Extending Scatterplots to Scalar Fields

Embedding high-dimensional data into a 2D canvas is a popular strategy for their visualization. It allows users to appreciate similarity relationships among the data points by their spatial organization on the 2D display. In this work we consider the case where the collection of data points also serves as a scalar field for one of the dataset’s attributes, essentially forming samples of the attribute’s continuous function in this embedded space. We study methods by which this continuous function can be estimated from the discrete samples, making certain assumptions on the function’s smoothness in high-dimensional space. Our method allows users to create distance fields, iso-contours, topographic maps, and even extrapolations to embed the possibly odd-shaped point assembly into a filled rectangular region.