Aiming at robust surface structure recovery, we extend the powerful optimization technique of variational shape approximation by allowing for several different primitives to represent the geometric proxy of a surface region. While the original paper only considered planes, we also include spheres, cylinders, and more complex rollingball blend patches. The motivation for this choice is the fact that most technical CAD objects consist of patches from these four categories. The robust segmentation and global optimization properties which have been observed for the variational shape approximation carry over to our hybrid extension. Hence, we can use our algorithm to segment a given mesh model into characteristic patches and provide a corresponding geometric proxy for each patch. The expected result that we recover surface structures more robustly and thus obtain better approximations with a smaller number of primitives, is validated and demonstrated on a number of examples.