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🌐 Geometric Transformations Between Surfaces in 3D

Transforming points between different surfaces in three-dimensional space is no easy task! 🚀 In swarm robotics 🤖, computer graphics 🎨, and geometric modeling 📐, preserving key properties like arc-lengths and angles is critical for reliable outcomes.

In our latest paper, we introduce a topological and geometric framework 🧩 that explains how such transformations can be understood, measured, and optimized. We propose the concept of “distortion” 📊—a measure of how well a transformation preserves distances and angles from a reference point.

🔑 Key Highlights:

• Preserving arc-lengths and angular relationships 🔄

• A distortion measure to quantify transformation accuracy 📏

• Proof that topological differences in surfaces set a minimum distortion bound ⛔

• Numerical methods and examples for practical applications 🖥️

This work bridges theory and practice by combining topology, geometry, and computation—offering valuable insights for fields like swarm robotics, shape analysis, and beyond! 🌟

Scientific World Research Awards🏆

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