In this paper, it is shown that the Enhanced Unified Camera Model, which is used to model fisheye cameras, projects straight lines into conic sections. Then a way to find equations of straight line projections is proposed. The method is applied to epipolar curves to adapt the Semi-Global Matching algorithm to fisheye stereo systems to compute a dense direct stereo correspondence without undistortion and rectification of fisheye images. It is done by efficient image sampling along an epipolar curve, using an algorithm for rasterization of implicit curves. A C++ implementation is available online.