Volume Decomposition is a fundamental issue that draws attention from researchers in different disciplines. In many contexts, a solid model that contains shape information needs to be partitioned into smaller, simpler or more meaningful sub-models to facilitate efficient or effective analysis. Much progress has been made so far on convex decomposition of polyhedra and relatively difficult geometry; general decomposition on a CAD model with arbitrary shapes to produce intelligent partitions is still highly challenging. The constrained and aggregated half space volume decomposition approach is aimed to improve efficiency and intelligence of decomposition by trimming and aggregating cutting surfaces. In this paper, two kinds of extending strategies: “internal” extending and “external” extending are identified and the algorithms for them are demonstrated.