SOFIA - Scalable Operators for Field-driven Iso/Ani Adaptation

What is SOFIA?

SOFIA is a pure Python library for 2D triangular mesh modification and remeshing. It provides robust, high-quality local operations to edit, refine, and optimize meshes while maintaining mesh conformity and quality.

Perfect for: - Computational scientists working with 2D simulations - Computer graphics professionals needing mesh processing - Numerical analysis requiring adaptive mesh refinement - Researchers in mesh generation and optimization

Features

Core Operations

• Edge Split - Midpoint and Delaunay-based splitting
• Edge Collapse - Quality-preserving mesh coarsening
• Edge Flip - Improve triangle quality through flipping
• Vertex Insertion/Removal - Add or remove mesh vertices
• Pocket Filling - Fill holes in meshes intelligently
• Boundary Operations - Safe manipulation of mesh boundaries

Quality & Robustness

• Quality Metrics - Min angle, area, shape measures
• Conformity Checks - Ensure valid mesh topology
• Amortized Validation - Fast incremental checking
• Strict Mode - Optional rigorous validation
• Area Preservation - Maintain geometric properties

Workflows

• Greedy Remeshing - Iterative quality improvement
• Patch-based Processing - Batch operations on mesh regions
• Visualization - Built-in plotting with Matplotlib
• Extensive Testing - 50+ unit tests for reliability

Installation

Using pip (Recommended)

bash pip install sofia-mesh

From Source

bash git clone https://github.com/youssef-mesri/sofia-mesh.git cd sofia-mesh pip install -e .

Requirements

• Python 3.8 or higher
• NumPy ≥ 1.20
• SciPy ≥ 1.7
• Matplotlib ≥ 3.3

Quick Start

Basic Example - Improve Mesh Quality

```python import numpy as np from sofia import PatchBasedMeshEditor

Create a simple mesh

points = np.array([ [0.0, 0.0], [1.0, 0.0], [0.5, 0.8], [0.0, 1.0], [1.0, 1.0] ]) triangles = np.array([ [0, 1, 2], [0, 2, 3], [1, 4, 2], [3, 2, 4] ])

Initialize editor

editor = PatchBasedMeshEditor(points, triangles)

Split an edge to refine the mesh

success = editor.splitedge(edgeid=0, method='midpoint') print(f"Edge split: {success}")

Get the updated mesh

newpoints = editor.pts newtriangles = editor.tris

Check mesh quality

minangle = editor.meshminangle() print(f"Minimum angle: {minangle:.2f}°") ```

Remeshing Example

```python from sofia.core.remeshdriver import greedyremesh

Iteratively improve mesh quality

improvededitor = greedyremesh( editor, targetminangle=25.0, # Target minimum angle in degrees max_iterations=100 )

print(f"Final quality: {improvededitor.meshmin_angle():.2f}°") ```

Documentation

• API Reference - Complete API documentation
• Examples - Practical usage examples
• Contributing - How to contribute

Examples

Check out the examples/ directory for more:

• basic_remeshing.py - Simple mesh refinement
• quality_improvement.py - Iterative quality optimization
• boundary_operations.py - Boundary manipulation

Roadmap

Current (v1.0.0) - Python Implementation

• Pure Python implementation
• All core features working
• Suitable for meshes up to ~10K triangles
• Easy installation, no compilation needed

Next (v2.0) - High-Performance C++ Backend

• 20-50x performance improvement
• Transparent integration (same API)
• Suitable for meshes up to 1M+ triangles
• Optional: falls back to Python if C++ unavailable
• Status: In development (private branch)

Future (v3.0+)

• GPU acceleration
• 3D tetrahedral mesh support
• Parallel batch processing
• Advanced anisotropic remeshing

Citation

If you use SOFIA in your research, please cite:

bibtex @software{sofia2025, author = {Mesri, Youssef}, title = {SOFIA: Scalable Operators for Field-driven Iso/Ani Adaptation}, year = {2025}, url = {https://github.com/youssef-mesri/sofia-mesh}, version = {1.0.0} }

Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

• Found a bug? Open an issue
• Have an idea? Start a discussion
• Want to contribute? Submit a pull request

License

SOFIA is released under the MIT License.

Acknowledgments

• Inspired by classical mesh modification algorithms
• Built with modern Python best practices
• Developed for research in computational geometry

Contact

Author: Youssef Mesri

• Issues: GitHub Issues
• Discussions: GitHub Discussions
• Email: youssef.mesri@minesparis.psl.eu
• ORCID: 0000-0002-5136-5435