Wide-Angle lenses are not often used for 3D reconstruction tasks, in spite of the potential advantages offered by their increased field-of-view, because (1) existing algorithms for high-distortion lens compensation perform poorly at image extremities and (2) procedures for the reconstruction of recti-linear images place a large burden on system resources. In this paper, a projection model based on quadric surfaces is presented which accurately characterizes the effect of wide-angle lenses across the entire image and allows for the use of novel feature matching strategies that do not require nonlinear distortion compensation.