In this paper, we propose a correlation-aware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific simulations. The core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information, spatial location, and correlation distribution using Bayes’ rule. This effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them, thus significantly reducing the computational cost. Furthermore, this enables reconstruction of the original data more accurately than existing methods. We demonstrate the effectiveness of our technique using six datasets, with the largest having one billion grid points. The experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost.

We present a novel method to construct compatible surface meshes with bounded approximation errors. Given two oriented and topologically equivalent surfaces and a sparse set of corresponding landmarks, our method contains two steps: (1) generate compatible meshes with bounded approximation errors and (2) reduce mesh complexity while ensuring that approximation errors are always bounded. Central to the first step is a parameterization-based remeshing technique, which is capable of isotropically remeshing the input surfaces to be compatible and error-bounded. By iteratively performing a novel edge-based compatible remeshing and increasing the compatible target edge lengths, the second step effectively reduces mesh complexity while explicitly maintaining compatibility, regularity, and bounding approximation errors. Tests on various pairs of complex models demonstrate the efficacy and practicability of our method for constructing high-quality compatible meshes with bounded approximation errors.

Abstract We present a novel method to compute bijective PolyCube‐maps with low isometric distortion. Given a surface and its pre‐axis‐aligned shape that is not an exact PolyCube shape, the algorithm contains two steps: (i) construct a PolyCube shape to approximate the pre‐axis‐aligned shape; and (ii) generate a bijective, low isometric distortion mapping between the constructed PolyCube shape and the input surface. The PolyCube construction is formulated as a constrained optimization problem, where the objective is the number of corners in the constructed PolyCube, and the constraint is to bound the approximation error between the constructed PolyCube and the input pre‐axis‐aligned shape while ensuring topological validity. A novel erasing‐and‐filling solver is proposed to solve this challenging problem. Centeral to the algorithm for computing bijective PolyCube‐maps is a quad mesh optimization process that projects the constructed PolyCube onto the input surface with high‐quality quads. We demonstrate the efficacy of our algorithm on a data set containing 300 closed meshes. Compared to state‐of‐the‐art methods, our method achieves higher practical robustness and lower mapping distortion.

Compatible remeshing provides meshes with common connectivity structures. The existing compatible remeshing methods usually suffer from high computational cost or poor quality. In this paper, we present a fast method for computing compatible meshes with high quality. Given two closed, oriented, and topologically equivalent surfaces and a sparse set of corresponding landmarks, we first compute a bijective inter-surface mapping, from which compatible meshes are generated. We then improve the remeshing quality by using a volume-enhanced optimization. In contrast to previous work, our method designs a fast volume-enhanced improvement procedure that directly reduces the isometric distortion of the map between the compatible meshes. Our method also tries to preserve the shapes of the input meshes by projecting the vertices of the compatible meshes onto the input surfaces. Central to this approach is the use of the monotone preconditioned conjugate gradient method, which minimizes the energies effectively and efficiently. Compared with state-of-the-art methods, our method performs about one order of magnitude faster with better remeshing quality. We demonstrate the efficiency and efficacy of our method using various model pairs.