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Three dimensional display methods in computer graphics pdf

Three dimensional display methods in computer graphics pdf
21/01/2008 · Computer Graphics by Dr. Sukhendu das, Dept. of Computer Science and Engineering, IIT Madras.
Three patients with intractable epilepsy, two with brain tumors, and one with encephalitis were imaged with magnetic resonance (MR) and positron emission tomography (PET). MR data were used to construct a three-dimensional (3D) computer model of …
A two-dimensional computer graphic display of a three-dimensional model depicting a human being is presented. The major body segments of the model are represented as non-uniform elliptic cylinders.
Describes a simple, rapid method for the display of three-dimensional surfaces which can be applied to complex objects, and is therefore ideally suited to the display of medical images.
Many graphics system use this method. Set of polygons are stored for object description. This simplifies and speeds up the surface rendering and display of object since all surfaces can be described with linear equations.
The three-dimensional reconstruction and display of nonbiomedical data has been an active field in com- From the collection of the Computer History Museum (www.computerhistory.org)
The three-dimensional (3-D) object data obtained from a scanner usually have unequal sampling frequencies in the x y and z directions. Generally the 3-D data is first interpolated between slices to obtain isotropic resolution reconstructed then operated on by object extraction and display algorithms.
Abstract. This paper briefly describes several research projects at UNC Chapel Hill involved with the display of 3D medical image data. A number of display methods is reviewed, and several new approaches outlined.
A computer graphic display method that produces two-dimensional perspective views of three-dimensional objects is presented. The method is applied to the reconstruction at a resolution of 2.2
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(PDF) Full parallax three-dimensional display with
https://www.youtube.com/embed/sstN1qvReb0

Computer graphic display method for visualizing three
25/09/2013 · With the latest release of the S2PLOT graphics library, embedding interactive, 3-dimensional (3-d) scientific figures in Adobe Portable Document Format (PDF) files is simple, and can be accomplished without commercial software.
GATE Preparation, nptel video lecture dvd, computer-science-and-engineering, computer-graphics, three-dimensional-viewing, computer graphics, Survey of computer
Even the growth of three dimensional computer graphics has followed this limitation. To improve and widen the range of applications of projectors, in this dissertation I present a single unified geometric framework for projector-based graphics. It is based on the notion of the projector as the dual of a camera. The geometric framework is based on (i) the analytical projection model, (ii) the
three dimensional display methods To obtain display of a three-dimensional scene that has been modeled in world coordinates. we must first set up a coordinate reference for the “camera”. This coordinate reference defines the position and orientation for the plane of the carnera film which is the plane we want to us to display a view of the objects in the scene.
Write, compile, and run a C++ program that declares three one-dimensional arrays named price, quantity, and amount. Each array should be declared in main() and be capable of holding 10…. Each array should be declared in main() and be capable of holding 10….

Incorporating interactive 3-dimensional graphics in astronomy research papers David G. Barnes∗ and Christopher J. Fluke Centre for Astrophysics and Supercomputing, Swinburne University of …
An edge, when point-sampled for display by a raster device and not aligned with a display axis, appears as a stair-case.This common aliasing artifact often occurs in computer images generated by two- and three-dimensional algorithms. The precise edge
Due to the increased use of 3D modeling software in the design and manufacture of products, careful evaluation needs to be made as to how the 3D model is represented on the computer display. The experiment’s hypothesis is that both rate in which projections of a rotating object are presented and

3D computer graphics or three-dimensional computer graphics (in contrast to 2D computer graphics), are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes …
We describe three computer-based visualization methods that share the common goal of displaying the interior structures of 3-D data, and we present the results of applying these methods to a set of fluid-flow data. Interactive peeling of smooth opaque contour surfaces is the best of the three methods: it gives excellent perception cues.
In the 2D system, we use only two coordinates X and Y but in 3D, an extra coordinate Z is added. 3D graphics techniques and their application are fundamental to the entertainment, games, and computer-aided design industries. It is a continuing area of research in scientific visualization.
We concentrate on the problem of producing three-dimensional displays of organ surfaces from computerized tomograms. The theory of such surfaces is discussed. This theory leads to efficient methods of surface detection, visible surface determination, and rendering. The methods …
•'” A simulated three-dimensional computer graphics display system was developed to address issues critical to the training of Air Force air weapons controllers; primarily those training issues related to air intercept tactics and geometry. The research and development system provided the capability to display and control up to three aircraft in a defined airspace, plus the addition of
This article is a tutorial on the methods used to create three-dimensional (3-D) images for use in displaying patient anatomy. This new view into anatomy has developed over the last 10 years from
14/04/2016 · Sadhguru Reveal The Secret of his Knowledge Power of Shiva Shambho Mantra Mystics of India2018 – Duration: 25:00. Mystics of India 1,820,311 views
A method for clip checking three dimensional images for display on a computer display system. The display system includes a computer having a central processing unit(CPU) coupled to a memory and a cathode ray tube (CRT) display.
https://www.youtube.com/embed/sstN1qvReb0
US7417634B2 Three dimensional display – Google Patents
CS3162 Introduction to Computer Graphics Helena Wong, 2000 1 5. Three Dimensional Transformations Methods for geometric transforamtions and object modelling in 3D are extended from 2D methods by including
Full parallax three-dimensional display with occlusion effect using computer generated hologram Article (PDF Available) in Optical Engineering 50(7) · July 2011 with 120 Reads DOI: 10.1117/1.3599871
Methods of hidden surface removal and shading for computer-displayed surfaces are proposed. If the surface to be displayed is approximated by a large number of square faces of restricted orientation, the methods proposed in this paper work at least an order of magnitude faster than previously published methods.
dimensional objects in the computer system using these representations. Now we have to Now we have to find a method to display these 3 dimensional objects on the 2 dimensional view window.
5.2.2 Three-Dimensional Display Methods For the representation of a three-dimensional scene, the worl d coordinates are used. In this regards the first step is to
The mathematics behind algorithms involved in generating three-dimensional images on a computer has stemmed from the analysis of the processes of sight and vision. These processes have been modeled to provide methods of visualising three-dimensional data sets. The applications of …yves chevallard transposition didactique pdffundamentals of three dimensional computer graphics Download fundamentals of three dimensional computer graphics or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get fundamentals of three dimensional computer graphics …
3.1 THREE DIMENSIONAL CONCEPTS We can rotate an object about an axis with any spatial orientation in three- dimensional space. Two-dimensional rotations, on the other hand, are always around an axis that is perpendicular to the xy plane. Viewing transformations in three dimensions are much more cornplicated because we have many more parameters to select when specifying how a three-dimensional
We are developing graphics systems, image preprocessing methods, and interactive manipulation techniques for a space-filling 3D display using a varifocal mirror principle. Our driving problem is a medical imaging need for presentation of three-dimensional intensity information. The major goal of both the image preprocessing and the interactive manipulation has been to overcome obscuration
Three-dimensional interactive graphics in X-ray crystallographic analysis Interaction between programmer and display is posible by means of input devices attached to the LDS-1.
Three dimensional concepts and display methods, Computer Graphics Three Dimensional Concepts and Display Methods Imagine yourself taking a picture by a camera.
In computer graphics one is often concerned with representing three-dimensional objects on a two-dimensional display surface. The choice of such a representation depends on several factors, including the purpose for which the representation is intended, the visual effects that are desired, and the shape of the object. This paper describes how two- dimensional views can be obtained using planar
Apparatuses, methods and computer program products for scan plane geometry definition in tomographic data acquisition via an interactive three-dimensional (3-D) graphical operator interface.
These methods are generally limited, however, to two-dimensional formats, and there is a growing need for three-dimensional display of information. The cylindrical holographic stereogram is an interesting medium which shows some promise for three-dimensional data display. This paper examines some of the possibilities and problems of this application of the holographic stereogram.
Three Dimensional Display for Radar Data Vaisala IRIS 3D View Features/Benefits Reflectivity, Velocity, Spectrum Width, or Rain rate in 3 dimensions Up to 4 iso-surfaces with adjustable opacity or volume rendering Pan, zoom, rotate, and animation Interrogate radar data products using cursor tools Display regional radar composites or single station radar sites 2D radar products as underlays
These unique methods of communicating with the display with allow the user to accomplish a variety of tasks with the 3D LED Display such as presenting text, interactive graphics…
APPLICATION OF THREE-DIMENSIONAL INTERACTIVE GRAPHICS
This thesis investigated the preference of two types of computer animation graphics displays — two and three dimensional. A preference was determined based on…
Three Dimensional Display Methods Three Dimensional Display Methods is the important topic of the Computer Graphics. Moreover, It is the Important subject of the Computer Science & Techn…
19/02/1991 · A display apparatus and a modelling method for computer graphics includes a first memory for storing a first three-dimensional model, a detailed model, of a body represented by at least one of desired first number of dimensions, a desired first number of parameters and desired first parametric quantities, an arithmetic unit for
How to hire a Graphic Designer – There is a huge demand for Graphic designers in the market right now. Everyone wants to hire a designer and make their site more attractive to the customers.
This has been adopted from computer graphics and com- three dimensional displays. putational photography where it describes the rendering of light traveling in a set of directions from an object [4]. A similar term used is free viewpoint TV where a synthetic camera is used to I. INTRODUCTION render views not captured by a physical camera. All displays re- produce some form of light field and
This paper describes a method for the computer reconstruction of surfaces from a sequence of electron micrographs, and a data structuring approach to the problem of representing and analyzing objects of physiological importance. The reconstruction technique involves the following stages: 1) object
A stereographic display terminal has been produced using the raster display (BRAD) recently developed at Brookhaven. The system uses a rotating refresh memory to feed standard television monitors.
COMPUTER GRAPHICS AND IMAGE PROCESSING (1975)4, (396-402) A Three Dimensional Computer Display* WILLIAM SIMON~” Division of Biomathematics, The University of Rochester School of Medicine and Dentistt3~, Rochester, New York 14642 Communicated by A. Rosenfeld Received March 20, 1975 A simple device for producing an autostereoscopic visual
Three-dimensional images of microscopic objects can be obtained by confocal scanning laser microscopy (CSLM). The imaging process in a CSLM consists of sampling a specific volume in the object and storing the result in a three-dimensional memory array of a digital computer. Methods …
Three-dimensional computer display

US5003497A Method for three-dimensional clip checking
https://www.youtube.com/embed/I9ROB8b1CKs
More specifically, it relates to methods of reducing the large computational loads associated with the computation of computer generated holograms when parts of three dimensional objects are not presented fully face-on to the observer. It also relates to systems capable of implementing the methods …
Three-Dimensional Graphics Use of a right-handed coordinate system esoaGap cs (consistent with math) Left-handed suitable to screens handed suitable to screens.
Computer Graphics Assignment Help, Three dimensional display methods – 2d clipping algorithms, Three dimensional display methods: Among the simplest three dimensional surface representations are the polygonal surfaces. A polygonal surface is described by vertices, edges and polygons. Vertex, edge and polygon tables are formed
The PowerPoint PPT presentation: “Threedimensional Graphics” is the property of its rightful owner. Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com.
The vast increase of the volume of three dimensional topographic data acquired by Airborne LIDAR extends the possibility of the visualization method. The maximum laser pulse frequency of modern LIDAR system has reached more than 250 kHz.
A computer graphics processor and a method for rendering a three-dimensional image on a display screen. The computer graphics processor comprises a rasterizer configured to perform pixel traversal of a primitive after projection of the primitive.
3 Dimensional Display Methods YouTube

Three-dimensional human display model
(2) Display systems where the graphics are rendered on the monitor screen (3) Hardcopy devices or printers through which the tangible graphics output is produced. Based on the logical interaction types the input devices can be broadly classified as –
3D Display Methods: In this section, we focus on a subgoals of realistic picture we have to first setup a coordinate reference for camera. This co-ordinate reference defines the position and orientation for the plane of the camera, as shown in Fig.4.3.
The most common form of graphics monitor employing a CRT is the raster scan display, based on television technology. In a raster scan system, the electron beam is swept across the screen, one row at a time from top to bottom.
iii ABSTRACT Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images
A major challenge in building practical wearable computer systems is the development of output devices to display or transmit information to the human user. Much effort has been devoted to visual displays that are lightweight and have high resolution.
28/04/1998 · FIELD OF THE INVENTION. This invention relates to computer graphics and, more particularly, to a method for preparing a three-dimensional image for editing in two-dimensions and for display.
GATE Preparation, nptel video lecture dvd, computer-science-and-engineering, computer-graphics, two-dimensional-viewing-functions, computer graphics, Survey of computer graphics, graphics systems, display devices, Video display devices, scan, Raster scan, Random scan systems, Graphics monitors, Workstations, Input devices, Hard copy, Devices
(PDF) Three-dimensional image display in medicine
CS3162 Introduction to Computer Graphics Helena Wong, 2000 7. Three-Dimensional Viewing Viewing in 3D involves the following considerations: – We …
clidean three-dimensional space isR3. The set of natural numbers (non-negative integers) is rep- The set of natural numbers (non-negative integers) is rep- resented by N.
The physical world around us is three-dimensional (3D), yet traditional display devices can show only two-dimensional (2D) flat images that lack depth (i.e., the third dimension) information. This fundamental restriction greatly limits our ability to perceive and to understand the complexity of real Computer display screens, although only two-dimensional, can simulate three- dimensional objects by creating perspective views similar to the perspective view of a cube shown in Figure 1-1.

Explain the three dimensional display methods

Lecure 8 Three Dimensional Graphics – YouTube
PPT – Threedimensional Graphics PowerPoint presentation
Three Dimensional Display Methods – Computer Graphics

RED RELIEF IMAGE MAP NEW VISUALIZATION METHOD FOR THREE
https://www.youtube.com/embed/6M1WBoM_SNA

Vector Geometry and Applications to Three-Dimensional

OSA Three-dimensional display technologies
THREE DIMENSIONAL SURFACE DISPLAY DEVICE

Download three dimensional reconstruction in biology or read online here in PDF or EPUB. Please click button to get three dimensional reconstruction in biology book now. All books are in clear copy here, and all files are secure so don’t worry about it.
Many graphics system use this method. Set of polygons are stored for object description. This simplifies and speeds up the surface rendering and display of object since all surfaces can be described with linear equations.
Due to the increased use of 3D modeling software in the design and manufacture of products, careful evaluation needs to be made as to how the 3D model is represented on the computer display. The experiment’s hypothesis is that both rate in which projections of a rotating object are presented and
A method for clip checking three dimensional images for display on a computer display system. The display system includes a computer having a central processing unit(CPU) coupled to a memory and a cathode ray tube (CRT) display.
We are developing graphics systems, image preprocessing methods, and interactive manipulation techniques for a space-filling 3D display using a varifocal mirror principle. Our driving problem is a medical imaging need for presentation of three-dimensional intensity information. The major goal of both the image preprocessing and the interactive manipulation has been to overcome obscuration

Three-dimensional visualization methods for confocal
Application Of Holographic Stereograms To Three

Abstract. This paper briefly describes several research projects at UNC Chapel Hill involved with the display of 3D medical image data. A number of display methods is reviewed, and several new approaches outlined.
3D Display Methods: In this section, we focus on a subgoals of realistic picture we have to first setup a coordinate reference for camera. This co-ordinate reference defines the position and orientation for the plane of the camera, as shown in Fig.4.3.
3D computer graphics or three-dimensional computer graphics (in contrast to 2D computer graphics), are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes …
This thesis investigated the preference of two types of computer animation graphics displays — two and three dimensional. A preference was determined based on…
Many graphics system use this method. Set of polygons are stored for object description. This simplifies and speeds up the surface rendering and display of object since all surfaces can be described with linear equations.
The vast increase of the volume of three dimensional topographic data acquired by Airborne LIDAR extends the possibility of the visualization method. The maximum laser pulse frequency of modern LIDAR system has reached more than 250 kHz.
Three dimensional concepts and display methods, Computer Graphics Three Dimensional Concepts and Display Methods Imagine yourself taking a picture by a camera.
Describes a simple, rapid method for the display of three-dimensional surfaces which can be applied to complex objects, and is therefore ideally suited to the display of medical images.
This paper describes a method for the computer reconstruction of surfaces from a sequence of electron micrographs, and a data structuring approach to the problem of representing and analyzing objects of physiological importance. The reconstruction technique involves the following stages: 1) object

Planar Geometric Projections and Viewing Transformations
7. Three-Dimensional Viewing CityU CS

•'” A simulated three-dimensional computer graphics display system was developed to address issues critical to the training of Air Force air weapons controllers; primarily those training issues related to air intercept tactics and geometry. The research and development system provided the capability to display and control up to three aircraft in a defined airspace, plus the addition of
In computer graphics one is often concerned with representing three-dimensional objects on a two-dimensional display surface. The choice of such a representation depends on several factors, including the purpose for which the representation is intended, the visual effects that are desired, and the shape of the object. This paper describes how two- dimensional views can be obtained using planar
How to hire a Graphic Designer – There is a huge demand for Graphic designers in the market right now. Everyone wants to hire a designer and make their site more attractive to the customers.
GATE Preparation, nptel video lecture dvd, computer-science-and-engineering, computer-graphics, two-dimensional-viewing-functions, computer graphics, Survey of computer graphics, graphics systems, display devices, Video display devices, scan, Raster scan, Random scan systems, Graphics monitors, Workstations, Input devices, Hard copy, Devices
19/02/1991 · A display apparatus and a modelling method for computer graphics includes a first memory for storing a first three-dimensional model, a detailed model, of a body represented by at least one of desired first number of dimensions, a desired first number of parameters and desired first parametric quantities, an arithmetic unit for

3D Display Methods Stereoscopy Rendering (Computer
The brain integrated three-dimensional display of MR and

3D Display Methods: In this section, we focus on a subgoals of realistic picture we have to first setup a coordinate reference for camera. This co-ordinate reference defines the position and orientation for the plane of the camera, as shown in Fig.4.3.
Apparatuses, methods and computer program products for scan plane geometry definition in tomographic data acquisition via an interactive three-dimensional (3-D) graphical operator interface.
This has been adopted from computer graphics and com- three dimensional displays. putational photography where it describes the rendering of light traveling in a set of directions from an object [4]. A similar term used is free viewpoint TV where a synthetic camera is used to I. INTRODUCTION render views not captured by a physical camera. All displays re- produce some form of light field and
fundamentals of three dimensional computer graphics Download fundamentals of three dimensional computer graphics or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get fundamentals of three dimensional computer graphics …
3.1 THREE DIMENSIONAL CONCEPTS We can rotate an object about an axis with any spatial orientation in three- dimensional space. Two-dimensional rotations, on the other hand, are always around an axis that is perpendicular to the xy plane. Viewing transformations in three dimensions are much more cornplicated because we have many more parameters to select when specifying how a three-dimensional
In computer graphics one is often concerned with representing three-dimensional objects on a two-dimensional display surface. The choice of such a representation depends on several factors, including the purpose for which the representation is intended, the visual effects that are desired, and the shape of the object. This paper describes how two- dimensional views can be obtained using planar
iii ABSTRACT Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images

Three Dimensional Display for Radar Data Vaisala IRIS 3D View
Resolution-independent method for displaying a three

25/09/2013 · With the latest release of the S2PLOT graphics library, embedding interactive, 3-dimensional (3-d) scientific figures in Adobe Portable Document Format (PDF) files is simple, and can be accomplished without commercial software.
Incorporating interactive 3-dimensional graphics in astronomy research papers David G. Barnes∗ and Christopher J. Fluke Centre for Astrophysics and Supercomputing, Swinburne University of …
Three-dimensional images of microscopic objects can be obtained by confocal scanning laser microscopy (CSLM). The imaging process in a CSLM consists of sampling a specific volume in the object and storing the result in a three-dimensional memory array of a digital computer. Methods …
3.1 THREE DIMENSIONAL CONCEPTS We can rotate an object about an axis with any spatial orientation in three- dimensional space. Two-dimensional rotations, on the other hand, are always around an axis that is perpendicular to the xy plane. Viewing transformations in three dimensions are much more cornplicated because we have many more parameters to select when specifying how a three-dimensional
GATE Preparation, nptel video lecture dvd, computer-science-and-engineering, computer-graphics, two-dimensional-viewing-functions, computer graphics, Survey of computer graphics, graphics systems, display devices, Video display devices, scan, Raster scan, Random scan systems, Graphics monitors, Workstations, Input devices, Hard copy, Devices
A computer graphics processor and a method for rendering a three-dimensional image on a display screen. The computer graphics processor comprises a rasterizer configured to perform pixel traversal of a primitive after projection of the primitive.
The PowerPoint PPT presentation: “Threedimensional Graphics” is the property of its rightful owner. Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com.
Three dimensional concepts and display methods, Computer Graphics Three Dimensional Concepts and Display Methods Imagine yourself taking a picture by a camera.

Computational Morphology Three-Dimensional Computer
APPLICATION OF THREE-DIMENSIONAL INTERACTIVE GRAPHICS

We describe three computer-based visualization methods that share the common goal of displaying the interior structures of 3-D data, and we present the results of applying these methods to a set of fluid-flow data. Interactive peeling of smooth opaque contour surfaces is the best of the three methods: it gives excellent perception cues.
dimensional objects in the computer system using these representations. Now we have to Now we have to find a method to display these 3 dimensional objects on the 2 dimensional view window.
Three dimensional concepts and display methods, Computer Graphics Three Dimensional Concepts and Display Methods Imagine yourself taking a picture by a camera.
19/02/1991 · A display apparatus and a modelling method for computer graphics includes a first memory for storing a first three-dimensional model, a detailed model, of a body represented by at least one of desired first number of dimensions, a desired first number of parameters and desired first parametric quantities, an arithmetic unit for
The three-dimensional reconstruction and display of nonbiomedical data has been an active field in com- From the collection of the Computer History Museum (www.computerhistory.org)
How to hire a Graphic Designer – There is a huge demand for Graphic designers in the market right now. Everyone wants to hire a designer and make their site more attractive to the customers.
Three-dimensional interactive graphics in X-ray crystallographic analysis Interaction between programmer and display is posible by means of input devices attached to the LDS-1.
Many graphics system use this method. Set of polygons are stored for object description. This simplifies and speeds up the surface rendering and display of object since all surfaces can be described with linear equations.
This has been adopted from computer graphics and com- three dimensional displays. putational photography where it describes the rendering of light traveling in a set of directions from an object [4]. A similar term used is free viewpoint TV where a synthetic camera is used to I. INTRODUCTION render views not captured by a physical camera. All displays re- produce some form of light field and

Computational Morphology Three-Dimensional Computer
Three-dimensional human display model

A major challenge in building practical wearable computer systems is the development of output devices to display or transmit information to the human user. Much effort has been devoted to visual displays that are lightweight and have high resolution.
iii ABSTRACT Leonard McMillan Jr. An Image-Based Approach to Three-Dimensional Computer Graphics (Under the direction of Gary Bishop) The conventional approach to three-dimensional computer graphics produces images
(2) Display systems where the graphics are rendered on the monitor screen (3) Hardcopy devices or printers through which the tangible graphics output is produced. Based on the logical interaction types the input devices can be broadly classified as –
clidean three-dimensional space isR3. The set of natural numbers (non-negative integers) is rep- The set of natural numbers (non-negative integers) is rep- resented by N.
These methods are generally limited, however, to two-dimensional formats, and there is a growing need for three-dimensional display of information. The cylindrical holographic stereogram is an interesting medium which shows some promise for three-dimensional data display. This paper examines some of the possibilities and problems of this application of the holographic stereogram.
Three patients with intractable epilepsy, two with brain tumors, and one with encephalitis were imaged with magnetic resonance (MR) and positron emission tomography (PET). MR data were used to construct a three-dimensional (3D) computer model of …
This article is a tutorial on the methods used to create three-dimensional (3-D) images for use in displaying patient anatomy. This new view into anatomy has developed over the last 10 years from
This thesis investigated the preference of two types of computer animation graphics displays — two and three dimensional. A preference was determined based on…
An edge, when point-sampled for display by a raster device and not aligned with a display axis, appears as a stair-case.This common aliasing artifact often occurs in computer images generated by two- and three-dimensional algorithms. The precise edge