Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.

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Large scale shadows from buildings in a city play an important role in determining the environmental quality of public spaces. They can be both beneficial, such as for pedestrians during summer, and detrimental, by impacting vegetation and by blocking direct sunlight. Determining the effects of shadows requires the accumulation of shadows over time across different periods in a year. In this paper, we propose a simple yet efficient class of approach that uses the properties of sun movement to track the changing position of shadows within a fixed time interval. We use this approach to extend two commonly used shadowing techniques, shadow maps and ray tracing, and demonstrate the efficiency of our approach. Our technique is used to develop an interactive visual analysis system, Shadow Profiler, targeted at city planners and architects that allows them to test the impact of shadows for different development scenarios. We validate the usefulness of this system through case studies set in Manhattan, a dense borough of New York City.

Fig. 1. Comparing two popular tourist locations -Rockefeller Center in New YorkCity (NYC) and Alcatraz Island in San Francisco (SF), using the pulse of these locations. The pulse, defined by a set of beats over multiple resolutions, captures the level of activity at a given location. In this example, the beats for the hourly and monthly resolutions are shown, based on Flickr activity. They are computed based on the topology of the time-varying scalar function that models the spatio-temporal distribution of the activity corresponding to a city. Dark green represents a significantly high activity at the location, while light green represents a relatively high activity compared to its neighboring locations. The similarity between the pulses of the two locations over the different resolution indicates that the level of activity is similar across time steps and resolutions even though one is located on the mainland, while the other is an island.Abstract-Cities are inherently dynamic. Interesting patterns of behavior typically manifest at several key areas of a city over multiple temporal resolutions. Studying these patterns can greatly help a variety of experts ranging from city planners and architects to human behavioral experts. Recent technological innovations have enabled the collection of enormous amounts of data that can help in these studies. However, techniques using these data sets typically focus on understanding the data in the context of the city, thus failing to capture the dynamic aspects of the city. The goal of this work is to instead understand the city in the context of multiple urban data sets. To do so, we define the concept of an "urban pulse" which captures the spatio-temporal activity in a city across multiple temporal resolutions. The prominent pulses in a city are obtained using the topology of the data sets, and are characterized as a set of beats. The beats are then used to analyze and compare different pulses. We also design a visual exploration framework that allows users to explore the pulses within and across multiple cities under different conditions. Finally, we present three case studies carried out by experts from two different domains that demonstrate the utility of our framework.

Major League Baseball (MLB) has a long history of providing detailed, high-quality data, leading to a tremendous surge in sports analytics research in recent years. In 2015, MLB.com released the StatCast spatiotemporal data-tracking system, which has been used in approximately 2,500 games since its inception to capture player and ball locations as well as semantically meaningful game events. This article presents a visualization and analytics infrastructure to help query and facilitate the analysis of this new tracking data. The goal is to go beyond descriptive statistics of individual plays, allowing analysts to study diverse collections of games and game events. The proposed system enables the exploration of the data using a simple querying interface and a set of flexible interactive visualization tools.