We present a novel generic method for the fast and accurate computation of geometric descriptors. While most existing approaches perform the computations directly on the geometric representation of the model, our method operates in parametric space, decoupling the computational complexity from the underlying mesh geometry. In contrast to other parametric space approaches, our method is not restricted to specic descriptors or parameterisations of the surface. By using the parametric space representation of the mesh geometry, we can trivially exploit massive parallel GPU architectures and achieve interactive computation times, while maintaining high accuracy. This renders the method suitable for computations involving large areas of support and animated shapes.