1. A system for providing substantially stable haptics, comprising: at least one computer configured to: identify a first subset and a second subset of haptic interaction geometric primitives associated with a virtual tool; determine based on the first subset, haptic forces in a first subspace; determine based on the second subset, haptic forces in a second subspace having at least one additional dimension to first subspace; wherein haptic forces in the additional dimension are only determined based on the second subset of haptic interaction geometric primitives, which is different than the first subset of haptic interaction geometric primitives; and determine a torque to constrain an orientation of the virtual tool, wherein determining the torque comprises defining a virtual tool normal and a haptic plane normal and using the virtual tool normal and haptic plane normal to calculate the torque.