Differential coordinates for interactive mesh editing
Differential coordinates for interactive mesh editing
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DOI：
10.1109/smi.2004.1314505
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发表时间：
2004-06
期刊：
影响因子：
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通讯作者：
Y. Lipman;O. Sorkine-Hornung;D. Cohen-Or;D. Levin;Christian Rössl;H. Seidel
中科院分区：
文献类型：
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作者：
Y. Lipman;O. Sorkine-Hornung;D. Cohen-Or;D. Levin;Christian Rössl;H. Seidel
编辑网格的主要挑战之一是在应用各种修改后保留曲面的视觉外观。在本文中，我们主张使用线性微分坐标作为手段，以保持高频细节的表面。微分坐标表示细节，并由网格顶点的线性变换定义。这允许通过求解满足最小二乘意义上的局部细节重建的线性系统来重建编辑过的表面。由于微分坐标是在全局坐标系中定义的，因此它们不是旋转不变的。为了补偿这一点，我们旋转它们以与近似局部框架的旋转一致。我们表明，线性最小二乘系统可以解决得足够快，以保证互动的响应时间，由于预先计算的系数矩阵的因式分解。我们证明了我们的方法可以编辑复杂的详细网格，同时保持其自然方向的细节形状。
One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. In this paper we advocate the use of linear differential coordinates as means to preserve the high-frequency detail of the surface. The differential coordinates represent the details and are defined by a linear transformation of the mesh vertices. This allows the reconstruction of the edited surface by solving a linear system that satisfies the reconstruction of the local details in least squares sense. Since the differential coordinates are defined in a global coordinate system they are not rotation-invariant. To compensate for that, we rotate them to agree with the rotation of an approximated local frame. We show that the linear least squares system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix. We demonstrate that our approach enables to edit complex detailed meshes while keeping the shape of the details in their natural orientation.