Operations on Signed Distance Functions

We present a theoretical overview of signed distance functions and analyze how this representation changes when applying an offset transformation. First, we analyze the properties of signed distance and the sets they describe. Second, we introduce our main theorem regarding the distance to an offset set in (X,||.||) strictly normed Banach spaces. An offset set of D in X is the set of points equidistant to D. We show when such a set can be represented by f(x)-c=0, where c denotes the radius of the offset. Finally, we explain these results for applications that offset signed distance functions.