We present a novel armature structure for 3D articulated shapes, called SBall short for skeletal balls, which includes two parts： a one-dimensional skeleton and incident balls. Our algorithm mainly focuses on constructing the armature structure. This structure is based on an approximation skeleton which is homotopy equivalent to the shape. Each ball in the structure connects a skeletal joint and an interior region of the shape. The boundary vertices on the shape surface are attached onto the SBall using the power diagram of the ball set. A bilateral O^tering algorithm and a variational segmentation algorithm are proposed to enhance the quality of SBall. Finally, applications of this structure are discussed.
UE-Brzier （unified and extended Brzier） basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved.
