The hyperboloid kernel, with no statistical meaning or stochastic interpretation, is a good contrary example.
Collision starts from a spherical droplet, and conserving volume between a tangent hyperboloid and the sphere.
British Dictionary definitions for hyperboloid
a geometric surface consisting of one sheet, or of two sheets separated by a finite distance, whose sections parallel to the three coordinate planes are hyperbolas or ellipses. Equations x²/a² + y²/b² – z²/c² = 1 (one sheet) or x²/a² – y²/b² – z²/c² = 1 (two sheets) where a, b, and c are constants
(hī-pûr'bə-loid') Either of two surfaces generated by rotating a hyperbola about either of its main axes and having a finite center, with certain plane sections that are hyperbolas and others that are ellipses or circles.