Abstract: A system for displaying sets of surface cubes with gradient vertex vectors first employs a pointer table constructed to order the surface cubes so as to generally cause a row by row and layer by layer ordering during model creation. During display, a viewpoint is selected and a scan controller causes cubes to be displayed according to this order of the pointer table. A test backprojection of cubes to image plane is performed to determine which pixels will be impinged by the cubes. For pixels which have not been updated, or pixels which have been updated by a less superficial cube than the current cube, projection rays are created through the center of impinged pixels in a direction opposite that of the backprojection. An intersection point of the ray with a surface within a current cube is determined. The data value and gradient vectors for the current cube are interpolated at this intersection point.

Abstract: A computer modeling and visualization system employs both 3D visual modeling and force feedback through a haptic device consistent with the visual display of the computer model. Force, or haptic, interaction is employed for exploring computer models. Point contact force equations were created for quickly computing forces directly from a model data which are provided to the haptic device, causing it to apply that force to an operator. The force equations employed are consistent with isosurface and volume rendering, providing a strong correspondence between visual and haptic rendering. The method not only offers the ability to see and feel the volumetric model but allows interactive modification and display of the model.