ElementsOfProjective geometry

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