The signed distance field of a surface can effectively support many geometry processing tasks such as decimation, smoothing, and Boolean operations since it provides efficient access to distance (error) estimates. In this paper we present an algorithm to compute a piecewise linear, not necessarily continuous approximation of the signed distance field for a given object. Our approach is based on an adaptive hierarchical space partition that stores a linear distance function in every leaf node. We provide positive and negative criteria for selecting the splitting planes. Consequently the algorithm adapts the leaf cells of the space partition to the geometric shape of the underlying model better than previous methods. This results in a hierarchical representation with comparably low memory consumption and which allows for fast evaluation of the distance field function.