampling remains a challenge.

Purpose of the Study:

• Introduce a novel stratified sampling technique for mesh surfaces.
• Provide user control over sampling density and anisotropy.
• Ensure high-quality sample distribution with minimal artifacts.

Main Methods:

• Utilize space-filling curves mapped onto mesh segments via tensor field-aligned parametrizations.
• Implement a preprocessing step for real-time sample generation.
• Conduct spectral and differential domain analysis for validation.

Main Results:

• Generated samples exhibit high quality, fulfilling the blue noise criterion.
• The technique accurately represents both isotropic and anisotropic densities.
• Achieved low discrepancy for even surface coverage.
• Real-time sample generation is possible after preprocessing.

Conclusions:

• The proposed stratified sampling technique offers precise user control over mesh surface sampling.
• The method produces high-quality, artifact-free, and evenly distributed samples.
• This approach is suitable for applications requiring controlled and efficient surface sampling.