Generation of 3D objects using Lie algebra models based on curvature analysis and comparison with B-spline fitting

This paper discusses 3D free object synthesis using models of linear and Hamiltonian Lie algebra, which can represent a wide class of non-algebra and compact shapes and recover the objects uniquely using their invariants with respect to Euclidean or affine transformations. A curvature analysis of the surfaces represented by these Lie algebra models is shown, based on which an efficient algorithm of shape generation is proposed. Then the description power of these Lie algebra object models is evaluated by comparing them with the B-splines model.