OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams.

Area of Science:

• Computational Geometry
• Computer Graphics
• Geometric Modeling

Background:

• Offset surfaces are essential in geometry processing, with applications in motion planning and modeling.
• Computing constant-radius offset surfaces is well-established, but variable-radius offset surfaces remain a significant challenge.

Purpose of the Study:

• To present OffsetCrust, a novel framework for efficiently computing variable-radius offset surfaces.
• To address limitations in existing methods, particularly misalignment issues in crust-based approaches.

Main Methods:

• Constructing a power diagram from carefully sampled base points and corresponding off-surface points.
• Utilizing a radius function (R) and R-dependent displacement directions.
• Implementing a lightweight fine-tuning procedure to mitigate misalignment.

Main Results:

• OffsetCrust efficiently computes accurate variable-radius offset surfaces.
• The method successfully mitigates misalignment issues prevalent in other crust-based techniques.
• Experimental validation confirms the framework's accuracy and efficiency.

Conclusions:

• OffsetCrust provides an effective solution for the challenging problem of variable-radius offset surface computation.
• The framework demonstrates practical utility in applications such as reconstructing surfaces from medial axis transforms (MAT).
• This work advances the state-of-the-art in geometry processing and computational modeling.