A Simple Push-Pull Algorithm for Blue-Noise Sampling.

Area of Science:

• Computer Graphics
• Computational Geometry

Background:

• Blue-noise sampling is crucial for rendering and geometric processing.
• Existing methods often struggle with balancing sampling quality and efficiency.
• Spatial constraints are key to achieving desired point distributions.

Purpose of the Study:

• To introduce a novel push-pull optimization (PPO) algorithm for blue-noise sampling.
• To enforce various spatial constraints on point sets for improved sampling.
• To offer flexibility in trading off between sampling targets like noise and aliasing.

Main Methods:

• The PPO algorithm enforces constraints on point sets using Delaunay triangulation topology.
• Constraints include minimum sample distance, maximum point-to-sample distance, and Voronoi cell capacity deviation.
• The algorithm allows for flexible trade-offs between noise and aliasing.

Main Results:

• The PPO algorithm demonstrates efficiency and robustness in various applications.
• Experimental results show superior remeshing quality compared to state-of-the-art methods.
• The approach successfully handles anti-aliasing, stippling, and non-obtuse remeshing.

Conclusions:

• The proposed PPO algorithm offers an effective and flexible approach to blue-noise sampling.
• It provides high-quality results in applications such as anti-aliasing and remeshing.
• The method surpasses current state-of-the-art techniques in remeshing quality.