The type for points.

dim is the dimension of points of type p3.

The type for matrices representing linear transformations of homogenous 3D space.

v x y z is the point (x y z).

x p is the x coordinate of p.

y p is the y coordinate of p.

y p is the z coordinate of p.

o is the point (0 0 0).

mid p q is the mid point (p + q)/2.

tr m p is the affine transform in homogenous 3D space of the point p by m.

Note. Since m is supposed to be affine the function ignores the last row of m. p is treated as a finite point (its last coordinate in homogenous space is 1). Use V3.tr to transform vectors (infinite points).