1.    Introduction

Three-dimensional metamorphosis (or morphing) is a widespread technique in entertainment and animation to generate a smooth transition from a source object to a target object. In this paper, we focus on morphs between two genus 0 3D polyhedra. In the literature, most polyhedral morphing techniques could consist of two main steps: one is to find one-to-one correspondence between two polyhedral meshes and the other is to define interpolation paths for each pair of corresponding vertices on the meshes to calculate the in-between shapes. A lot of previous work has been published in the area of 3D polyhedral morphing. There are two excellent surveys of 3D morphing to be referred to in [1,2].

 In this paper, our design goal is to provide animators the easy control of morphs and the fast creation of morphs. There are two-level controls for animators to intuitively establish correspondence. First, animators specify scatter features to decompose the models into the corresponding patches, i.e., called morphing patches in this paper. This higher-level control provides the approximate correspondence between two models. If the finer correspondence is required on each patch, the lower-level control allows the animators to specify extra feature points on each patch. With the help of the lower-level control, animators only need to identify few corresponding morphing patches. Therefore, in contrast to other methods such as [3], manual interaction times can be reduced. Afterwards, there are three techniques designed to automatically and efficiently establish a complete one-to-one correspondence between models. In contrast to most other approaches, the proposed methods are very fast and can be computed within a few seconds. These proposed schemes are the main contributions of this paper and are listed below:

l          An efficient relaxation method is proposed to embed (i.e., map) 3D morphing patches to 2D regular polygons. In contrast to other relaxation methods such as in [4], our method is computed within a few seconds (usually less than 1 second for our examples).

l          A foldover-free warping method is used to align corresponding feature vertices between two embeddings of morphing patches. This is a very essential part in the lower-level control of correspondence.

l          An efficient but simple merging method is presented to create a merged embedding that contains the faces, edges and vertices of two given embeddings. The SMCC (structures of minimal contour coverage) is designed to speed up the merging process and the merging is always computed in less a second. In addition, there are several lookup tables are used for easy and efficient implementation.

The rest of our paper is organized as follows. Section 2 reviews the related work of 3D polyhedral metamorphosis. The proposed techniques are presented in Section 3. We experimentally evaluate the proposed schemes and experimentally compare with other wok in Section 4. Finally, the conclusion and future work are given in Section 5.