A system and method of real-time collision detection between solid geometric objects is provided. The system includes a computer system, a computer-generated geometric model and a haptic device in communication with the computer system having a haptic end effector for transmitting information between a user and the geometric objects. The method includes the steps of representing a moving object as a point cloud and a stationary object as a mesh, and partitioning the mesh into an organized data structure. The method also includes the steps of identifying a constraint set and a collision set. The method further includes the steps of rendering the constraint set by moving the moving object so that the set of active points do not penetrate into the mesh, and providing force feedback through the haptic device relative to the movement of the moving object to satisfy the constraint.