Cubic Hermite Interpolations of Signed Distance Fields

Signed distances are frequently employed concepts in computer graphics and geometric modeling.In highperformance applications, these are most often approximated by bilinearly filtered regular grids of signed distance samples.However, this framework does not preserve the fundamental properties and behavior of signed distance functions, such as unit length gradients and the recently proposed null closest point energies.Hermite interpolation, in particular its cubic realization, has been well established in the domain of signal processing.Although these have been also shown to be efficient means to approximate signed distance functions from a general loss perspective, their relation to these properties have not been investigated previously.We present a comparative empirical study on various Hermite interpolation constructs focusing on how the resulting approximants deviate from the properties of true signed distance functions.