First Order Signed Distance Fields

Abstract

This paper investigates a first order generalization of signed distance fields. We show that we can improve accuracy and storage efficiency by incorporating the spatial derivatives of the signed distance function into the distance field samples. We show that a representation in power basis remains invariant under barycentric combination, as such, it is interpolated exactly by the GPU. Our construction is applicable in any geometric setting where point-surface distances can be queried. To emphasize the practical advantages of this approach, we apply our results to signed distance field generation from triangular meshes. We propose storage optimization approaches and offer a theoretical and empirical accuracy analysis of our proposed distance field type in relation to traditional, zero order distance fields. We show that the proposed representation may offer an order of magnitude improvement in storage while retaining the same precision as a higher resolution distance field.