Preserving intrinsic surface distances. Application to electrode grid manipulation

Presents a method for modeling deformable surfaces with a specific property-under a deformation the intrinsic surface distance between any two points does not change, i.e. the surface allows only isometric deformation. First the authors discuss continuous solutions to the problem and then present a motivation to model the surface as a damped-spring net. The net is damped in order to prevent oscillations and the model is iteratively solved until it reaches a steady state, i.e. until all the springs reach their rest lengths. By doing this on preserves the distances along the surface. Nonlinear springs are added to approximately enforce C/sub 1/ continuity of the surface. The method can be extended to surface deformations under which the intrinsic distances change. The authors apply the method to interactive manipulation of subdural electrode grids in post operative MRI datasets used in neurosurgery, since the grids are not extended or compressed while manipulated during the implantation, i.e. they keep zero Gaussian curvature.