Silvia Mabel Castro

Integrating Semantics into the Visualization Process

Most of todays visualization systems give the user considerable control over the visualization process. Many parameters might be changed until the obtention of a satisfactory visualization. The visualization process is a very complex exploration activity and, even for skilled users, it can be difficult to arrive at an effective visualization. We propose the construction of a visualization prototype to assist users and designers throughout the stages of the visualization process, and the integration of such process with a reasoning procedure that allows the configuration of the visualization, based on the entailed conclusions. We are working on a formal representation of the Visualization field. We aim to establish a common visualization vocabulary, include the underlying semantics, and enable the definition of visualization specifications that can be executed by a visualization engine with ontological support. An ontological description of a visualization should be enough to specify the visualization and, thus, to generate a runtime environment that is able to bring that visualization to life. The visualization ontology defines the vocabulary. With the addition of inference rules to the system, we can derive conclusions about visualization properties that allow to enhance the visualization, and guide the user throughout the entire process toward an effective result.

Multiresolution volume representation: the wavelet approach

A novel method for multiresolution volume representation is presented. The method is based on wavelets and it can be used for representing volumetric data defined on non structured grids. The basic contribution is the extension of wavelets to volumetric domains of arbitrary topological type. This extension is made by constructing a wavelet basis defined on any tetrahedrized volume. This basis construction is achieved using a multiresolution analysis and lifting scheme.

T-Splines: a new schema for C/sup 2/ spline interpolation

Interactive CAGD systems produce faster and more accurate curve and surface analysis and design by means of geometric or algebraic interpolation algorithms, where users can directly modify and edit the position and shape of curves or surfaces. For this reason, many claim that interpolation schemata are more flexible and intuitive than approximation schemata. Also, in engineering and architectural design problems there are position and slope constraints to fulfill that, with standard approximation schemata, are harder to produce. However, interpolation methods are limited with respect to the analytic properties of the resulting curves and surfaces. Piecewise polynomial interpolation methods only guarantees a C/sup 1/ continuity order, which is usually unacceptable. In this work we propose an interpolation method, named T-Splines or tangent splines. Starting with interpolating points and derivatives, a T-Spline is the (approximating) cubic Spline over an ancillary control graph, whose approximation is also a solution of the required interpolation. We present the necessary conditions for finding the ancillary control graph from the interpolation points and derivatives. In addition we give a nonuniform parametrization schema such that a nonuniform B-Spline approximation of the ancillary control points is a C/sup 2/ piecewise polynomial interpolation of the original control points. Some applications are also discussed.