Laplacian Guided Editing, Synthesis, and Simulation
Laplacian Guided Editing, Synthesis, and Simulation
复制标题
DOI：
10.1109/pg.2007.69
复制
发表时间：
2007-10
期刊：
影响因子：
--
通讯作者：
Yizhou Yu
中科院分区：
文献类型：
--
作者：
Yizhou Yu
仅提供摘要形式。拉普拉斯算子在许多科学和工程问题中起着核心作用。它在计算机图形学中也很受欢迎。这个演讲介绍了我们的一系列工作，利用拉普拉斯在网格编辑，纹理合成和流动模拟。首先，回顾了网格编辑使用微分坐标和泊松方程，其中涉及到拉普拉斯算子。这种方法的显着特点是，它修改了原始的几何形状隐式通过梯度场操纵。这种方法可以为全局和局部编辑操作（例如变形、对象合并和去噪）产生所需的结果。这种技术涉及计算，因为它需要解决一个大型稀疏线性系统。为了克服这个困难，一个高效的多重网格算法专门为几何处理已经开发出来。这种多重网格算法能够交互式地处理具有数十万个顶点的网格。在我们的最新工作中，基于拉普拉斯的编辑已被推广到变形网格序列，并设计了有效的用户交互技术。其次，本演讲提出了一种基于拉普拉斯的表面纹理合成和混合方法。在纹理合成过程中，消除纹理拼接缝是一个重要的问题。在我们的技术中，它是通过执行拉普拉斯纹理重建，保留高频细节，但计算新的一致的低频分量来解决的。第三，提出了一种流形表面无粘流动的数值模拟方法。该方法通过求解离散的泊松方程来实现封闭曲面的不可压缩性。与以前的工作不同，它直接在三角形网格上进行模拟，从而消除了参数化失真。
Summary form only given. The Laplacian has been playing a central role in numerous scientific and engineering problems. It has also become popular in computer graphics. This talk presents a series of our work that exploits the Laplacian in mesh editing, texture synthesis and flow simulation. First, a review is given on mesh editing using differential coordinates and the Poisson equation, which involves the Laplacian. The distinctive feature of this approach is that it modifies the original geometry implicitly through gradient field manipulation. This approach can produce desired results for both global and local editing operations, such as deformation, object merging, and denoising. This technique is computationally involved since it requires solving a large sparse linear system. To overcome this difficulty, an efficient multigrid algorithm specifically tailored for geometry processing has been developed. This multigrid algorithm is capable of interactively processing meshes with hundreds of thousands of vertices. In our latest work, Laplacian-based editing has been generalized to deforming mesh sequences, and efficient user interaction techniques have also been designed. Second, this talk presents a Laplacian-based method for surface texture synthesis and mixing from multiple sources. Eliminating seams among texture patches is important during texture synthesis. In our technique, it is solved by performing Laplacian texture reconstruction, which retains the high frequency details but computes new consistent low frequency components. Third, a method for inviscid flow simulation over manifold surfaces is presented. This method enforces incompressibility on closed surfaces by solving a discrete Poisson equation. Different from previous work, it performs simulations directly on triangle meshes and thus eliminates parametrization distortions.