Abstract: This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (i.e; exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. Using a new, numerically stable representation for quadratic error functions, we develop an octree-based method for simplifying contours produced by this method. We next extend our contouring method to these simplified octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching." We conclude with a simple test for preserving the topology of the contour during simplification.