Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation. In contrast to other image and geometry processing techniques, the screening term is defined over a sparse set of points rather than over the full domain. We show that these sparse constraints can nonetheless be integrated efficiently. Because the modified linear system retains the same finite-element discretization, the sparsity structure is unchanged, and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster, higher-quality surface reconstructions.

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In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh M J that has subdivision connectivity and is guaranteed to be within a specified tolerance.The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches.

Level-of-detail (LOD) representations are an important tool for realtime rendering of complex geometric environments. The previously introduced progressive mesh representation defines for an arbitrary triangle mesh a sequence of approximating meshes optimized for view-independent LOD. In this paper, we introduce a framework for selectively refining an arbitrary progressive mesh according to changing view parameters. We define efficient refinement criteria based on the view frustum, surface orientation, and screen-space geometric error, and develop a real-time algorithm for incrementally refining and coarsening the mesh according to these criteria. The algorithm exploits view coherence, supports frame rate regulation, and is found to require less than 15% of total frame time on a graphics workstation. Moreover, for continuous motions this work can be amortized over consecutive frames. In addition, smooth visual transitions (geomorphs) can be constructed between any two selectively refined meshes.A number of previous schemes create view-dependent LOD meshes for height fields (e.g. terrains) and parametric surfaces (e.g. NURBS). Our framework also performs well for these special cases. Notably, the absence of a rigid subdivision structure allows more accurate approximations than with existing schemes. We include results for these cases as well as for general meshes.

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