## 3 Geometry ¶

### 3.1 Transformations ¶

Transformations consist in either generic transformations, which can be applied on any kind of geometric objects, or projections, which are only defined for points.

#### Generic transformations ¶

`translation(o, u)`

  Translation of object o using vector u.

`reflection(o, l)`

  Reflection of object o with respect to line l.

`symmetric(o, A)`

  Symmetric (i.e. 180° rotation) of object o with respect to point A.

`rotation(o, A, a)`

  Rotation of object o with respect to point A, using angle a.

`homothecy(o, A, x)`

  Homothecy (i.e. reduction or dilation) of object o with respect to point A, using scale x.

#### Projections ¶

`projection(A, l)`

  Orthogonal projection of point A on line l.

`projection(A, l, l')`

  Projection of point A on line l using direction of line l'.