We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.