Primate visual cortex contains a set of maps of visual space. These maps are fundamental to early visual processing, yet their form is not fully-understood in humans. This is especially true for the central and most important part of the visual field - the fovea. We used functional Magnetic Resonance Imaging (fMRI) to measure the mapping geometry of human V1 and V2 down to 0.5° of eccentricity. By applying automated atlas fitting procedures to parametrize and average retinotopic measurements of 8 brains, we provide a reference standard for the 2-dimenional geometry of early human visual cortex of unprecedented precision and analyze this high quality mean dataset with respect to the 2-dimensional cortical magnification morphometry. The analysis indicates that 1) area V1 is meridional isotropic in areal projection: equal areas of visual space are mapped to equal areas of cortex at any given eccentricity. 2) V1 has a systematic pattern of local anisotropies: cortical magnification varies between iso-polar and iso-angle lines and 3) the shape of V1 deviates systematically from the complex-log model, whose fit is particularly poor close to the fovea. We therefore propose two modified models that result in a more accurate description of V1 shape. 4) V2 is elongated by a factor of 2 in eccentricity direction relative to V1 and has significantly more local anisotropy. We propose that V2 has systematic intrinsic curvature, but V1 is intrinsically flat.