Implicit Curves: From Discrete Extraction to Applied Formalism

This paper addresses the issue of visualizing the right information among large data sets by proposing to represent raw data as a set of mathematically-based implicit curves. Implicit curves are proving to be a powerful yet underused tool. The methodology we propose not only allows a more relevant visualization of information, but also a faster and efficient access to it: (1) since curves are extracted and compressed during precomputation, real-time rendering is possible on the end-user’s computer, even for very large datasets; (2) this property can be extended by enabling real-time data access and transfer at the server level – i.e. simultaneously saving local storage costs and increasing raw data security. Our proposal also achieved a high compression ratio (3%) while maintaining the visual significance of the data and reducing discrete artifacts such as curve gaps and pixel aliasing. We based our tests using two-dimensional height maps, but extending it to more dimensions is not a problem since we can consider any two-dimensional slice in these data.