TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware

Multivariate Topology Simplification

Topological simplification of scalar and vector fields is well-established as an effective method for analysing and visualising complex data sets. For multivariate (alternatively, multi-field) data, topological analysis requires simultaneous advances both mathematically and computationally. We propose a robust multivariate topology simplification method based on “lip”-pruning from the Reeb space. Mathematically, we show that the projection of the Jacobi set of multivariate data into the Reeb space produces a Jacobi structure that separates the Reeb space into simple components. We also show that the dual graph of these components gives rise to a Reeb skeleton that has properties similar to the scalar contour tree and Reeb graph, for topologically simple domains. We then introduce a range measure to give a scaling-invariant total ordering of the components or features that can be used for simplification. Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation similar to the contour tree or Reeb graph

On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation

We present a method for hierarchical data approximation using curved quadratic simplicial elements for domain decomposition. Scientific data defined over two- or three-dimensional domains typically contain boundaries and discontinuities that are to be preserved and approximated well for data analysis and visualization. Curved simplicial elements make possible a better representation of curved geometry, domain boundaries, and discontinuities than simplicial elements with non-curved edges and faces. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are $C^0$-continuous everywhere except where field discontinuities occur whose locations we assume to be given. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. Our method can be used for hierarchical data processing and visualization

Feature preserving simplification techniques for tetrahedral meshes

Due to the wide use of increasingly larger tetrahedral meshes in volumetric visualization, simplification of tetrahedral meshes has become more and more popular in last two decades. In this thesis, we first introduce a basic tetrahedral mesh simplification algorithm based on cell collapse. Then, we present a new feature preserving simplification algorithm for tetrahedral meshes. The algorithm decimates the original dataset by iteratively removing tetrahedra without significantly altering boundary or interior field features. In a pre-processing step, we apply a level set method to find a segmentation of the volume dataset, and then label vertices on the region boundaries that potentially contribute to visually perceptible features in the rendered volume. The simplification algorithm preserves these labeled vertices as much as possible. Both incremental and greedy strategies are used to decimate tetrahedra that contain at most one labeled vertex. Field gradients, tetrahedral aspect ratio changes and variances of interior region values are further used so as to maintain features of the original dataset in regional interiors. A possible extension of combining edge collapse also presented to achieve higher decimation rates. We have implemented these algorithms and tested them using a number of standard volumetric datasets. The results have shown that the feature preserving simplification algorithm is able to preserve more features at the same decimation rates in comparison to other simplification algorithms

Simplificación poligonal guiada por máscaras visuales

La visualización interactiva en ambientes exteriores requiere de la simplificación poligonal de los modelos involucrados; proceso que introduce artefactos geométricos que degradan la calidad visual resultante. Maximizar la tasa de simplificación mientras se minimiza la degradación visual no resulta una tarea trivial. La idea es encontrar un balance entre la calidad visual y la conservación de la topología, notando una característica principal: una región escasamente iluminada reduce en apariencia la distorsión geométrica que una muy iluminada. En este contexto, el algoritmo propuesto para la simplificación de los objetos en el escenario exterior ha sido guiado primariamente por una métrica geométrica (curvatura local), y luego combinado con un criterio basado en la percepción visual que evalúa la influencia de la iluminación en cada elemento. La calidad y la robustez del indicador propuesto resultan de la medición del volumen encerrado entre las aproximaciones generadas y los modelos reales. La solución propuesta está concebida inicialmente para entornos donde el cambio de iluminación, y consecuente recálculo de la malla, es poco frecuente; permitiendo obtener mallas con una cantidad manejable de elementos y con un proceso de renderizado eficiente.VII Workshop Computación Gráfica, Imágenes y Visualización (WCGIV

Simplificación poligonal guiada por máscaras visuales

La visualización interactiva en ambientes exteriores requiere de la simplificación poligonal de los modelos involucrados; proceso que introduce artefactos geométricos que degradan la calidad visual resultante. Maximizar la tasa de simplificación mientras se minimiza la degradación visual no resulta una tarea trivial. La idea es encontrar un balance entre la calidad visual y la conservación de la topología, notando una característica principal: una región escasamente iluminada reduce en apariencia la distorsión geométrica que una muy iluminada. En este contexto, el algoritmo propuesto para la simplificación de los objetos en el escenario exterior ha sido guiado primariamente por una métrica geométrica (curvatura local), y luego combinado con un criterio basado en la percepción visual que evalúa la influencia de la iluminación en cada elemento. La calidad y la robustez del indicador propuesto resultan de la medición del volumen encerrado entre las aproximaciones generadas y los modelos reales. La solución propuesta está concebida inicialmente para entornos donde el cambio de iluminación, y consecuente recálculo de la malla, es poco frecuente; permitiendo obtener mallas con una cantidad manejable de elementos y con un proceso de renderizado eficiente.VII Workshop Computación Gráfica, Imágenes y Visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI

Simplificación poligonal guiada por máscaras visuales

La visualización interactiva en ambientes exteriores requiere de la simplificación poligonal de los modelos involucrados; proceso que introduce artefactos geométricos que degradan la calidad visual resultante. Maximizar la tasa de simplificación mientras se minimiza la degradación visual no resulta una tarea trivial. La idea es encontrar un balance entre la calidad visual y la conservación de la topología, notando una característica principal: una región escasamente iluminada reduce en apariencia la distorsión geométrica que una muy iluminada. En este contexto, el algoritmo propuesto para la simplificación de los objetos en el escenario exterior ha sido guiado primariamente por una métrica geométrica (curvatura local), y luego combinado con un criterio basado en la percepción visual que evalúa la influencia de la iluminación en cada elemento. La calidad y la robustez del indicador propuesto resultan de la medición del volumen encerrado entre las aproximaciones generadas y los modelos reales. La solución propuesta está concebida inicialmente para entornos donde el cambio de iluminación, y consecuente recálculo de la malla, es poco frecuente; permitiendo obtener mallas con una cantidad manejable de elementos y con un proceso de renderizado eficiente.VII Workshop Computación Gráfica, Imágenes y Visualización (WCGIV)Red de Universidades con Carreras en Informática (RedUNCI

Dynamic view-dependent visualization of unstructured tetrahedral volumetric meshes

Visualization of large volumetric datasets has always been an important problem. Due to the high computational requirements of volume-rendering techniques, achieving interactive rates is a real challenge. We present a selective refinement scheme that dynamically refines the mesh according to the camera parameters. This scheme automatically determines the impact of different parts of the mesh on the output image and refines the mesh accordingly, without needing any user input. The view-dependent refinement scheme uses a progressive mesh representation that is based on an edge collapse-based tetrahedral mesh simplification algorithm. We tested our view-dependent refinement framework on an existing state-of-theart volume renderer. Thanks to low overhead dynamic view-dependent refinement, we achieve interactive frame rates for rendering common datasets at decent image resolutions. © 2012 The Visualization Society of Japan

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization