Shape transformation for polyhedral objects

Interactive surface decomposition for polyhedral morphing

“…Parent [34,35] has also described a method for deformation of polyhedral objects based on implicit functions. Kent et al [26,27] have presented a shape transformation algorithm for genus-zero polyhedra that involves projecting the models onto a sphere. Chen et al [9] have produced 3D morphs of cylindrical images.…”

“…A number of algorithms have been proposed by Kent et al [26], Maillot et al [32], and Eck et al [15]. One possible solution is to use harmonic maps.…”

“…Kent and colleagues [26] suggest using Hermite interpolation between the corresponding vertices with the tangents pointing along normal directions. Similarly, we allow the user to represent the trajectory as a Bézier curve for each pair of extremal vertices.…”

Earth Mover’s Morphing: Topology-Free Shape Morphing Using Cluster-Based EMD Flows

“…Polygonal/polyhedral shape morphing: Sederberg [19] proposed a 2D polygonal shape morphing method based on work minimization of the vertex deformation. Kent et al [20] extended the idea to 3D polyhedral shape and computed a transformation process by interpolating between corresponding vertex positions. These methods is, however, not applicable to free-form shape.…”

“…On the other hand, the shape morphing problem is treated predominantly as a shape contour/surface deformation problem because of its compact expression [19] [20]. The morphing target is, however, limited to shapes with the same genus; in other words, most of the existing methods cannot deal with morphing of shapes with different genera, such as morphing from a disk to an annulus in a 2D domain ( Fig.…”