Adaptive approximation of signed distance fields through piecewise continuous interpolation.

In this paper, we present an adaptive structure to represent a signed distance field through trilinear or tricubic interpolation of values, and derivatives, that allows for fast querying of the field. We also provide a method to decide when to subdivide a node to achieve a provided threshold error. Both the numerical error control, and the values needed to build the interpolants, require the evaluation of the input field. Still, both are designed to minimize the total number of evaluations. C 0 continuity is guaranteed for both the trilinear and tricubic version of the algorithm. Furthermore, we describe how to preserve C 1 continuity between nodes of different levels when using a tricubic interpolant, and provide a proof that this property is maintained. Finally, we illustrate the usage of our approach in several applications, including direct rendering using sphere marching. • Computation of Signed Distance Field(SDF) adaptative grid from triangle meshes. • Method for storing approximations of distance fields for fast query operations. • Adaptive structure built regarding a target error. • The structure guarantees C0 and C1 continuity. [ABSTRACT FROM AUTHOR]