About the Project
Hyperbolic Web UI is a web-based interactive interface designed for exploring and visualizing hyperbolic geometry.
This project provides a dynamic environment to create, manipulate, and study geometric objects in four hyperbolic models:
- Poincaré Disk Model: Lines are represented as circular arcs orthogonal to the disk's boundary.
- Poincaré Half-Plane Model: A representation in the upper half of the complex plane.
- Beltrami-Klein Disk Model: Hyperbolic lines appear as straight chords.
- Hyperboloid Model: A 3D representation of hyperbolic space on a hyperboloid (Minkowski model).
Our goal is to make this fascinating branch of mathematics accessible while offering powerful tools for enthusiasts, educators, and researchers.
Key Features
Interactive Tools
- Add Objects: Points, lines, segments, and circles.
- Modify Space: Rotations, transformations, drag & drop, and centering at origin.
- Interactive Zoom: Zoom in and out of each view to focus on specific details.
- Remove Objects: Delete specific or clear everything.
Procedural Generation
- Generate regular tilings ({7,3}, {3,7}, {4,5}, {5,4}).
- Complex patterns (hyperbolic trees, nested circles).
- Configurable depth and branches.
Real-Time Visualization
Dynamically visualize transformations applied to geometric objects with immediate feedback.
Measurement Tools
- Distance: Calculate hyperbolic distance between two points.
- Angle: Measure hyperbolic angle ABC between three points.
- Real-time Output: View results immediately in the dedicated measurement area.
Import/Export
Save and load your geometric configurations using JSON files to preserve your work.
Educational Resources
Access guided tutorials to understand hyperbolic geometry concepts through interactive examples.
Origins and Acknowledgments
This project originated from a Java Swing application developed during an engineering degree in computer science at ISEN Lille (2012-2013), in collaboration with Rémi Rousselle.
Originally written as a Java Swing software when graduating a M.D in Engineering and Computer Sciences.
We extend our gratitude to:
- Gabriel Chênevert & Benjamin Parent, our mathematics teachers.
- Theon, French Wikipedian, for providing formulas for Hyperbolic Circles in the Beltrami-Klein model.
- The JavaGeom Project which was partially used to plot ellipses.
Useful Resources & References
Future Developments
- Fixes: Improve coordinate precision, fix window resizing issues and vertical line rendering.
- Advanced Selection: Place points on object intersections or precisely between other points.
- UI/UX: Object selection & highlighting, custom colors/naming, history (undo/redo) and detachable panes.
- Advanced Generation: Arbitrary paths, custom reflections and isometries.
How to Contribute
Interested in contributing to Hyperbolic Web UI? You can:
- Report bugs or suggest ideas via GitLab Issues.
- Contribute directly to the code by submitting a merge request.
Let's make hyperbolic geometry more accessible and interactive together!
View on Framagit (GitLab)