A method for generating a discrete, signed 3D distance field is proposed. Distance fields are used in a number of contexts. In particular the popular level set method is usually initialized by a distance field. The main focus of our work is on simplifying the computation of the sign when generating signed distance fields. Previous methods largely rely on scan conversion to classify voxels as being inside or outside. In contrast, our method relies on defining a pseudo normal, the angle weighted normal, which is used to determine, for each grid point, whether that point is inside or outside. This leads to a method for generating signed distance fields which is a simple and straightforward extension of the method for generating unsigned distance fields. We prove that our choice of pseudo normal leads to a correct technique for computing the sign.