parameterizing subdivision surfaces

we present a method for parameterizing subdivision surfaces in an as-rigid-as-possible fashion. while much work has concentrated on parameterizing polygon meshes, little if any work has focused on subdivision surfaces despite their popularity. we show that polygon parameterization methods produce suboptimal results when applied to subdivision surfaces and describe how these methods may be modified to operate on subdivision surfaces. we also describe a method for creating extended charts to further reduce the distortion of the parameterization. finally we demonstrate how to take advantage of the multi-resolution structure of subdivision surfaces to accelerate convergence of our optimization.