Surface gradients are useful to surface reconstruction in single view modeling, shape-from-shading, and photometric stereo. Previous algorithms minimize a complex, nonlinear energy functional, or require dense surface gradients to perform integration to generate 3D locations, or require user-input heights to constrain the solution space, or produce severe distortion and smooth out surface details. Most single-view algorithms output a Monge patch (height-field), which may introduce further surface distortion along object silhouettes and surface orientation discontinuities. Our proposed algorithm operates on a single view of complete or incomplete data. The data can be gradients without 3D locations, or 3D locations without gradients. The output surface, which is not necessarily a height-field, preserves salient depth and orientation discontinuities. Experimental comparisons on both simple and complex data show that our method produces better surfaces with significantly less distorti...