Abstract Surface‐based pattern simulations have proven valuable for texture design and scientific visualization, but existing methods face several limitations. Most simulations either target a narrow range of pattern types (e.g. spots, branching) or support a broad range of patterns at the cost of time‐consuming parameter tuning. In either case, local and global control over the character of patterns is desirable, but often not supported. Additionally, transferring 2D simulations to 3D surfaces can introduce distortions, and is sensitive to mesh topology and quality. Finally, colourization further complicates the use of simulations for texturing, often relying on ad hoc mapping of simulation values to colours. To address these challenges, we introduce a unified framework for generating expressive, controllable patterns that are naturally embedded on curved surfaces. We reformulate Physarum polycephalum slime mold simulations in terms of continuous rates and PDEs, allowing greater consistency across varying space and time discretizations. We introduce agent‐based stochastic chemical kinetics to regulate agent turnover, which permits direct control over the uniformity of final patterns. Together, these modifications enable fine‐grained control of pattern synthesis using spatially varying parameter maps, directional biases, stimuli, and agent sinks/sources. We demonstrate that our approach allows for the generation of new pattern classes in Physarum slime mold simulations, including stripes, branching, and hierarchical structures. To eliminate distortion and artifacts, we re‐purpose intrinsic triangulations proposed for geometry processing to dynamic simulations. Finally, we introduce a simple colourization method to transfer colours from an exemplar image to simulation results. Notably, while demonstrated through slime mold simulations, our framework generalizes to other patterning models (e.g. reaction‐diffusion), thus providing a versatile tool for complex, controllable surface‐based pattern synthesis.

Abstract When moving along 3D curves, one may require local coordinate frames for visited points, such as for animating virtual cameras, controlling robotic motion, or constructing sweep surfaces. Often, consecutive coordinate frames should be similar, avoiding sharp twists. Previous work achieved this goal by using various methods to approximate rotation minimizing frames (RMFs) with respect to a curve's tangent. In this work, we use Householder transformations to construct preliminary tangent‐aligned coordinate frames and then optimize these initial frames under the constraint that they remain tangent‐aligned. This optimization minimizes the weighted sum of squared distances between selected vectors within the new frames and fixed vectors outside them (such as the axes of previous frames). By selecting different vectors for this objective function, we reproduce existing RMF approximation methods and modify them to consider additional objectives beyond rotation minimization. We also provide some example computer graphics use cases for this new frame tracking.

Abstract Physical representations of data offer physical and spatial ways of looking at, navigating, and interacting with data. While digital fabrication has facilitated the creation of objects with data‐driven geometry, rendering data as a physically fabricated object is still a daunting leap for many physicalization designers. Rendering in the scope of this research refers to the back‐and‐forth process from digital design to digital fabrication and its specific challenges. We developed a corpus of example data physicalizations from research literature and physicalization practice. This survey then unpacks the “rendering” phase of the extended InfoVis pipeline in greater detail through these examples, with the aim of identifying ways that researchers, artists, and industry practitioners “render” physicalizations using digital design and fabrication tools.

In this article, we introduce two local surface averaging operators with local inverses and use them to devise a method for surface multiresolution (subdivision and reverse subdivision) of arbitrary degree. Similar to previous works by Stam, Zorin, and Schröder that achieved forward subdivision only, our averaging operators involve only direct neighbours of a vertex, and can be configured to generalize B-Spline multiresolution to arbitrary topology surfaces. Our subdivision surfaces are hence able to exhibit Cdcontinuity at regular vertices (for arbitrary values ofd) and appear to exhibit C1continuity at extraordinary vertices. Smooth reverse and non-uniform subdivisions are additionally supported.

Textures composed of individual discrete elements are found in everything from human-made glass-tilings to forests and tropical coral. We propose an interactive sketch-based system for synthesizing scenes consisting of many discrete element textures. We have implemented an example-palette, a design window where a user can use our sketch-based tools to create discrete element textures and then paint those textures into a scene or back into the example-palette to create new textures. Our interactive sketch-based tools use a new and fast region-growing algorithm that iteratively synthesizes new elements around previously synthesized elements. To support discrete element textures with different scales in the same output, we parameterize our region-growing algorithm on a per-element basis. Our method is capable of synthesizing structured and stochastic example discrete element textures. We explore applications of our system for building virtual worlds (such as for video games) and for sketch-based modeling.

Building and interacting with 3D agent-based simulations that contain a large number of agents is a significant challenge. What if we want to create an intricate new arrangement of agents, or reconfigure a large number of agents? We present LifeBrush, a cyberworld for interactively painting large and elaborate multi-agent simulations with commodity virtual reality systems that we can then simulate and explore. Our main methodology uses sketch-based discrete element texture synthesis to paint agent arrangements. We define a map to convert agents to elements in this framework when we paint and back to agents when we simulate. Like creating new colors on a paint palette, we create example agent arrangements and configurations in an example palette. We paint new agents into a scene with sketch-based generative brushes. We also use those brushes to reconfigure agents to match examples created in the palette. Then we simulate, pause the simulation and modify the agents with our sketch-based tools. This iteration loop enables new levels of interactivity for the design, simulation, and exploration of agent-based simulations.

Abstract Landscape models of geospatial regions provide an intuitive mechanism for exploring complex geospatial information. However, the methods currently used to create these scale models require a large amount of resources, which restricts the availability of these models to a limited number of popular public places, such as museums and airports. In this paper, we have proposed a system for creating these physical models using an affordable 3D printer in order to make the creation of these models more widely accessible. Our system retrieves GIS relevant to creating a physical model of a geospatial region and then addresses the two major limitations of affordable 3D printers, namely the limited number of materials and available printing volume. This is accomplished by separating features into distinct extruded layers and splitting large models into smaller pieces, allowing us to employ different methods for the visualization of different geospatial features, like vegetation and residential areas, in a 3D printing context. We confirm the functionality of our system by printing two large physical models of relatively complex landscape regions.

The rapid growth in global sensor networks is leading to an explosion in the volume, velocity and variety of geospatial and geoscientific data. This coupled with the increasing integration of geospatial data into our everyday lives is also driving an increasing expectation of spatial information on-demand, and with minimal delay. The challenge we face in meeting these expectations is how to convert the vast and increasing volume of data being delivered from an increasingly diverse network of sensor things into meaningful information in a timely fashion. A key factor in meeting these challenges is the development and implementation of international standards (through the Open Geospatial Consortium [OGC®] and other international standards bodies) focused on establishing common methods and protocols that enable machine-to-machine transfer of data from sensors to people via the internet. However, until recently there has been a gap in the standardization of the spatial data architectures and technologies used to manage the geospatial data at the server-side and this has led to numerous ad-hoc and bespoke spatial data infrastructures being constructed which are potentially incompatible with each other and the wider ecosystem of the Internet of Things. Over the past 3 years the OGC has been working at filling this gap through the development the first international standard for Discrete Global Grid Systems (DGGS), with this new standard expected to be published in 2017. DGGS are a form of Earth reference system that represents the Earth using a hierarchical equal-area tessellation of the surface of the Earth and are designed to ensure a repeatable representation of measurements that is better suited to today's requirements and technologies. A DGGS presents a common framework that is capable of linking very large multi-resolution and multi-domain datasets together to enable the next generation of analytic processes to be applied. To date, DGGS haven't been used directly in the context of sensor networks. This paper proposes to demonstrate the application of DGGS to the Internet of Things and to highlight the immense benefit and value of using standards to enable interoperability in the era of Big Data.

There is explosive growth in both the variety and the volume of spatial data and processing resources, along with a growing understanding of the tremendous benefit that can be derived from enabling interoperability between them. On the other side of this deluge of spatial content is a growing demand by decision-makers for a participatory environment where content can be accessed directly from diverse contributors and used with other content without reliance on time-consuming and costly geographic transformation processes. The Open Geospatial Consortium (OGC®) has released a new candidate standard for Discrete Global Grid Systems (DGGS) that defines a set of rules for defining highly efficient architectures for spatial data storage and analytics. The goal of a DGGS is to enable rapid integration of spatial data without the difficulties of working with legacy coordinate systems. This paper presents the new OGC standard and its application to the next generation of Geoscience Information Systems.

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries.

In this paper, we present an approximating multiresolution framework of arbitrary degree for curves on the surface of a sphere. Multiresolution by subdivision and reverse subdivision allows one to decrease and restore the resolution of a curve, and is typically defined by affine combinations of points in Euclidean space . While translating such combinations to spherical space is possible, ensuring perfect reconstruction of the curve remains challenging. Hence, current spherical multiresolution schemes tend to be interpolating or midpoint-interpolating, as achieving perfect reconstruction in these cases is more straightforward. We use a simple geometric construction for a non-interpolating and non-midpoint-interpolating multiresolution scheme on the sphere, which is made up of easily generalized components and based on a modified Lane–Riesenfeld algorithm.

We present a sketch-based system for the creation and editing 3D content such as Digital Elevation Models, vegetation and bodies of water for Digital Earth representations. The proposed system employs a set of sketch-based tools to integrate commonly available data sources, such as orthophotos and Digital Elevation Models (DEM), to facilitate the rapid creation and integration of detailed geospatial content. Consequently, our system can be used to enhance the quality of Digital Earth data by enabling the straightforward creation of new 3D landscape elements.

Given a set of symmetric/antisymmetric filter vectors containing only regular multiresolution filters, the method we present in this article can establish a balanced multiresolution scheme for images, allowing their balanced decomposition and subsequent perfect reconstruction without the use of any extraordinary boundary filters. We define balanced multiresolution such that it allows balanced decomposition i.e. decomposition of a high-resolution image into a low-resolution image and corresponding details of equal size. Such a balanced decomposition makes on-demand reconstruction of regions of interest efficient in both computational load and implementation aspects. We find this balanced decomposition and perfect reconstruction based on an appropriate combination of symmetric/antisymmetric extensions near the image and detail boundaries. In our method, exploiting such extensions correlates to performing sample (pixel/voxel) split operations. Our general approach is demonstrated for some commonly used symmetric/antisymmetric multiresolution filters. We also show the application of such a balanced multiresolution scheme in real-time focus+context visualization.

Multidimensional projection techniques provide an appealing approach for multivariate data analysis, for their ability to translate high-dimensional data into a low-dimensional representation that preserves neighborhood information. In recent years, pushed by the ever increasing data complexity in many areas, numerous advances in such techniques have been observed, primarily in terms of computational efficiency and support for interactive applications. Both these achievements were made possible due to the introduction of the concept of control points, which are used in many different multidimensional projection techniques. However, little attention has been drawn towards the process of control points selection. In this work we propose a novel multidimensional projection technique based on radial basis functions (RBF). Our method uses RBF to create a function that maps the data into a low-dimensional space by interpolating the previously calculated position of control points. We also present a built-in method for the control points selection based on "forward-selection" and "Orthogonal Least Squares" techniques. We demonstrate that the proposed selection process allows our technique to work with only a few control points while retaining the projection quality and avoiding redundant control points.

Energy systems are under pressure to transform in order to address concerns about climate change. The modeling and visualization of energy systems can play an important role in communicating the costs, benefits and tradeoffs of energy systems choices. We introduce a visualization tool that provides an interface for exploring time-varying, multiattribute and spatial properties of a particular energy system. The tool integrates several visualization techniques to facilitate exploration of a particular energy system. These techniques include flow diagram representation to show energy flow, 3D interaction with flow diagrams for expanding viewable data attributes such as emissions and an interactive map integrated with flow diagrams for simultaneous exploration of spatial and abstract information. We also perform level of detail exploration on flow diagrams and use smooth animation across the visualizations to represent time-varying data. As a means of preliminary evaluation, we have included feedback on this tool from our energy system collaborators.

In this paper, we present the construction of a multilevel focus context visualization framework for the navigation and exploration of large-scale 2D and 3D images. The presented framework utilizes a balanced multiresolution (BMR) technique supported by a balanced wavelet transform (BWT). This devised framework extends the mode of focus context visualization, where spatially separate magnification of regions of interest (ROIs) is performed, as opposed to in-place magnification. Each resulting visualization scenario resembles a tree structure, where the root constitutes the main context, each non-root internal node plays the dual roles of both focus and context, and each leaf solely represents a focus. We use the local multiresolution filters of quadratic B-spline to construct the BWT. Our developed prototype supports interactive manipulation of the visualization hierarchy, such as addition and deletion of ROIs and desired changes in their resolutions at any level of the hierarchy on the fly. Changes in the spatial locations of query windows that define the ROIs trigger on-demand reconstruction queries. We describe in detail how to efficiently process such reconstruction queries within the hierarchy of details (wavelet coefficients) contained in the BWT in order to ensure real-time feedback. As the BWT need only be constructed once in a preprocessing phase on the server-side and robust on-demand reconstruction queries require minimal data communication overhead, our presented framework is a suitable candidate for efficient web-based visualization and exploration of complex large-scale imagery.

Sketching and doodling are two techniques commonly used by choreographers to design a dance sequence. These sketches usually represent the trajectory of the dancer in the scene. A set of annotations can be used to differentiate the various dance movements. In order to have more control over the choreographed dance, a 3D animation is preferable. This paper presents a novel sketch-based approach to assist dance choreographers authoring dance motions in a 3D environment. The proposed approach allows a choreographer to story board a dance using stick figure sketches of a dancer. Inspired by traditional choreography, a set of simple annotations is introduced for ballet. These annotations help to retrieve and blend ballet 'mini-motions' in order to create a synthesized dance. To build the mini-motions, we have analyzed and processed several ballet movements available in a MoCap database.

We present a Sketch-Based Interface that allows non-expert users to create an animation from just pencil and paper. The interface works as a fast mockup tool for creating animations - turning the user's freehand 2D sketches into 3D animations. To facilitate animation construction in offline or computer-scarce scenarios, special emphasis is placed on paper-based instead of tablet-based sketches. The interface makes use of stroke shape, proximity, and orientation to give the user's drawings an animated interpretation. These Sketches use a 2D vocabulary of symbols, representing actors, actions and their relations. Custom symbols are defined by the user, and then associated with the relevant 3D assets within a database. The final composition of the sketches is passed into the system, employing image processing techniques for symbol recognition, and finally converting the user's intentions into a 3D animation.

Modern techniques in area preserving projections used by cartographers and other glossarial researchers have closed forms when projecting from the sphere to the plane, as based on their initial derivations. Inversions, from the planar map to the spherical approximation of the Earth which are important for modern 3D analysis and visualizations, are slower, requiring iterative root finding approaches, or not determined at all. We introduce optimization techniques for Snyder's inverse polyhedral projection by reducing iterations, and using polynomial approximations for avoiding them entirely. Results including speed up, iteration reduction, and error analysis are provided.

Panoramic projections are often defined by the geometric surfaces used to derive the projections' equations (e.g., spherical and cylindrical panoramas). The parameterization of these surfaces greatly affects the resulting projection equations and image properties. Problematically, unusual parameterization can reproduce panoramas associated with other shapes. In this paper, we ensure an explicit link between surface shape and projection behavior by suggesting use of projection surfaces parameterized by arc-length, binding rendering behavior to surface modeling. This allows us to create new panorama variations beyond the conventional for creating panoramas of CG environments as well as for resampling panoramas created from cameras. Further we describe an interface for composing these panoramas and show how this technique lends itself to controlling distortion and composition of panoramic projections. Additionally we provide details on rendering these projections.

This paper develops a framework for locally deforming either a parametric surface or hierarchical subdivision surface to match a set of positional and energy minimizing constraints. The positional constraints can be obtained from a wide variety of existing interfaces, and the framework produces a smooth, local and stable deformation through solving a simple local least-squares. We use an indexing scheme to localize optimization to only contributing control points. These points are found and measured by using basis functions or by tracking subdivision mask operations. We demonstrate our framework on B-spline and Loop subdivision surfaces.

We present an illustrative visualization system for real-time and high quality rendering of clinical volumetric medical data. Our technique is inspired by a medical illustration technique for depicting contextual close-up views of selected regions of interest where internal anatomical features are rendered in high detail. Our method integrates four important components: decimation of original volume for interactivity, B-spline subdivision for super-resolution rendering, fast gradient quantization technique for feature extraction and GPU fragment shaders for gradient dependent rendering and transfer functions. Examples with clinical CT and MRI data demonstrate the capabilities of our system.

This work presents a new algorithm and technique for rendering triangular surfaces in pen-and-ink edge-based strokes. Our technique integrates two very important illustration strategies for depicting shape features: selection of drawing direction and the use of light. Drawing direction is given by four stroke directional fields. For lighting, we introduce the idea of "spotlight silhouettes" for fast illumination computation, with target tone matched by adaptive stroke length adjustment. Stroke style is achieved by path perturbation and noise-based weight control. Our technique also allows visual effects of reverse tone values and depth cueing. Examples with models from anatomy and archeology demonstrate the capabilities of our system.

Abstract Drawings made with precise pen strokes accurately reveal the geometric forms that give subjects their characteristicshape. We present a system for non‐photorealistic rendering of precise drawing strokes over dense 3Dtriangle meshes with arbitrary topology. During an automatic pre‐process, we construct an extended version ofthe edge‐buffer data structure to allow the calculation of shape measures at each mesh edge, by adapting numericalmethods used in geomorphology. At runtime, feature edges related to shape measures are extracted andrendered as strokes with varying thickness and pen marking styles. Stroke thickness is automatically adjusted byconsidering surface curvature. Pen marking styles and visual effects of ink distribution are both controlled by theuser. We demonstrate precise drawing strokes over complex meshes revealing a variety of shape characteristics.

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models (Samavati and Bartels, Computer Graphics Forum, 18(2):97–119, June 1999). As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In Bartels and Samavati (Journal of Computational and Applied Mathematics, 119:29–67, 2000) we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here, we construct multiresolution surfaces of arbitrary topologies by locally reversing the Doo subdivision scheme. In a Doo subdivision, a coarse surface is converted into a fine one by the contraction of coarse faces and the addition of new adjoining faces. We propose a novel reversing process to convert a fine surface into a coarse one plus an error. The conversion has the property that the subdivision of the resulting coarse surface is locally closest to the original fine surface, in the least squares sense, for two important face geometries. In this process, we first find those faces of the fine surface which might have been produced by the contraction of a coarse face in a Doo subdivision scheme. Then, we expand these faces. Since the expanded faces are not necessarily joined properly, several candidates are usually at hand for a single vertex of the coarse surface. To identify the set of candidates corresponding to a vertex, we construct a graph in such a way that any set of candidates corresponds to a connected component. The connected components can easily be identified by a depth first search traversal of the graph. Finally, vertices of the coarse surface are set to be the average of their corresponding candidates, and this is shown to be equivalent to local least squares approximation for regular arrangements of triangular and quadrilateral faces.

This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least‐squares data fitting, and wavelets. We show how least‐squares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization. Some insights that this work brings forth are that the inner product used in a multiresolution analysis in uences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes. We illustrate our findings using an example curve, grey‐scale image, and tensor‐product surface.