We present the application of a low dimensional manifold model (LDMM) on hyperspectral image (HSI) reconstruction. An important property of hyperspectral images is that the patch manifold, which is sampled by the three-dimensional blocks in the data cube, is generally of a low dimensional nature. This is a generalization of low-rank models in that hyperspectral images with nonlinear mixing terms can also fit in this framework. The point integral method (PIM) is used to solve a Laplace-Beltrami equation over a point cloud sampling the patch manifold in LDMM. Both numerical simulations and theoretical analysis show that the sample points constraint is correctly enforced by PIM. The framework is demonstrated by experiments on the reconstruction of both linear and nonlinear mixed hyperspectral images with a significant number of missing voxels and several entirely missing spectral bands.

In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to allow modeling of various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple kinds of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach.

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Surface flow phenomena, such as rain water flowing down a tree trunk and progressive water front in a shower room, are common in real life. However, compared with the 3D spatial fluid flow, these surface flow problems have been much less studied in the graphics community. To tackle this research gap, we present an efficient, robust and high-fidelity simulation approach based on the shallow-water equations. Specifically, the standard shallow-water flow model is extended to general triangle meshes with a feature-based bottom friction model, and a series of coherent mathematical formulations are derived to represent the full range of physical effects that are important for real-world surface flow phenomena. In addition, by achieving compatibility with existing 3D fluid simulators and by supporting physically realistic interactions with multiple fluids and solid surfaces, the new model is flexible and readily extensible for coupled phenomena. A wide range of simulation examples are presented to demonstrate the performance of the new approach.