Most rendering engines subdivide arbitrary polygons into a collection of triangles, which are then rendered independently of each other. This procedure can introduce severe artifacts when rendering texture-mapped quadrilaterals. These errors result from a fundamental limitation: the impossibility of performing general projective mappings using only the information available at the vertices of a single triangle. Texture mapping involving arbitrary quadrilaterals has practical importance in applications that use real images as textures, such as in image-based modeling and rendering. This paper presents an efficient adaptive-subdivision solution to the problem, which, due to its simplicity, can be easily incorporated into graphics APIs.