Abstract: A system and method for geometric singularity is presented. In one aspect, the system and method are employed for detecting and quantifying envelope singularities of one or more solid shapes in relative movement. In an implementation, a solid shape having a motion is defined. A set of points in a space in which the motion of the solid shape occurs are sampled. For each point in the set of points, the following values are determined: an inverted motion of the motion; one or more inverted trajectories that correspond to points of the space associated with the inverted motion; one or more intersections between the inverted trajectories and a boundary defined by the motion of the solid shape; and one or more tangencies between the inverted trajectories and the boundary.