Efficient Spherical Joint Limits with Reach Cones

We describe a simple and fast method of creating and using joint sinus reach cones to limit the range of motion on universal and ball-and-socket joints. Reach cones can be created interactively or based on results from biomechanics. A reach cone is specified as a spherical polygon on the surface of a reach sphere that defines all positions the longitudinal segment axis beyond the joint can take. Reach polygons can be concave or convex, and cover more than one hemisphere. Longitudinal axis rotation limits can also be defined for locations in the reach cone. Calculations to determine whether a segment is within the reach cone are based on the relation of the segment longitudinal axis to the planes defining the reach cone, and are done in the local coordinate space of the segment. The calculations have no discernible effect on the speed of interactive display or animation.