We present AuxiScope, a novel AR-based system designed to enhance personalized data exploration on large wall displays (LWDs) by integrating handheld tablets as auxiliary visualization interfaces. While LWDs offer expanded visual real estate and intuitive embodied interaction, they pose challenges related to effective interfaces for data exploration and analysis, specifically in multi-user settings. AuxiScope addresses these by overlaying supplementary visualizations onto corresponding LWD content, enabling individualized exploration without interference with the visual data displayed on the LWD. To achieve this, we have designed a geometric alignment pipeline that synchronizes the auxiliary visualizations atop the virtual scene. Specifically, by leveraging AR technology, AuxiScope resolves the tablet physical localization, viewpoint computation, and user interaction translation into the virtual space. Subsequently, based on a client-server architecture, it employs remote rendering and delegates computational tasks to the LWD compute nodes in order to minimize memory load on portable devices. We demonstrate the potential of AuxiScope through multiple AR-based interaction techniques across information and scientific visualization scenarios, for both 2D and 3D contexts.

Understanding visual attention is key to designing efficient human-computer interaction, especially for virtual reality (VR) and augmented reality (AR) applications. However, the relationship between 3D spatial attributes of visual stimuli and visual attention is still underexplored. Thus, we design an experiment to collect a gaze dataset in VR, and use it to quantitatively model the probability of first attention between two stimuli. First, we construct the dataset by presenting subjects with a synthetic VR scene containing varying spatial configurations of two spheres. Second, we formulate their selective attention based on a probability model that takes as input two view-specific stimuli attributes: their eccentricities in the field of view and their sizes as visual angles. Third, we train two models using our gaze dataset to predict the probability distribution of a user's preferences of visual stimuli within the scene. We evaluate our method by comparing model performance across two challenging synthetic scenes in VR. Our application case study demonstrates that VR designers can utilize our models for attention prediction in two-foreground-object scenarios, which are common when designing 3D content for storytelling or scene guidance. We make the dataset and the source code to visualize it available alongside this work.

We present VoxAR, a method to facilitate an effective visualization of volume-rendered objects in optical see-through head-mounted displays (OST-HMDs). The potential of augmented reality (AR) to integrate digital information into the physical world provides new opportunities for visualizing and interpreting scientific data. However, a limitation of OST-HMD technology is that rendered pixels of a virtual object can interfere with the colors of the real-world, making it challenging to perceive the augmented virtual information accurately. We address this challenge in a two-step approach. First, VoxAR determines an appropriate placement of the volume-rendered object in the real-world scene by evaluating a set of spatial and environmental objectives, managed as user-selected preferences and pre-defined constraints. We achieve a real-time solution by implementing the objectives using a GPU shader language. Next, VoxAR adjusts the colors of the input transfer function (TF) based on the real-world placement region. Specifically, we introduce a novel optimization method that adjusts the TF colors such that the resulting volume-rendered pixels are discernible against the background and the TF maintains the perceptual mapping between the colors and data intensity values. Finally, we present an assessment of our approach through objective evaluations and subjective user studies.

Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes concepts and computing methods and turns them into executable programs. What has been lacking is a principled approach that supports all central concepts of discrete math---especially predicate logic---and that directly and precisely connects math notations with executable programs. This paper introduces such an approach. It is based on the use of a powerful language that extends the Python programming language with proper logic quantification ("for all'' and "exists some''), as well as declarative set comprehension (also known as set builder) and aggregation (e.g., sum and product). Math and logical statements can be expressed precisely at a high level and be executed directly on a computer, encouraging declarative programming together with algorithmic programming. We describe the approach, detailed examples, experience in using it, and the lessons learned.