Course notes rotational symmetries on surfaces

Designing rotational symmetries on surfaces is a necessary task for a wide variety of graphics applications, such as surface parameterization and remeshing, painterly rendering and pen-and-ink sketching, and texture synthesis. In these applications, the topology of a rotational symmetry field such as singularities and separatrices can have a direct impact on the quality of the results. In this paper, we present a design system that provides control over the topology of rotational symmetry fields on surfaces. As the foundation of our system, we provide comprehensive analysis for rotational symmetry fields on surfaces and present efficient algorithms to identify singularities and separatrices. We also describe design operations that allow a rotational symmetry field to be created and modified in an intuitive fashion by using the idea of basis fields and relaxation. In particular, we provide control over the topology of a rotational symmetry field by allowing the user to remove singularities from the field or to move them to more desirable locations. At the core of our analysis and design implementations is the observations that N-way rotational symmetries can be described by symmetric N-th order tensors, which allows an efficient vector-based representation that not only supports coherent definitions of arithmetic operations on rotational symmetries but also enables many analysis and design operations for vector fields to be adapted to rotational symmetry fields. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing.

This paper describes an approach for interactive visualization of mixed scalar and vector fields, in which vector icons are generated from pre-voxelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field and the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. Subject Terms: data visualisation; interactive systems; graphical user interfaces; rendering (computer graphics); interactive visualization; scalar fields; vector fields; vector icons; pre-voxelized icon templates; volume-rendered; volumetric scalar data; incremental image update; real-time animation; zooming lens; local probe

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 86, Issue 2 p. 150-150 Book Review Book Review: Helmut Ratschek and Jon Rokne, Geometric Computations with Interval and New Robust Methods. Applications in Computer Graphics, GIS and Computational Geometry G. Alefeld, G. Alefeld KarlsruheSearch for more papers by this author G. Alefeld, G. Alefeld KarlsruheSearch for more papers by this author First published: 20 January 2006 https://doi.org/10.1002/zamm.200690009AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume86, Issue2February 2006Pages 150-150 RelatedInformation

We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a time-accurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them.

In this paper, we propose a novel vector field, called a camera-sampling field, to represent the sampling density distribution of a pinhole camera. We give the derivation and discuss some essential properties of the camera-sampling field, including flux, divergence, curl, gradient, level surface, and sampling patterns. This vector field reveals camera-sampling concisely and facilitates camera sampling analysis. The usage for this vector field in several computer graphics applications is introduced, such as determining the splat kernel for image-based rendering, texture filtering, mipmap level selection, level transition criteria for LOD, and LDI-construction.

Deformable models are a useful tool in computer vision and computer graphics. A deformable model is a curve (in two dimensions) or a surface (in three dimensions), whose shape, position, and orientation are controlled through a set of parameters. Deformable models can represent manufactured objects, human faces and skeletons, and even bodies of fluid. In computer graphics, we use deformable models for animations and simulations, whereas in computer vision applications, such as tracking and fitting, deformable models help to restrict the family of possible solutions. We introduce the use of a directed acyclic graph (DAG) to describe the position and Jacobian of each point on the surface of deformable models. This data structure, combined with a topological description of the points, is simple, powerful, and extremely useful for both computer vision and computer graphics applications. We show a computer vision application, 3D deformable face tracking, and a computer graphics application, cyberglove data visualization and calibration.

A practical guide to finite-element-method (FEM) simulation of 3D deformable solids reviews essential offline FEM simulation techniques: complex nonlinear materials, invertible treatment of elasticity, and model-reduction techniques for real-time simulation.

This paper presents a novel software model for public crisis management system in the modern city. Urban emergency such as various hazards will result in serious casualties and property loss. With the development of information technology, scientific crisis management system aided by computers should be constructed to mitigate the disasters. On the one hand, the application of Computer Graphics (CG) and Geographic Information System (GIS) for urban crisis management system is discussed. On the other hand, the integration of CG and GIS in the field of emergency management is proposed for the reference of government agencies.

Computer graphics applications, software, and hardware research, are examined and evaluated in Continental Western Europe. Growth has been slow. The reasons are the high cost of hardware and the complexity of the required software. The past reveals a rather dim picture. Mechanical engineering applications have shown some promising success. Electrical engineering applications have been effective mainly for PCB and IC mask layout only. Interactive graphic software has not yet effectively found its way outside Fortran. APL-G seems an interesting graphic extension of the language APL. Promising trends appear to be on the horizon. They are related to hardware and software trade-offs, as, for example, in the TALENT System.The need for computer graphics still exists. The hardware and software tradeoffs will receive more attention. Success in computer graphics will depend upon advances in computer systems design, especially programming languages and systems. Computer graphics has yet to come of age.

The analysis of data that consists of multiple vector fields can be greatly facilitated by the simultaneous visualization of the vector fields. An effective visualization must accurately reflect the key physical structures of the fields in a way that does not allow for an unintended bias toward one distribution. While there are several effective techniques to visualize a single vector field through equally spaced streamlines, applying these techniques to individual vector fields and combining them in a single image yields undesirable artifacts. In this paper, we present strategies for the effective visualization of two vector fields through the use of streamlines.

This paper reports the simulated results of modified anhysteretic remanence (MAR) in rotating vectorial AC bias fields, by a two-axis vibrating sample magnetometer (VSM). The effects of perpendicular component and rotation of the head fields on the MAR are clarified. It is found that a rotating vectorial AC bias head field needs about 1.2 times smaller magnitude than a scalar AC bias head field to acquire the same level of MAR, and that MAR in vectorial fields has a large perpendicular component. The effects on MAR of the sample orientation and the direction of measurement with respect to the sample shape are also discussed.

A person's emotions and state of mind are apparent in their face and eyes. As a Latin proverb states: The face is the portrait of the mind; the eyes, its informers.. This presents a huge challenge for computer graphics researchers in the generation of artificial entities that aim to replicate the movement and appearance of the human eye, which is so important in human-human interactions. This State of the Art Report provides an overview of the efforts made on tackling this challenging task. As with many topics in Computer Graphics, a cross-disciplinary approach is required to fully understand the workings of the eye in the transmission of information to the user. We discuss the movement of the eyeballs, eyelids, and the head from a physiological perspective and how these movements can be modelled, rendered and animated in computer graphics applications. Further, we present recent research from psychology and sociology that seeks to understand higher level behaviours, such as attention and eye-gaze, during the expression of emotion or during conversation, and how they are synthesised in Computer Graphics and Robotics.

We review the recent application of computer graphics to problems in the history and interpretation of master artworks. Carefully constructed computer graphics models of tableaus in paintings allow scholars to explore what if scenarios concerning lighting, geometry, placement of subjects, physical properties (such as color and reflectance characteristics), and more. A special application of computer graphics is to dewarp images depicted in spherical mirrors, such as appear in works from the northern Renaissance, thus revealing new views into artists' studios. We present a number of methodological recommendations to help ensure the results of such studies are valid. We describe some successes of these new techniques and conclude by discussing several outstanding problems and future directions for the use of computer graphics in the analysis of realist art.

Subdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having C^{1} smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

In order to better meet user needs, user-oriented interactive design introduces computer graphics technology to generate, process, and transmit graphical information more effectively, thereby enhancing the practicality, simplicity, convenience, and enjoyment of interactive media. This paper aims to discuss the application of computer graphics in interactive media design. In order to analyze and compare the use of different computer graphics (CG) technologies in different scenarios, this paper classifies the interactive media into three categories according to the different focuses of the purposes, namely distributed interaction media, commercial interaction media and informational interaction media, and discusses the application of computer graphics in interactive media design with specific examples. This paper analyzes and compares the use of different CG technologies in interactive media according to their different purposes, namely distributed interaction media, commercial interaction media and informational interaction media. The paper concludes with a summary of the current applications of computer graphics in interactive media design, and an outlook on the future use of CG technology in interactive media design.