Visual analysis of large time-series data often requires transformations over multivariate time series. Existing methods struggle to meet interactive response time requirements, relying on full transformations that incur high computation costs. We propose a visualization-oriented transformation system PIVOT that incrementally generates accurate visualizations by selectively transforming only essential data samples. At its core is a transformation-aware query mechanism that efficiently computes point-wise transformations by leveraging cached hierarchical data on the server. To support responsive interaction, we introduce a pixel-based error-bound guarantee that estimates the accuracy of intermediate visualizations without requiring a reference, enabling a balance between latency and visual fidelity. Experiments show that PIVOT achieves highly accurate visualizations with interactive response times, outperforming existing error-free methods by up to an order of magnitude on billion-scale datasets.

We present a novel visualization-driven illumination model for density plots, a new technique to enhance density plots by effectively revealing the detailed structures in high- and medium-density regions and outliers in low-density regions, while avoiding artifacts in the density field's colors. When visualizing large and dense discrete point samples, scatterplots and dot density maps often suffer from overplotting, and density plots are commonly employed to provide aggregated views while revealing underlying structures. Yet, in such density plots, existing illumination models may produce color distortion and hide details in low-density regions, making it challenging to look up density values, compare them, and find outliers. The key novelty in this work includes (i) a visualization-driven illumination model that inherently supports density-plot-specific analysis tasks and (ii) a new image composition technique to reduce the interference between the image shading and the color-encoded density values. To demonstrate the effectiveness of our technique, we conducted a quantitative study, an empirical evaluation of our technique in a controlled study, and two case studies, exploring twelve datasets with up to two million data point samples.