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'.