New Visualization of Surfaces in Parallel Coordinates

Title: New Visualization of Surfaces in Parallel Coordinates

Research Question: How can we create a more accurate and unambiguous representation of surfaces in parallel coordinates?

Methodology: The researchers proposed a new method to represent surfaces in parallel coordinates. Instead of considering the surface as the envelope of the polygonal lines representing its points, they suggested considering it as the envelope of its tangent planes. Each tangent plane was represented by n-1 points, and the surface was represented as the collection of these planar points.

Results: The researchers found that this new representation eliminated ambiguity and allowed for the proper classification and recognition of surface properties. They also showed that the image of a surface in Rn could be a region whose boundary is also an algebraic curve of degree 2. An efficient construction algorithm for the representation of quadratic surfaces was provided.

Implications: This new method provides a more accurate and unambiguous representation of surfaces in parallel coordinates, which is beneficial for applications such as scientific visualization and the approximation of complex surfaces based on their planar images. Additionally, it allows for the representation of non-convex surfaces that were previously problematic.

Link to Article: https://arxiv.org/abs/0403004v1 Authors: arXiv ID: 0403004v1