Constraint-based six degree-of-freedom haptic rendering of volume-embedded isosurfaces

A method for 6-DOF haptic rendering of isosurface geometry embedded within sampled volume data is presented. The algorithm uses a quasi-static formulation of motion constrained by multiple contacts to simulate rigid-body interaction between a haptically controlled virtual tool (proxy), represented as a point-sampled surface, and volumetric isosurfaces. Unmodified volume data, such as computed tomography or magnetic resonance images, can be rendered directly with this approach, making it particularly suitable for applications in medical or surgical simulation. The algorithm was implemented and tested on a variety of volume data sets using several virtual tools with different geometry. As the constraint-based algorithm permits simulation of a massless proxy, no artificial mass or inertia were needed nor observed. The speed and transparency of the algorithm allowed motion to be responsive to extremely stiff contacts with complex virtualized geometry. Despite rendering stiffnesses that approach the physical limits of the interfaces used, the simulation remained stable through haptic interactions that typically present a challenge to other rendering methods, including wedging, prying, and hooking.