In this study, the authors describe an objective smoothness assessment method for volume data. The metric can predict the extent of the difference in smoothness between a reference model, which may not be of perfect quality, and a distorted version. The proposed metric is based on the wavelet characterisation of Besov function spaces. The comparison of Besov norms between two models can resolve the global and local differences in smoothness between them. Experimental results from volume datasets with smoothing and sharpening operations demonstrate its effectiveness. By comparing direct volume rendered images, the experimental results show that the proposed smoothness index correlates well with human perceived vision. Finally, the metric can help the analyse compression distortions when they compare volume data with different smoothness.

An adaptive filtering method for volume data is presented in this paper. In this filtering method, the input data set is re-sampled to create a hierarchy of multiple-level data sets. A data classification task is performed at each level of the data pyramid to decide the local structure types. Data voxels are classified aslinear,planar, orblobstructures, based on the gradients and the eigenvalues ofHessianmatrices. The classification results are used to adjust the shapes and orientations of filters such that noises are suppressed while key features are preserved.

Doppler radars are useful facilities for weather forecasting. The data sampled by using Doppler radars are used to measure the distributions and densities of rain drops, snow crystals, hail stones, or even insects in the atmosphere. In this paper, we propose to build up a graphics-based software system for visualizing Doppler radar data. In the system, the reflectivity data gathered by using Doppler radars are post-processed to generate virtual cloud images which reveal the densities of precipitation in the air. An optical flow based method is adopted to compute the velocities of clouds, advected by winds. Therefore, the movement of clouds is depicted. The cloud velocities are also used to interpolate reflectivities for arbitrary time steps. Therefore, the reflectivities at any time can be produced. Our system composes of three stages. At the first stage, the raw radar data are re-sampled and filtered to create a multiple resolution data structure, based on a pyramid structure. At the second stage, a numeric method is employed to compute cloud velocities in the air and to interpolate radar reflectivity data at given time steps. The radar reflectivity data and cloud velocities are displayed at the last stage. The reflectivities are rendered by using splatting methods to produce semi-transparent cloud images. Two kinds of media are created for analyzing the reflectivity data. The first kind media consists of a group of still images of clouds which displays the distribution and density of water in the air. The second type media is a short animation of cloud images to show the formation and movement of the clouds. To show the advection of clouds, the cloud velocities are displayed by using two dimensional images. In these images, the velocities are represented by arrows and superimposed on cloud images. To enhance image quality, gradients and diffusion of the radar data are computed and used in the rendering process. Therefore the cloud structures are better portrayed. In order to achieve interactive visualization, our system is also comprised with a view-dependent visualization module. The radar data at far distance are rendered in lower resolutions, while the data closer to the eye position is rendered in details.

A new multiple resolution volume rendering method for finite element analysis (FEA) data is presented. Our method is composed of three stages: in the first stage, the Gauss points of the FEA cells are calculated. The function values, gradients, diffusions, and influence scopes of the Gauss points are computed. By representing the Gauss points as graph vertices and connecting adjacent Gauss points with edges, an adjacency graph is created. The adjacency graph is used to represent the FEA data in the subsequent computation. In the second stage, a hierarchical structure is established upon the adjacency graph. Any two neighboring vertices with similar function values are merged into a new vertex. The similarity is measured by using a user-defined threshold. Consequently, a new adjacency graph is constructed. Then the threshold is increased, and the graph reduction is triggered again to generate another adjacency graph. By repeating the processing, multiple adjacency graphs are computed, and a level of detail (LoD) representation of the FEA data is established. In the third stage, the LoD structure is rendered by using a splatting method. At first, a level of adjacency graph is selected by users. The graph vertices arc sorted based on their visibility orders and projected onto the image plane in back-to-front order. Billboards are used to render the vertices in the projection. The function values, gradients, and influence scopes of the vertices are utilized to decide the colors, opacities, orientations, and shapes of the billboards. The billboards are then modulated with texture maps to generate the footprints of the vertices. Finally, these footprints are composited to produce the volume rendering image.

This paper presents an out-of-core approach for interactive streamline construction on large unstructured tetrahedral meshes containing millions of elements. The out-of-core algorithm uses an octree to partition and restructure the raw data into subsets stored into disk files for fast data retrieval. A memory management policy tailored to the streamline calculations is used such that, during the streamline construction, only a very small amount of data are brought into the main memory on demand. By carefully scheduling computation and data fetching, the overhead of reading data from the disk is significantly reduced and good memory performance results. This out-of-core algorithm makes possible interactive streamline visualization of large unstructured-grid data sets on a single mid-range workstation with relatively low main-memory capacity: 5-15 megabytes. We also demonstrate that this approach is much more efficient than relying on virtual memory and operating system's paging algorithms.

Streamline construction is one of the most fundamental techniques for visualizing steady flow fields. Streamribbons and streamtubes are extensions for visualizing the rotation and the expansion of the flow. The paper presents efficient algorithms for constructing streamlines, streamribbons, and streamtubes on unstructured grids. A specialized Runge-Kutta method is developed to speed up the tracing of streamlines. Explicit solutions are derived for calculating the angular rotation rates of streamribbons and the radii of streamtubes. In order to simplify mathematical formulations and reduce computational costs, all calculations are carried out in the canonical coordinate system instead of the physical coordinate system. The resulting speed up in overall performance helps explore large flow fields.

The plotting of streamlines is an effective way of visualizing fluid motion in steady flows. Additional information about the flowfield, such as local rotation and expansion, can be shown by drawing in the form of a ribbon or tube. In this paper, we present efficient algorithms for the construction of streamlines, streamribbons and streamtubes on unstructured grids. A specialized version of the Runge-Kutta method has been developed to speed up the integration of particle paths. We have also derived closed-form solutions for calculating angular rotation rate and radius to construct streamribbons and streamtubes, respectively. According to our analysis and test results, these formulations are two to four times better in performance than previous numerical methods. As a large number of traces are calculated, the improved performance could be significant.