Our polygons/points method is octree based, uses interval and point sampling of the surface curvature to drive the subdivision, and uses a pruning algorithm to generate points that are rendered where the surface curvature is high, or around non-manifold features. This approach allows us to visualise both manifold and non-manifold implicit surfaces of high complexity. We discuss necessary modifications of the dual grid method to polygonise the surfaces. The main advantage of the dual grid is that cracks do not form between shared plotting node faces that are at different depths. Polygons are formed as a mixture of triangles and quadrilaterals. We also discuss improvements to the grid so that slither triangles do not form. We render a variety of non-manifold implicit surfaces to demonstrate the results from our algorithm. We also discuss the advantages of this approach.