Eduardo Tejada

Point-based stream surfaces and path surfaces

We introduce a point-based algorithm for computing and rendering stream surfaces and path surfaces of a 3D flow. The points are generated by particle tracing, and an even distribution of those particles on the surfaces is achieved by selective particle removal and creation. Texture-based surface flow visualization is added to show inner flow structure on those surfaces. We demonstrate that our visualization method is designed for steady and unsteady flow alike: both the path surface component and the texture-based flow representation are capable of processing time-dependent data. Finally, we show that our algorithms lend themselves to an efficient GPU implementation that allows the user to interactively visualize and explore stream surfaces and path surfaces, even when seed curves are modified and even for time-dependent vector fields.

Large steps in GPU-based deformable bodies simulation

Abstract The interactive deformation and visualization of volumetric objects is still a challenging problem for many application areas. We present a novel integrated system which implements physically-based deformation and volume visualization of tetrahedral meshes on modern graphics hardware by exploiting the last features of vertex and fragment shaders. We achieve fast and stable deformation of tetrahedral meshes by means of a GPU-based implicit solver and present a hardware-based single-pass raycaster for deformed tetrahedral meshes. Thus, direct visualization of the inner structures of the deformed mesh is possible, while keeping the data on the graphics hardware throughout the entire simulation.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Hardware-accelerated extraction and rendering of point set surfaces

Point-based models are gaining lately considerable attention as an alternative to traditional surface meshes. In this context, Point Set Surfaces (PSS) were proposed as a modeling and rendering method with important topological and approximation properties. However, ray-tracing PSS is computationally expensive. Therefore, we propose an interactive ray-tracing algorithm for PSS implemented completely on commodity graphics hardware. We also exploit the advantages of PSS to propose a novel technique for extracting surfaces directly from volumetric data. This technique is based on the well known predictor-corrector principle from the numerical methods for solving ordinary differential equations. Our technique provides good approximations to surfaces defined by a certain property in the volume, such as iso-surfaces or surfaces located at regions of high gradient magnitude. Also, local details of the surfaces could be manipulated by changing the local polynomial approximation and the smoothing parameters used. Furthermore, the surfaces generated are smooth and low frequency noise is naturally handled.

Curvature-driven Modeling and Rendering of Point-Based Surfaces

In this work we address the problem of computing point-based surface approximations from point clouds. Our approach is based on recently presented methods that define the approximated surface as the set of stationary points for an operator that projects points in the space onto the surface. We present a novel projection operator that differs from the defined in previous work in that it uses principal curvatures and directions approximation and an anisotropic diffusion equation to ensure an accurate approximation to the surface. We show how to estimate the principal curvatures and directions for point clouds and discuss the usefulness of the curvature information in the context of point-based surface modeling and rendering

Improved visual clustering of large multi-dimensional data sets

Lowering computational cost of data analysis and visualization techniques is an essential step towards including the user in the visualization. In this paper we present an improved algorithm for visual clustering of large multi-dimensional data sets. The original algorithm is an approach that deals efficiently with multi-dimensionality using various projections of the data in order to perform multi-space clustering, pruning outliers through direct user interaction. The algorithm presented here, named HC-Enhanced (for human-computer enhanced), adds a scalability level to the approach without reducing clustering quality. Additionally, an algorithm to improve clusters is added to the approach. A number of test cases is presented with good results.

Robust and Adaptive Surface Reconstruction using Partition of Unity Implicits

Implicit surface reconstruction from unorganized point sets has been recently approached with methods based on multi-level partition of unity. We improve this approach by addressing local approximation robustness and iso-surface extraction issues. Our method relies on the J1 A triangulation to perform both the spatial subdivision and the iso-surface extraction. We also make use of orthogonal polynomials to provide adaptive local approximations in which the degree of the polynomial can be adjusted to accurately reconstruct the surface locally. Finally, we compare our results with previous work to demonstrate the robustness of our method.

Pre-integrated Flow Illustration for Tetrahedral Meshes

Previous work has demonstrated the clarity and usefulness of illustrative techniques for visualizing flow data. However, previous systems were limited to applying these techniques to uniform grids. Since unstructured grids have emerged as a common basis for computing flow simulations, we present a method to apply and extend the flow illustration approach to tetrahedral meshes using pre-integrated GPU-accelerated raycasting. Our illustrative rendering techniques can also be applied for other pre-integrated volume rendering systems. Additionally, we explore new feature illustration techniques for flow visualization.