Embodiments relate to tracking a pose of a 3D object. In embodiments, a 3D computer model, consisting of geometry and joints, matching the 3D real-world object may be used for the tracking process. Processing the 3D model may be done using collision constraints generated from interpenetrating geometry detected in the 3D model, and by angular motion constraints generated by the joints describing the connections between pieces/segments/bones of the model. The depth data in its 3D (point cloud) form, supplied by a depth camera, may be used to create additional constraints on the surface of the 3D model thus limiting its motion. Combined together, all the constraints, using linear equation processing, may be satisfied to determine a plausible pose of the 3D model that matches the real-world pose of the object in front of the 3D camera.