Browsing by Author "Tejada-Gamero, Eduardo Jose"

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Open Access
Towards meshless volume visualization
(2008) Tejada-Gamero, Eduardo Jose; Ertl, Thomas (Prof. Dr.)
In this thesis, novel meshless methods for surface and volume data reconstruction and rendering are proposed. Surface reconstruction from unorganized point sets is first addressed with projection operators. Specifically, a curvature-driven projection operator is presented which defines an approximate surface for a given point cloud based on a diffusion equation and on curvature estimation for point sets. Implicit formulations for surface approximation are also addressed. An implicit surface definition based on approximate moving least-squares approximation is introduced, which is able to provide high-order local approximations to the surface without requiring to solve systems of equations. Bilateral filters are introduced into this surface definition in order to better represent sharp features by robustly estimating normal vectors. An adaptive implicit formulation based on partition of unity and orthogonal polynomials is also proposed. This formulation addresses approximation and robustness issues presented by previous work on partition of unity implicits. To accelerate the rendering of these surface definitions, hardware-accelerated ray-casting of implicit surfaces and surfaces defined by projection operators is also discussed. The results obtained for surface approximation are then applied to volume data in order to extract surfaces that represent some feature in the volume. Regarding scalar data, a moving least-squares surface definition is proposed which is able to approximate iso-surfaces and surfaces located are regions with high gradient magnitude. The rendering of such surfaces is performed on graphics hardware to accelerate the computations. Visualization of vector fields is also addressed, specifically the interactive computation and rendering of streamsurfaces and of the novel path-surfaces. To that end, a hardware-accelerated streamlines and path-lines generation process is presented, which is able to produce a quasi regular sampling of the surface. This allows the use of known point-based surface rendering algorithms to interactively visualize the streamsurface or path-surface. Volume visualization is then addressed using meshless methods. These visualization methods are based on a meshless volume model extracted from the data. This model is obtained using the moving least-squares approximation method. In order to preserve details in the reconstruction of the volumetric data, bilateral filtering is used which, together with the use of orthogonal polynomials, provides a matrix-free detail-preserving reconstruction of the volume data. To further accelerate the computation of the function reconstruction, the use of approximate approximation is also explored in this context. To that end, an anisotropic iterated approximate moving least-squares approximation of the volume data is defined, which converges to an ellipsoidal-basis-functions interpolation of the data. Finally, volume deformation by means of moving least-squares is addressed and a closed formulation for nonlinear polynomial deformations is proposed. An implementation of the set of moving least-squares deformations on hardware graphics is also presented and used to interactively compute volume deformations by means of displacement maps.