Abstract: Ray tracing and other techniques employ algorithms which require the intersection between a 3D parametric ray and an object to be computed. The object to intersect is typically a sphere, triangle, or polygon but many surface types are possible. In this work we consider intersections between rays and the simplest parametric surface, the bilinear patch. Unlike other surfaces, solving the ray-bilinear patch intersection with simple algebraic manipulations fails. We present a complete, efficient, robust, and graceful formulation to solve ray-bilinear patch intersections quickly. Source code is available online.