This paper presents a method for estimating models for such operations by clustering fiber orientations. Our approach is applied to ball-and-stick diffusion models, which include an isotropic tensor and multiple sticks encoding fiber volume and orientation. We consider operations which can be generalized to a weighted combination of fibers and present a method for representing such combinations with a mixture-of-Watsons model, learning its parameters by Expectation Maximization. We evaluate this approach with two experiments. First, we show it is effective for filtering in the presence of synthetic noise. Second, we demonstrate interpolation and averaging by construction of a tractography atlas, showing improved reconstruction of white matter pathways. These experiments indicate that our method is useful in estimating multi-fiber ball-and-stick diffusion volumes resulting from a range of image analysis operations.