Sparse data volume visualization a finite element based approach
Johnny P. Ziebarth, Yingcai Xiao · 1994
Volume visualization is a new and important research field in computer science. Sparse data volume visualization is a challenging area within volume visualization and is used to model and render variations of sparsely sampled data. Existing grid-based approaches to sparse data volume visualization suffer many problems. They cannot handle data with discontinuities or data with irregular geometries and may generate physically meaningless results. They require sample data to be dense to satisfy the Whittaker-Shannon criterion. They are not flexible or efficient and there is no error estimation associated with most of the approaches. A new approach, the finite element based approach, is presented. It is a new framework for sparse data volume visualization and consists of three parts: tessellation, computation and rendering. A sample implementation is given to demonstrate the capabilities of the new approach. Compared to the existing approaches, this new method has several advantages. It can handle discontinuities using the double layer technique and can tessellate irregular geometries using finite element networks. It employs the finite element method to integrate crucial information into the solution system and to generate physically meaningful results. It does not require sparse data to be dense to satisfy the Whittaker-Shannon criterion because the problem has been converted from an interpolation problem to a boundary value problem. It is flexible and efficient and it provides error estimation and error control. This approach has led to new research opportunities in visualization. For example, one can improve the accuracy of the visualization system by using higher-order elements or using the p-version technique. One can extend the approach to model and render time dependent sparse data. One may even solve the reverse problem of detecting unknown data discontinuities using the approach. These and other new research topics are discussed in the dissertation.