We could add an object tentatively called an open cone, which would be a cone with no height, i.e. one that extends infinitely into one direction. Such an object has one parameter less than the Cone. The radius and the height (both meaningless for this infinite object) are replaced by the single opening angle parameter. The fact that there is one less parameter, may make fitting easier. In the case of sundials, this is then the preferred option, since it does not actually make sense to limit the cone in height and radius, as we must do now.
We could add an object tentatively called an open cone, which would be a cone with no height, i.e. one that extends infinitely into one direction. Such an object has one parameter less than the Cone. The radius and the height (both meaningless for this infinite object) are replaced by the single opening angle parameter. The fact that there is one less parameter, may make fitting easier. In the case of sundials, this is then the preferred option, since it does not actually make sense to limit the cone in height and radius, as we must do now.