Occlusion-Free Conformal Lensing for Spatiotemporal Visualization in 3D Urban Analytics

TL;DR

This work tackles occlusion and visual clutter in immersive 3D urban spatiotemporal visualization by introducing an occlusion-free lens that combines a view-dependent cutaway with a conformal, footprint-aware temporal display. The core method partitionizes irregular building footprints into regular primitives and computes conformal maps via Schwarz–Christoffel mapping, stitching them into layered temporal ribbons that conform to facade geometry. A controlled user study demonstrates that the proposed EmbeddedV+Xray lens improves task accuracy, reduces completion time, and lowers navigation effort compared to baseline and x-ray-augmented alternatives, validating the approach. The results yield design recommendations for spatially embedded lenses in 3D urban analytics and highlight promising directions for future research on dynamic, data-driven lens shapes and multi-attribute spatiotemporal encodings.

Abstract

The visualization of temporal data on urban buildings, such as shadows, noise, and solar potential, plays a critical role in the analysis of dynamic urban phenomena. However, in dense and geographically constrained 3D urban environments, visual representations of time-varying building data often suffer from occlusion and visual clutter. To address these two challenges, we introduce an immersive lens visualization that integrates a view-dependent cutaway de-occlusion technique and a temporal display derived from a conformal mapping algorithm. The mapping process first partitions irregular building footprints into smaller, sufficiently regular subregions that serve as structural primitives. These subregions are then seamlessly recombined to form a conformal, layered layout for our temporal lens visualization. The view-responsive cutaway is inspired by traditional architectural illustrations, preserving the overall layout of the building and its surroundings to maintain users' sense of spatial orientation. This lens design enables the occlusion-free embedding of shape-adaptive temporal displays across building facades on demand, supporting rapid time-space association for the discovery, access and interpretation of spatiotemporal urban patterns. Guided by domain and design goals, we outline the rationale behind the lens visual and interaction design choices, such as the encoding of time progression and temporal values in the conforming lens image. A user study compares our approach against conventional juxtaposition and x-ray spatiotemporal designs. Results validate the usage and utility of our lens, showing that it improves task accuracy and completion time, reduces navigation effort, and increases user confidence. From these findings, we distill design recommendations and promising directions for future research on spatially-embedded lenses in 3D visualization and urban analytics.

Figures (10)

• Figure 1: Pipeline illustrating our conformal mapping algorithm. (Top) The first stage decomposes the building footprint into smaller parallelogram approximations. The recursive decomposition proceeds through successive subdivisions $S_i$, each introducing additional polygonal subregions and corresponding graph nodes, ultimately forming a hierarchical topological graph. (Bottom) The second stage computes a conformal map for each partition, and subsequently stitches them together to form a unified geometric layout.
• Figure 2: Double-sided cutaway rendering (left) and conformal lens layout with layered ribbons encoding distinct time instances (right).
• Figure 3: Tree-ring chronology (left) and a cross-sectional view illustrating high-density temporal data (right).
• Figure 4: Color-coded lens visualizations using coarse (b) and fine (c) resolutions. Arrow glyphs aligned with section curves convey temporal progression (a). Two alternatives for encoding time-varying attribute values along ribbons are shown: plain color-coding is more space-efficient, and two-tone pseudocoloring enhances perceptual precision (d).
• Figure 5: Illustration of a lens function that modulates the visual prominence of selected attribute ranges in a two-tone pseudo coloring: low-value ranges are suppressed to visually accentuate high-value regions.