ElementsOfProjective geometry

ivan gabrovski

Contains ads

About this app

App elements of Projective geometry: Homography, Pascal's Theorem, Desargues Theorem, Double relation.
Android application (Java), multilingual with four interactive scenes. The dots are dragged with a finger.
1. **Homography** – the unit square is plotted on a quadrilateral ABCD
(3×3 matrix of 4 pairs of points, Gaussian method). The vanishing points V₁, V₂ are shown.
and the horizon – the image of the infinite line.
2. **Pascal's Theorem** – hexagon inscribed in an ellipse; X, Y, Z are collinear.
3. **Desargues' Theorem** – two perspective triangles and the perspective axis.
4. **Double relation** – central projection of 4 points; (A,B;C,D) remains the same.

All geometry is in homogeneous coordinates (`geometry/Vec3`):
line through two points = cross product, intersection of two lines = cross product.
Infinite points are handled without special cases.

## Languages
English (default), Bulgarian, French, German and Spanish. The language is changed from a menu in the toolbar and does not depend on the device language (`AppCompatDelegate.setApplicationLocales`).
The selection is saved; on Android 13+, the language can also be changed from the app's system settings.

## Structure
- `geometry/` – Vec3, Projective, Homography (pure Java, no Android)
- `view/` – GeometryView (base class: dragging, drawing lines) and the four scenes
- `MainActivity` – tabs (TabLayout), tooltip, numeric information, "Reset" button