Efficient Morphing of Shape-preserving Star Coordinates

Abstract

Data tours follow an exploratory multi-dimensional data visualization concept that provides animations of projections of the multidimensional data to a 2D visual space. To create an animation, a sequence of key projections is provided and morphings between each pair of consecutive key projections are computed, which then can be stitched together to form the data tour. The morphings should be smooth so that a user can easily follow the transformations, and their computations shall be fast to allow for their integration into an interactive visual exploration process. Moreover, if the key projections are chosen to satisfy additional conditions, it is desirable that these conditions are maintained during morphing. Shape preservation is such a desirable condition, as it avoids shape distortions that may otherwise be caused by a projection. We develop a novel efficient morphing algorithms for computing shape-preserving data tours, i.e., data tours constructed for a sequence of shape-preserving linear projections. We propose a stepping strategy for the morphing to avoid discontinuities in the evolution of the projections, where we represent the linear projections using a star-coordinates system. Our algorithms are less computationally involved, produce smoother morphings, and require less user-defined parameter settings than existing state-of-the-art approaches.