Methods and systems of representation and manipulation of surfaces with perceptual geometric features, using a computer graphics rendering system, include executing algorithmic instructions to compute a plurality of vertices, edges and surfaces in a mesh for the purpose of defining representations of surfaces on grids. Normals and distances are determined for triangular surfaces to be considered. Additionally, height fields of a function are defined. A set of feature curves and a set of feature points are determined, based on the defined function. Infinitesimal movements along the representations of the surfaces are determined, along with determinations of properties of representations of continuous surfaces. Additional determinations of perceptual geometric features include determinations such as zero crossings, parabolic curves, flecnodes, ruffles, gutterpoints, conical points and biflecnodes in a given mesh. After these determinations are made, visual representations are rendered which capture perceptually important features for smoothly varying shapes.