We present an efficient, user-guided volumetric approximation algorithm, specifically designed for physically based animation. Our method combines automatic and interactive segmentation methods to give users an intuitive and easy way to approximate 3D meshes. Our approach first constructs the simplified medial axis transform of the input mesh object, and segments the medial axis into parts in terms of swept sphere volumes using a region growing method. Then, we decompose the object surface into regions based on the mapping between the segmented medial axis and the object surface. Each segmented region is approximated with a swept sphere volume. These decomposed surface regions can be interactively refined further by splitting and/or merging using a sketch-based input. Experimental results show that our approach produces good volumetric approximation results for different types of object shapes. Moreover, rigid-body dynamics simulation based on our volumetric approximation provides a visually pleasing result. Copyright © 2012 John Wiley & Sons, Ltd.