复用拉普拉斯算子的高效网格融合方法

针对传统基于测地线的泊松融合方法中插值旋转场与尺度场计算量大而影响交互建模的应用，提出了基于复用拉普拉斯算子的高效融合方法.该方法将几何融合、旋转场与尺度场的插值问题均转化为拉普拉斯（泊松）方程进行求解，仅需一次Cholesky分解和多次回代计算，得到融合所需的8个标量场，比起传统基于测地线的插值方法快两个数量级；随后，运用基于约束Delaunay三角化与离散极小曲面的鲁棒方法对融合边界处的网格进行优化，实现网格的高效融合.同时，再次复用拉普拉斯算子，在进行几何融合的同时，实现了纹理坐标的快速融合.该算法不仅能够处理具有复杂拓扑与多个边界模型，并获得与传统泊松融合方法相媲美的实验结果，而且显著地提高了效率，能够满足交互响应的需求.

Efficient Mesh Merging Method with Reusable Laplacian Operator

Traditional geodesic-based Poison merging method requires time-consuming computation of rotational and scale fields, which restricts its interactive applications. This study proposed an efficient mesh merging method with reusable Laplacian operator. The method reduces problems of geometry merging, interpolation of rotational and scale fields into solving linear equations with the same Laplace matrix. It obtains eight scalar fields used in merging step by conducting Cholesky decomposition once and back substitutions several times, which is two orders of magnitude faster than the traditional geodesic-based method. To optimize the mesh nearby the merging boundary, it uses a robust method based on constrained Delaunay triangulation and discrete minimal surface. Meanwhile, it adopts reusable Laplacian operator again to merge the texture coordinates along with the geometry merging. The proposed method can handle models with complex topology and multiple boundaries, and the results are comparable to the traditional Poisson method but with much less time cost. The advantages make it capable of meeting the requirements of interactive response.