1. A computer-implemented method for tessellating a displaced subdivision surface associated with a scene object, the method comprising: receiving a subdivision surface that includes a first patch and a second patch that share two vertices; transforming the first patch into a first transformed patch and the second patch into a second transformed patch, wherein each of the first and second transformed patches is defined by four vertices, and each vertex is associated with a position vector, a first partial vector in a first parameter, a second partial vector in a second parameter, and two twist vectors; sampling each of the first and second transformed patches to generate a limit surface that includes a plurality of sample points; evaluating the sample points included in the limit surface to generate an approximation mesh that includes a plurality of evaluated vertices, wherein each evaluated vertex includes at least a position vector and a normal vector; and displacing each evaluated vertex of the approximation mesh based on a displacement map to generate a displaced approximation mesh that is reflective of the displaced subdivision surface and is used to render the scene object.