To solve the Laplace-Beltrami eigenproblem on 3D models, we develop an efficient and fast computation method based on surface fitting and linear subspace. First, our method generates a finite subdivision surface to approximate the original high-resolution model. Then, we restrict the eigenproblem by constructing a subdivision linear subspace, whose basis is generated during the surface fitting process. Finally, we obtain the required eigenpairs by solving the restricted eigenproblem, whose scale is much smaller than that of the original model. Experimental results demonstrate that our eigenvalues and eigenvectors effectively approximate the ground truth. Especially, in the low-frequency band, the spectrum of our method performs much better than those of comparisons. Moreover, the eigenvectors mapped to the original mesh keep the orthogonality, making themselves a set of filtering basis on the original mesh. Meanwhile, our method also shows good performance on time and memory consumption.

为了解决3D模型中的Laplace-Beltrami特征问题，我们开发了一种基于曲面拟合和线性子空间的高效，快速的计算方法。首先，我们的方法生成有限的细分曲面以逼近原始的高分辨率模型。然后，我们通过构造细分线性子空间来限制特征问题，其基础是在曲面拟合过程中生成的。最后，我们通过求解限制本征问题来获得所需的本征对，该问题的规模远小于原始模型。实验结果表明，我们的特征值和特征向量有效地逼近了地面真相。尤其是在低频频段，我们的方法的频谱性能比比较方法要好得多。此外，映射到原始网格的特征向量保持正交性，使其成为基于原始网格的一组过滤基础。同时，我们的方法在时间和内存消耗上也表现出良好的性能。