Previously published algorithms to construct isosurfaces with sharp edges and corners require 'Hermite' data, the exact intersection points of grid edges and the isosurface and the exact gradients at those intersection points. We are interested in constructing iso-surfaces with sharp edge and corners from regular grid of scalar data without any information about intersection points or gradients at those intersection points. We decompose the problem into two parts: 1) Compute gradients at grid vertices from scalar data; 2) Compute an isosurface with sharp edges and vertices from a regular grid of scalar and gradient values. We focus on the second problem, computing an isosurface from scalar and gradient data. We also describe a method for visualizing and evaluating the accuracy of a reconstructiong of sharp features.