Contouring Signed Distance Fields by Approximating Gradients

Abstract Signed distance fields are often represented by discrete samples (e.g., on a grid). Recovering the contour implicitly represented by the distance samples requires an approximation algorithm. Several recent approaches have shown that exploiting the information carried in each distance sample by explicitly constructing a surface point gives better results than classical contouring algorithms. We explore the idea of generating surface points by simply approximating the gradient of the signed distance function from a tesselation of the sample locations. The distance value together with gradient yields a potential surface point. To avoid problems resulting from bad approximation, surface points are removed if they are too close to any of the distance samples. Using the regular triangulation as tesselation facilitates this filtering. The resulting approximation algorithm is conceptually simple, easy to implement, and significantly faster than existing alternatives, yielding reconstructions that are on par.