We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.

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We present a method for simulating water and smoke on an unrestricted octree data structure exploiting mesh refinement techniques to capture the small scale visual detail. We propose a new technique for discretizing the Poisson equation on this octree grid. The resulting linear system is symmetric positive definite enabling the use of fast solution methods such as preconditioned conjugate gradients, whereas the standard approximation to the Poisson equation on an octree grid results in a non-symmetric linear system which is more computationally challenging to invert. The semi-Lagrangian characteristic tracing technique is used to advect the velocity, smoke density, and even the level set making implementation on an octree straightforward. In the case of smoke, we have multiple refinement criteria including object boundaries, optical depth, and vorticity concentration. In the case of water, we refine near the interface as determined by the zero isocontour of the level set function.

In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.

Figure 1: Completing a hole in a point-based model. In the darker colored region we removed sample points to demonstrate the surface completion technique. In the middle right the region is filled with a smooth patch conforming with the densely sampled areas, and the result of our context-based surface completion is on the right. Sampling complex, real-world geometry with range scanning devices almost always yields imperfect surface samplings. These “holes ” in the surface are commonly filled with a smooth patch that conforms with the boundary. We introduce a context-based method: the characteristics of the given surface are analyzed, and the hole is iteratively filled by copying patches from valid regions of the given surface. In particular, the method needs to determine best matching patches, and then, fit imported patches by aligning them with the surrounding surface. The completion process works top down, where details refine intermediate coarser approximations. To align an imported patch with the existing surface, we apply a rigid transformation followed by an iterative closest point procedure with nonrigid transformations. The surface is essentially treated as a point set, and local implicit approximations aid in measuring the similarity between two point set patches. We demonstrate the method at several point-sampled surfaces, where the holes either result from imperfect sampling during range scanning or manual removal.

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This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with regular hexahedral cells in a single mesh. This hybrid mesh offers both accuracy near obstacles and efficiency in open regions.

This paper presents a new algorithm for multi-view reconstruction that demonstrates both accuracy and efficiency. Our method is based on robust binocular stereo matching, followed by adaptive point-based filtering of the merged point clouds, and efficient, high-quality mesh generation. All aspects of our method are designed to be highly scalable with the number of views. Our technique produces the most accurate results among current algorithms for a sparse number of viewpoints according to the Middlebury datasets. Additionally, we prove to be the most efficient method among non-GPU algorithms for the same datasets. Finally, our scaled-window matching technique also excels at reconstructing deformable objects with high-curvature surfaces, which we demonstrate with a number of examples.

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two new developments. First, a weighted locally optimal projection operator produces a set of denoised, outlier-free and evenly distributed particles over the original dense point cloud, so as to improve the reliability of local PCA for initial estimate of normals. Next, an iterative framework for robust normal estimation is introduced, where a priority-driven normal propagation scheme based on a new priority measure and an orientation-aware PCA work complementarily and iteratively to consolidate particle normals. The priority setting is reinforced with front stopping at thin surface features and normal flipping to enable robust handling of the close-by surface sheet problem. We demonstrate how a point cloud that is wellconsolidated by our method steers conventional surface generation schemes towards a proper interpretation of the input data. 1