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 filtering algorithm and a variational segmentation algorithm are proposed to enhance the quality of SBall. Finally, applications of this structure are discussed.
Resorting to cubic spline function instead of parametric spline representation,an explicit fairness indicator and an efficient fairing algorithm for 2D curves are presented.The input point sequence is firstly partitioned into several overlapped function segments.For each segment,a cubic spline function is used as the representation tool which entails a polyline approximation of curvature plot.Based on the extrinsic relationship between the polyline and the positions of data points,a coarse-to-fine faring method is proposed which efficiently identifies and eliminates the unnecessary inflection points.Our algorithm generates the best results to date,which is validated by numerous practical examples.
A novel representation of a triangular mesh surface using a set of scale-invariant measures is proposed.The measures consist of angles of the triangles(triangle angles) and dihedral angles along the edges(edge angles)which are scale and rigidity independent. The vertex coordinates for a mesh give its scale-invariant measures, unique up to scale, rotation, and translation. Based on the representation of mesh using scale-invariant measures, a two-step iterative deformation algorithm is proposed, which can arbitrarily edit the mesh through simple handles interaction.The algorithm can explicitly preserve the local geometric details as much as possible in different scales even under severe editing operations including rotation, scaling, and shearing. The efficiency and robustness of the proposed algorithm are demonstrated by examples.
In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.
