Developable Approximation via Isomap on Gauss Image.

Area of Science:

• Computer Graphics
• Computational Geometry
• Differential Geometry

Background:

• Developing accurate developable surfaces from arbitrary meshes is crucial in fields like computer-aided design and manufacturing.
• Existing methods often struggle with maintaining mesh fidelity or clearly defining seam curves.

Purpose of the Study:

• To propose a novel method for generating developable approximations of triangular meshes.
• To improve upon the fidelity and seam curve distinctness of current state-of-the-art techniques.

Main Methods:

• Utilizing Isomap, a nonlinear dimensionality reduction technique, to fit general curves on the sphere for Gauss image representation.
• Assigning target normals to each triangle after local fitting.
• Globally deforming the mesh iteratively to match target normals, achieving the developable approximation.

Main Results:

• The proposed method successfully generates developable approximations for various triangular meshes.
• Results show higher fidelity to the original input mesh compared to existing methods.
• The method produces more prominent and visually distinct undevelopable seam curves.

Conclusions:

• The Isomap-based approach offers a robust and effective way to create high-fidelity developable surface approximations.
• This method advances the state-of-the-art in mesh developability, providing clearer seam definition.