Frequency-based Progressive Rendering of Continuous Scatterplots

Abstract

Continuous scatterplots are a consistent tool for the visual representation and exploration of continuous multivariate data defined on a continuous domain. Due to the complexity of the construction algorithm, application of continuous scatterplots is limited in terms of data size and screen resolution when interactive frame rates are desired. Progressive rendering is a paradigm of displaying an approximative visual outcome early on, which iteratively and incrementally gets improved until convergence to the final result is reached. This approach maintains the interactivity of the system and allows the user to make decisions immediately, i.e., much earlier than the end of the computation process. We propose a method for progressive rendering of continuous scatterplots based on a Fourier representation. By iteratively advancing from low to high frequencies and inverting the spectrum representation after each iteration, a series of scatterplots converging to the final result is generated and rendered. We demonstrate that this convergence is monotonic and that the proposed approach is more efficient than state-of-the-art methods, i.e., we can faster produce high-quality approximations. We propose to embed this idea into a hybrid approach which allows balancing the trade-off between quality of the image appearing first and its computation time. The proposed algorithms were implemented on the GPU.