Piecewise Developable Modeling via Implicit Neural Deformation and Feature-Guided Cutting.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Modeling complex shapes often requires complex surface representations.
• Achieving developable surfaces is crucial for manufacturing processes like fabrication and unfolding.
• Existing methods may struggle with tessellation independence and analytical curvature computation.

Purpose of the Study:

• To propose a novel, automatic method for shape modeling using a minimal set of discrete developable patches.
• To leverage implicit neural shape representation for tessellation independence and analytical Gaussian curvature calculation.
• To improve the trade-off between the number of developable patches and approximation error compared to state-of-the-art methods.

Main Methods:

• Utilizing implicit neural shape representation for analytical Gaussian curvature.
• Deforming input shapes into almost developable forms with salient feature curves.
• Converting implicit fields to triangle meshes, cutting along feature curves to achieve disk topology.
• Alternatingly optimizing discrete developability, manufacturability constraints, and patch merging.

Main Results:

• Demonstrated feasibility and practicability across various shapes.
• Achieved analytical Gaussian curvature computation due to implicit representation.
• Successfully generated piecewise developable meshes with optimized patch count and approximation error.

Conclusions:

• The proposed method offers an effective and automatic way to model shapes using developable patches.
• Implicit neural representation is key to achieving tessellation independence and analytical curvature.
• The method presents a superior trade-off between approximation accuracy and the number of developable patches for shape modeling.