Haptic rendering using C1 continuous reconstructed distance fields

Existing haptic rendering algorithms are limited in the complexity of the models that can be simulated realistically without artifacts such as extraneous force discontinuities or pop-through. High haptic update rates for realistic feedback require fast collision detection methods, such as those achievable using distance fields. We introduce an efficient algorithm for reconstructing a C¹ distance field from discretely sampled distances and gradients. Our Coons-patch based interpolation method supports 50 kHz 3-DOF haptic rendering of complex models with high accuracy, while eliminating undesirable force discontinuities and pop-through. The approximation error of our representation on a 256 times 256 times 256 grid is similar to that of polygonal model reconstructions containing hundreds of thousands of polygons, an accuracy previously unobtainable with haptic force rendering.