Volume Data Visualization Algorithm Based On Data Modeling

This dissertation researches the problem of modeling-based visualization of volumetric dat& The modeling methods include four-dimensional(4D) super-surface modeling and three-dimensional(3D) surface reconstruction. This presentation consists of two main parts. In the first part, we preprocess the data by 4D super-surface modeling and reveal the character inside the scientific data based on continuous functions. Given enough knowledge of the given data field, some fitting model methods are good candidates. Reconstructing B-spline super-surface can tackle universal data field. Then we further study super-surface visualizing methods, including 4D global illuminating model, super-surface rendering and volume image projecting techniques. To implement the 4D data visualization based on 4D super-surface rendering techniques, we adopt different illuminating models from traditional methods. We generalize the 3D Whitted illuminating model to 4D space and obtain 4D global illuminating model, wlich can reveal the information near the sampled data, while the results using traditional models are synthetic effect of the sampled data along the rays. The second part explores surface reconstruction from volumetric data using the technique of REF (Radial Basis Function) based implicit interpolation. REF-based interpolation costs expensive computation, so we propose a quick iterative method to reduce the scale and complexity of the problem. We also study quick calculation of RBF function value. First we add off-surface points to restrict the inner and outer side of the reconstructed surface and resolve the ambiguous solution to the original interpolation problem. Because within certain error bound we can represent REF function using only a subset of original center points, we use greedy algorithm to reduce the center point dataset. Then we propose one choice of the neighboring dataset of approximate cardinal REF base function in iterative method to accelerate the converging speed. The fast calculation of REF function value is based on fast multipole methods, which follow space subdivision principle and introduce the combination of far field expansion method to obtain approximate function value in given error bound and direct calculation technique. We render the reconstructed implicit surface by polygonizing the surface and using ray-tracing method.