Accurate Isosurface Interpolation with Hermite Data

In this work we study the interpolation problem in contouring methods such as Marching Cubes. Traditionally, linear interpolation is used to define the position of an is vertex along a zero-crossing edge, which is a suitable approach if the underlying implicit function is (approximately) piecewise linear along each edge. Non-linear implicit functions, however, are frequently encountered and linear interpolation leads to inaccurate is surfaces with visible reconstruction artifacts. We instead utilize the gradient of the implicit function to generate more accurate is surfaces by means of Hermite interpolation techniques. We propose and compare several interpolation methods and demonstrate clear quality improvements by using higher order interpolants. We further show the effectiveness of the approach even when Hermite data is not available and gradients are approximated using finite differences.