基于Hermite插值的网格拼接和融合-CIDE2013

网格模型的拼接和融合是3维形状编辑和造型中的一个重要方面。基于Hermite插值技术，提出了一种适用于具有一般边界点空间分布的三角网格模型之间无缝光滑拼接和融合方法。首先查找网格模型待拼接区域的边缘点集，并利用二次B样条曲线插值边缘点集分别得到边缘曲线；然后对边缘曲线进行Hermite插值得到拼接区域连续曲面；最后对拼接曲面分别进行三角网格化和Laplacian光顺平滑处理以实现网格模型的光滑拼接和融合。由于利用B样条曲线插值待拼接模型边界，本文方法适用于具有各种不同边界情形的网格模型拼接和融合，它不仅仅可以处理平面边界曲线情形也可以处理空间边界曲线情形。结合Hermite曲面插值拼接过渡区域，使得产生的拼接网格能光滑地衔接待拼接模型。实验结果表明，本文方法能够有效地实现三角网格模型的光滑拼接、模型修复和模型融合。

Mesh stitching and fusion based on Hermite interpolation scheme-CIDE2013

Mesh stitching and fusion is a fundamental operation in a lot of 3D shape editing and modeling applications. For example, it always need to assemble different mechanical apparatuses together in the area of computer-aided industrial design, creating new toys from some existing ones in the area of digital entertainment and reassembling fractured archeological artifacts in the area of cultural relic protection, etc. In general, to blend two under-stitching meshes or fuse several interested sub-parts together, it is widely recognized that the transition surface connecting them should possess the following properties. The transition surface should smoothly combine the underlying meshes in a seamless natural manner for different joining boundaries, whilst the local geometric details should also be preserved as soon as possible in the vicinity of the stitching boundaries. Based on the Hermite interpolation scheme, a novel approach of mesh seamless stitching and fusion is presented in this paper, which can be adapted for blending two meshes with the arbitrary distributed boundary point sets. Firstly, their boundary point sets of two under-joining meshes are automatically selected to form the blending region. The two joining boundary curves can thus be interpolated by two quadratic B-spline curves separately. Then, the transition surface can be constructed by Hermite functional blending scheme under the geometric position and the tangential direction limitations of two boundary curves. Finally, the transition region can be created by triangulating its discretely sampled vertices and applying Laplacian smoothing to form the resultant blending mesh. Compared with the traditional mesh fusion methods, owing to interpolating the two boundary curves of two under-fusion meshes by using B-spine curves, our mesh stitching and fusion scheme can be applied to blend the underlying meshes with different types of boundary curves, that is, it is not only adaptable for the meshes with planar boundary curves but also for the meshes with spatial boundary curves. Meanwhile, due to constructing the transition region by Hermite interpolation scheme that can satisfy the position and the tangential continuity constraints of the stitching boundary curves, the generated transition surface can smoothly blend the underlying meshes and reconstruct the local geometric details in the vicinity of the joining boundaries. Moreover, different from representing the blending surface by an implicit function, our explicit Hermite interpolation scheme is both simple and efficient. The experimental results illustrate the effectiveness and the robustness of our presented mesh blending approach in many applications, such as the mesh stitching and mesh repair operation for artifact scanned models, the dental crown restoration in the practical dentistry CAD application, and the extended mesh fusion application for combining several parts of different scanned models into a single object. Here, as an extension of mesh stitching and mesh repair, the mesh fusion operation can also be efficiently conducted by Hermite interpolation between every two boundaries of several shapes, which can provide the users in the digital entertainment area or the engineers in the industrial design area a convenient modeling tool to easily create various desired interesting complex 3D shapes.