Steiner and Poisson Traversal Initializations: Initial Curve Optimization for Geometric Flow-based Surface Filling.

Area of Science:

• Computer Graphics
• Computational Geometry

Background:

• Surface-filling curves are essential for uniformly covering 3D object surfaces.
• Current methods using geometric flows lack robust and efficient initialization strategies.
• Existing initialization techniques are often slow, inflexible, or unreliable.

Purpose of the Study:

• To develop novel, efficient, and robust initialization algorithms for surface-filling curve generation.
• To address the performance limitations of existing curve initialization methods.
• To improve the applicability of surface-filling curves in various domains.

Main Methods:

• Proposed Steiner Traversal Initialization (STI) using approximate minimum Steiner trees on dual graphs.
• Developed Poisson Traversal Initialization (PTI) employing geodesic Poisson disk sampling for tree construction.
• Evaluated algorithms on diverse mesh qualities, including those with sliver triangles.

Main Results:

• STI achieves up to 37.14x speedup on high-quality meshes but degrades on meshes with sliver triangles.
• PTI offers up to 32.63x speedup and maintains robustness on poorly tessellated meshes.
• Both methods demonstrate significant performance improvements over existing initialization techniques.

Conclusions:

• STI and PTI provide complementary solutions for surface-filling curve initialization.
• The proposed methods enhance the speed and robustness of generating surface-filling curves.
• These advancements facilitate broader application of surface-filling curves in 3D modeling and related fields.