compas.geometry.is_coplanar(points, tol=0.01)[source]

Determine if the points are coplanar.

  • points (sequence[point]) – A sequence of point locations.

  • tol (float, optional) – A tolerance for planarity validation.


bool – True if the points are coplanar. False otherwise.


Compute the normal vector (cross product) of the vectors formed by the first three points. Include one more vector at a time to compute a new normal and compare with the original normal. If their cross product is not zero, they are not parallel, which means the point are not in the same plane.

Four points are coplanar if the volume of the tetrahedron defined by them is 0. Coplanarity is equivalent to the statement that the pair of lines determined by the four points are not skew, and can be equivalently stated in vector form as (x2 - x0).[(x1 - x0) x (x3 - x2)] = 0.