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1987, The Visual Computer
Until relatively recently, researchers in computer graphics paid scant attention to the numerics of their computations. Computation was used as a simple tool to evaluate algorithms or transform data into some appropriate pictoral representation. Thus standard computer graphics texts have little to say about numerical methods, just as earlier numerical analysis textbooks had little to say about computer graphics. This is now changing, for the important reasons outlined in this paper.
2001
Current computer graphics research tend to be more concerned with applications than image production techniques. Most of the latter research is concerned more with global illumination models than local illumination models. Does this mean that everything that could be said about fundamental algorithms have already been said? Examples of how reformulations of mathematical formulas have led to faster algorithms especially for shading will be given in this paper. A comparison of three different techniques for bivariate shading will exemplify that better formulations of old problems are still possible and necessary.
Vietnam Journal of Mathematics
Case studies Calibration and large-step time integration in elastodynamics Image and surface processing Conclusions Visual computing: where the "eyeball-norm" rules
Computer Graphics involves display, manipulation and storage of pictures and experimental data for proper visualization using a computer. It would be difficult to exaggerate the importance of computer graphics and multimedia in our lives. Activities as wide ranging as film making, publishing, and education have experienced revolutionary changes as these technologies alter the ways in which we conduct our daily activities. The combination of computers, multimedia, and the complex human visual system, through computer graphics, has been instrumental in these advances and has led to new ways of displaying information and recognizing the virtual worlds. This paper presents modelling, animation, rendering of geometrical objects. The transformations of objects along with different shading and discrete techniques have also been discussed in detail.
Early man used drawings to communicate even before he learnt to talk, write, or count. Incidentally, these ancient hieroglyphics (picture-writings) communicate as well today, as they must have done thousands of years ago, this fully supports the saig that A picture is worth a thousand words ad i the ea of oputes e a add o to it o e a as ell eise the saig to A computer is worth a million pictures!”; so, you can estimate the power of a computer as a communication system. Now, with the advances in computer hardware and software, graphics has come a full circle and, more and more people are teaching and learning, communicating and sharing their ideas through the medium of graphics. By graphics, we mean any sketch, drawing, special artwork or other material that pictorially depict an object or a process or otherwise conveys information, as a supplement to or instead of written descriptions, and the utilisation of computers to accomplish such tasks leads to a new discipline of computer graphics. Traditionally, graphics has referred to engineering drawings of buildings, bridges, machine parts etc. and scientific drawings such as x-y curves, network and process flowcharts. In recent decades, graphics has ventured into industrial design, advertising and other artistic endeavours. During the last few years, even newspapers and periodicals aimed at the common man have begun to utilise graphics to present quantitative news such as selection results and production statistics. Computer graphics can do all this and more. In fact, the power and easy availability of computer graphics have increased the use of pictures to replace and augment words to describe, educate, or inform a wide variety of audiences, on a wide variety of subjects.
The computer is an information processing machine. It is a tool for storing, manipulating and correcting data. There are many ways to communicate the processed information to the user. The computer graphics is one of the most effective and common way to communicate the processes information to the users. It displays the information in the form of graphics objects. Such as pictures, diagrams, and graphs instead of simple text. That means with the help of computer graphics, we can express the data in pictorial form.
1995
Before going into the details of various image synthesis algorithms, it is worth considering their general aspects, and establishing a basis for their comparison in terms of eciency, ease of realization, image quality etc., because it is not possible to understand the specic steps, and evaluate the merits or drawbacks of dierent approaches without keeping in mind the general objectives. This chapter is devoted to the examination of algorithms in general, what has been called algorithmics after the excellent book of D.
Computer-Aided Design, 1989
It is a classical principle in mathematics that polynomials in a single variable of degree n are essentially equivalent to symmetric polynomials in n variables that are linear in each variable separately. We shall apply this principle to the Bezier and B-spline curves and surfaces that are used in computer aided geometric design. The main result is a method of labeling the Bezier points that control a curve segment or surface patch or the de Boor points that control a B-spline curve with symmetric, multivariate labels. The properties of these labels make it simple to understand or to reconstruct the basic algorithms in this area, such as the de Casteljau Algorithm and the de Boor Algorithm.
Mathematical optimization has a fundamental importance for the solution of many problems in computer graphics and vision. This fact is apparent from a quick look at the SIGGRAPH proceedings, where a significant percentage of the papers employ in one way or another mathematical optimization techniques. This course will provide a conceptual analysis of the problems in computer graphics and discuss the mathematical models used to solve them. The goal is to develop an understanding of the importance of optimization techniques in graphics and vision. The course will also give an overview of combinatorial, continuous and variational optimization methods, focusing on graphical applications. The prerequisites for the course are: (i) background on linear algebra and calculus of one and several variables; (ii) computational experience on algorithms and programming; (iii) knowledge of geometric modeling, animation, image processing, image analysis and visualization. These notes originated from a set of notes in Portuguese written for a course on this topic at the Brazilian Mathematical Colloquium in July of 1999 and at Brazilian Congress of Applied Mathematics in October of 2000. We wish to thank Jonas Gomes and Luiz Henrique de Figueiredo who collaborated with us to produce the portuguese notes. Syllabus This tutorial is divided into two parts. The first part will give an overview of computer graphics, focusing on problems and describing the mathematical models used to solve them. This is a short introduction to motivate the study of optimization techniques. The subject will be taught in such a way to make it clear the need to use optimization techniques in the solution of a large family of problems. The second part will introduce the subject of optimization and provide a classification of the optimization techniques into different categories: continuous, variational and combinatorial methods. Several examples in computer graphics will be given to illustrate each category of problems.
2006
This lecture note covers the following topics: Introduction to Graphics, Curves, Transformations, Coordinate Free Geometry, 3D Objects, Camera Models, Visibility, Basic Lighting and Reflection, Basic Ray Tracing, Radiometry and Reflection, Distribution Ray Tracing, Parametric Curves And Surfaces and Animation.
Springer eBooks, 1997
3D graphics libraries play an important role in aiding both mathematicians and engineers to visualize their data and results. One of the most common graphics libraries is given by the GL (resp. OpenGL) implementation [1] by Silicon Graphics, Inc. However, the results from the GL/OpenGL are not acceptable for high-quality images. The reason for this in inadequacy is due to the missing Phong interpolation of normal vectors [2], the absence of global illumination models and the deficiency of configurable shaders and procedural textures. We present a new 3D graphics library, which combines both the speed of the OpenGL and the rendering quality of professional commercial products. This improvement was achieved by a flexible and extensible concept which integrates the use of different renderer types, user-definable shading procedures and an optimal adaption to many different hardware platforms. Our graphics library allows to preview a complex scene e.g. on a fast SGI machine and produce a high-quality ray traced image from the same source code by changing one line of code when the previewed image is satisfying. Several examples built with our graphics library will be presented along with the introduction of our modelling language. The latter is a comfortable and powerful tool for creating hierarchical scenes which can be imported into our graphics library through the concept of display lists. An outlook to future enhancements of our library will conclude the presentation.
IEEE Computer Graphics and Applications, 2021
Computer graphics are widely used in many area of research. This work presents an overview and the usage of computer graphics in different purposes: Graphs and Charts, Computer-Aided Design (CAD), Virtual Reality (VR), Data visualization, Education and training, Image processing, Computer Art, Entertainment and Graphical User Interface (GUI). This work descript also current related research and its example in order to clarify of computer graphic and how its work.
1993
Abstract. We describe a new method for numeric computations, which we call a ne arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and sub-formulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables.
Scholarpedia, 2007
Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. Such problems originate generally from real-world applications of algebra, geometry and calculus, and they involve variables which vary continuously; these problems occur throughout the natural sciences, social sciences, engineering, medicine, and business. During the past half-century, the growth in power and availability of digital computers has led to an increasing use of realistic mathematical models in science and engineering, and numerical analysis of increasing sophistication has been needed to solve these more detailed mathematical models of the world. The formal academic area of numerical analysis varies from quite theoretical mathematical studies (e.g. see [5]) to computer science issues (e.g. see [1], [11]). With the growth in importance of using computers to carry out numerical procedures in solving mathematical models of the world, an area known as scientific computing or computational science has taken shape during the 1980s and 1990s. This area looks at the use of numerical analysis from a computer science perspective; see [20], [16]. It is concerned with using the most powerful tools of numerical analysis, computer graphics, symbolic mathematical computations, and graphical user interfaces to make it easier for a user to set up, solve, and interpret complicated mathematical models of the real world.
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