We address the problem of reconstructing a high-resolution surface representing an object from a single image. We present Surface HOF, which takes an image of an object as input and generates a mapping function for surface generation. The mapping function takes samples from a canonical domain and maps each sample to a local tangent plane on the 3D reconstruction of the object. By efficiently learning a continuous mapping function, the surface can be generated at arbitrary resolution in contrast to other methods which generate fixed resolution outputs. Experiments show that Surface HOF is more accurate and uses more efficient representations than other state of the art methods for surface reconstruction. Surface HOF is also easier to train: it requires minimal input pre-processing and output post-processing and generates surface representations that are more parameter efficient. Its accuracy and convenience make Surface HOF an appealing method for single image reconstruction.