February 2010

Master of Computer Application (MCA) – Semester 3

MC0072 – Computer Graphics

Assignment Set - 1

1. Describe the following:

A) Image Processing as Picture Analysis

B) Advantages of Interactive Graphics

C) Representative Uses of Computer Graphics

Ans –

A) Image Processing as Picture Analysis

The computer graphics is a collection, contribution and representation of real or imaginary objects from their computer-based models. Thus we can say that computer graphics concerns the pictorial synthesis of real or imaginary objects. However, the related field image processing or sometimes called picture analysis concerns the analysis of scenes, or the reconstruction of models of 2D or 3D objects from their picture. This is exactly the reverse process. The image processing can be classified as

· Image enhancement

· Pattern detection and recognition

· Scene analysis and computer vision

The image enhancement deals with the improvement in the image quality by eliminating noise or by increasing image contrast. Pattern detection and recognition deal with the detection and clarification of standard patterns and finding deviations from these patterns. The optical character recognition (OCR) technology is an practical example of pattern detection and recognition. Scene analysis and computer vision deals with the recognition and construction of 3D model of scene from several 2 D images.

The above three fields of image processing proved their importance in many area such as finger print detection and recognition, modeling of building, ships, automobiles etc. , and so on.

We have discussed the two fields: computer graphics and image processing of computer processing of picture. In the initial stages they were quite separate disciplines. But now a days they use some common features, and overlap between them is growing. They both uses raster displays.

B) The advantages of Interactive Graphics

Let us discuss the advantages of interactive graphics.

· Today, a high quality graphics display of personal computer provide one of the most natural means of communication with a computer.

· It provides tools for producing pictures not only of concrete, “real-world” objects but also of abstract, synthetic objects, such as mathematical surfaces in 4D and of data that have no inherent geometry, such as survey results.

· It has an ability to show moving pictures, and thus it is possible to produce animations with interactive graphics.

· With interactive graphics use can also control the animation by adjusting the speed, the portion of the total scene in view, the geometric relationship of the objects in the scene to one another, the amount of detail shown and so on.

· The interactive graphics provides tool called motion dynamics. With this tools user can move and tumble objects with respect to a stationary observer, or he can make objects stationary and the viewer moving around them. A typical example is walk throughs made by builder to show flat interior and building surroundings. In many case it is also possible to move both objects and viewer.

· The interactive graphics also provides facility called update dynamics. With update dynamics it is possible to change the shape, colour or other properties of the objects being viewed.

· With the recent development of digital signal processing (DSP) and audio synthesis chip the interactive graphics can now provide audio feedback along with the graphical feedbacks to make the simulated environment even more realistic.

In short, interactive graphics permits extensive, high-bandwidth user-computer interaction. It significantly enhances the ability to understand information, to perceive trends and to visualize real or imaginary objects either moving or stationary in a realistic environment. It also makes it possible to get high quality and more precise results and products with lower analysis and design cost.

C) Representative Uses of Computer Graphics

The use of computer graphics is wide spread. It is used in various areas such as industry, business, government organizations, education, entertainment and most recently the home. Let us discuss the representative uses of computer graphics in brief.

· User Interfaces: User friendliness is one of the main factors underlying the success and popularity of any system. It is now well established fact that graphical interfaces provide and attractive and easy interaction between users and computers. The built-in graphics provided with user interfaces use visual control items such as buttons, menus, icons, scroll bar etc, which allows user to interact with computer only by mouse-click. Typing is necessary only to input text to be stored and manipulated.

· Plotting of graphics and chart: In industry, business, government and educational organizations, computer graphics is most commonly used to create 2D and 3D graphs of mathematical, physical and economic functions in form of histograms, bars and pie-charts. These graphs and charts are very useful for decision making.

· Office automation and Desktop Publishing: The desktop publishing on personal computers allow the use of graphics for the creation and dissemination of information. Many organizations does the in-house creation and printing of documents. The desktop publishing allows user to create documents which contains text, tables, graphs and other forms of drawn or scanned images or pictures. This is one approach towards the office automation.

· Computer-aided Drafting and Design: The computer-aided drafting uses graphics to design components and systems electrical, mechanical, electromechanical and electronic devices such as automobile bodies, structures of building, airplane, ships, very large-scale integrated (VLSI) chips, optical systems and computer networks.

· Simulation and Animation: Use of graphics in simulation makes mathematical models and mechanical systems more realistic and easy to study. The interactive graphics supported by animation software proved their use in production of animated movies and cartoons films.

· Art and Commerce: There is a lot of development in the tools provided by computer graphics. This allows user to create artistic pictures which express messages and attract attentions. Such pictures are very useful in advertising.

· Process Control: By the use of computer now it is possible to control various processes in the industry from a remote control room. In such cases, process systems and processing parameters are shown on the computer with graphic symbols and identifications. This makes it easy for operator to monitor and control various processing parameters at a time.

· Cartography: Computer graphics is also used to represent geographic maps, weather

maps, oceanographic charts, contour maps, population density maps and so on.

2. Explain the following with the help of relevant real time applications:

A) Classification of Applications

B) Development of Hardware and Software for Computer Graphics

Ans –

A) Classification of Applications

In the last section we have seen various uses of computer graphics. These uses can be classified as shown in the figure below. As shown in the figure below the use of computer graphics can be classified according to dimensionality of the object to be drawn: 2D or 3D. It can also be classified according to kind of picture: Symbolic or Realistic. Many computer graphics applications are classified by the type of interaction. The type of interaction determines the user’s degree of control over the object and its image. In controllable interaction user can change the attributes of the images. Role of picture gives the another classification. Computer graphics is either used for representation or it can be an end product such as drawings. Pictorial representation gives the final classification to use computer graphics. It classifies the use of computer graphics to represent pictures such as line drawing, black and white, colour and so on.

B) Development of Hardware and Software for Computer Graphics

The development of hardware of computer graphics involves the development of input and output device technology. Therefore, in all development of computer graphics involves the development in three fields:

1. Output technology

2. Input technology and

3. Software technology

1.6.1 Output Technology

Figure below shows the historical development in the output technology. In early days of computer the hardcopy devices such as teletype printer and line printer were in use with computer driven CRT displays. In mid fifties command and control CRT display consoles were introduced. The more display devices developed in mid-sixties and in common use until the mid-eighties, are called vector, stroke, line drawing or calligraphic displays. The term vector is used as a synonyms for line; a stroke is a short line, and characters are made of sequence of such strokes.

Architecture of a Vector Display

Vector Scan CRT

As shown in Figure above vector scan CRT display directly traces out only the desired lines on CRT i.e If we want a line connection point A with point B on the vector graphics display. We simply drive the beam deflection circuitry which will cause beam to go directly from point A to B. If we want to move the beam from point A to point B without showing a line between points, we can blank the beam as we move it. To move the beam across the CRT, the information about both, magnitude and direction is required. This information is generated with the help of vector graphics generator.

The figure below shows the typical vector display architecture. It consists of display controller, Central Processing Unit (CPU), display buffer memory and a CRT. A display controller is connected as an I/O peripheral to the central processing unit (CPU). The display buffer memory stores the computer produced display list or display program. The program contains point and line plotting commands with (x,y) or (x,y,z) end point coordinates, as well as character plotting commands. The display controller interprets commands for plotting points, lines and characters and sends digital and point coordinates to a vector generator. The vector generator then converts the digital coordinates values to analog voltages for beam-deflection circuits that displace an electron beam writing on the CRT’s phosphor coating.

In vector displays beam is deflected from end point to end point, hence this technique is also called random scan. We know as beam, strikes phosphor it emits light. But phosphor light decays after few milliseconds and therefore it is necessary to repeat through the display list to refresh the phosphor at least 30 times per second to avoid flicker. As display buffer is used to store display list and it is used for refreshing, the display buffer memory is also called refresh buffer.

Architecture of a Raster Display

The figure gbelow shows the architecture of a raster display. It consists of display controller, central processing unit (CPU), video controller, refresh buffer, keyboard, mouse and the CRT.

Architecture of a raster display

As shown in the Figure above, the display images stored in the form of 1s and 0s in the refresh buffer. The video controller reads this refresh buffer and produces the actual image on the screen. It does this by scanning one scan line at a time, from top to bottom and then back to the top.

Raster Scan CRT

In this method, the horizontal and vertical deflection signals are generated to move the beam all over the screen in a pattern shown in the Figure above.

Here, the beam is swept back forth from left to right across the screen. When the beam is moved from the left to right, it is ON. The beam OFF, when it is moved from right to left as shown by dotted line in Figure above.

When the beam reaches the bottom of the screen, it is made OFF and rapidly retraced back to the top to start again. A display produced in this way is called raster scan display. Raster scanning process is similar to reading different lines on the page of a book. After completion of scanning of one line, the electron beam files back to the start of next line and process repeats. In the raster scan display, the screen images is maintained by repeating scanning the same image. This process is known as refreshing of screen.

Vector Scan Display Raster Scan Display

1. In vector scan display the beam is moved between the end points of the graphics primitives

1. In raster scan display the beam is moved all over the screen one scan line at a time, from top to bottom and then back to top.

2. Vector display flickers when the number of primitives in the buffer becomes too large.

2. In raster display, the refresh process is independent of the complexity of the image.

3. Scan conversion is not required.

3. Graphics primitives are specified in terms of their endpoints and must be scan converted into their corresponding pixels in the frame buffer.

4. Scan conversion hardware is not required.

4. Because each primitive must be scan converted, real time dynamics is far more computational and requires separate scan conversion hardware.

5. Vector display draws a continuous and smooth lines

5. Raster display can display mathematically smooth line, polygons and boundaries of curved primitives only by approximating them with pixels on the raster grid.

6. Cost is more. 6. Cost is low.

7. Vector display only draws lines and characters.

7. Raster display has ability to display areas filled with solid colors or patterns.

Direct-view storage tubes

In last sixties, the direct-view storage tube (DVST) was introduced in the display technology. The direct-view storage tubes (DVST) give the alternative method of maintaining the screen image. A DVST uses the storage grid which stores the picture information as a charge distribution just behind the phosphor-coated screen.

The Figure below shows the general arrangement of the DVST. It consists of two electron guns: a primary gun and a flood gun.

Arrangement of DVST

A primary gun stores the picture pattern and the flood gun maintains the picture display. A primary gun produces high speed electrons which strike on the storage grid to draw the picture pattern. As electron beam strikes on the storage grid with high speed, it knocks out electrons from the storage grid keeping the positive charge. The knocked out electrons are attracted towards the collector. The net positive charges on the storage grid is nothing but the picture pattern. The continuous low speed electrons from flood gun pass through the control grid and are attracted to the positive charged areas of the storage grid. The low speed electrons then penetrate the storage grid and strike the phosphor coating without affecting the positive charge pattern on the storage grid. During this process the collector just behind the storage grid smooth out the flow of flood electrons.

Advantages of DVST

1. Refreshing of CRT is not required.

2. Because no refreshing is required, very complex pictures can be displayed at very high resolution without flicker.

3. It has flat screen.

Disadvantages of DVST

1. They do not display colors and are available with single level of line intensity.

2. Erasing requires removal of change on the storage grid. Thus erasing and redrawing process takes several seconds.

3. Selective or part erasing of screen is not possible.

4. Erasing of screen produces unpleasant flash over the entire screen surface which prevents its use of dynamic graphics applications.

5. It has poor contrast as a result of the comparatively low accelerating potential applied to the flood electrons.

6. The performance of DVST is some what inferior to the refresh CRT.

In early seventies the inexpensive raster graphics displays were developed. Raster displays store the display primitives (such as lines, characters solid and filled patterns) in a refresh buffer in terms of their corresponding pixels.

Input Technology

Input technology has also improved greatly over the years. Number of input devices were developed over the years. These devices are punch cards, light pens, keyboard, tables, mouse and scanners.

Software Technology

Like output and input technology there is a lot of development in the software technology. In early days low level software were available. Over the years software technology moved from low level to device dependent and then to device independent packages. The device independent packages are high level packages with can drive a wide variety of display and printer devices. As a need for the device independent package a standardization is made and specification are decided. The first graphics specification to be officially standardized was GKS (the Graphical Kernel System). GKS supports the grouping of logically related primitives such as lines, polygons, and character strings and their attributes in collected form called segments. In 1988, a 3D extension of GKS, became an official standard, as did a much more sophisticated but even more complex graphics system called PHIGS (Programmer’s Hierarchical Interactive Graphics System).

PHIGS, as its name implies, supports nested hierarchical grouping of 3D primitives, called structures. In PHIGS, all primitives are subjected to geometric transformations such as scaling, rotation and translation to accomplish dynamic movement. PHIGS also supports a database of structures the programmer may edit and modify. PHIGS automatically updates the display whenever the database has been modified.

3. Explain the following with respect to Graphics Hardware:

A) Graphics Workstation B) Video Controller

C) Color Tables

Ans –

A) Graphics Workstation

Graphics Workstation is the Graphics Kernel System’s (GKS) term for a graphical device that can display graphical output or accept graphical input or both.

The figure below shows the block diagram of typical graphics station. It consists of CPU, display processor, memory, display devices, recorder, plotter, joystick, keyboard, light pen mouse, scanner etc, the main hardware components of a graphics workstation are CPU and Display Processor. The display processor is also called a graphics controller or a display coprocessor. It makes CPU free from the graphical chores. In addition to the system memory, a separate display processor memory area is provided in graphics workstations. Graphics workstations have a provision to interface video cameras and television set. The size of the display device, colors supported by it, whether it is a raster or line drawing device are the main properties of the graphics workstation. The graphics workstation is always supported with graphics software. Graphics software acts as a very powerful tool to create scenes, images, pictures and also animated pictures.

block diagram of typical workstation

B) Video Controller

We know that the video controller receives the intensity information of each pixel from frame buffer and display them on the screen. Let us see the internal organization of a video controller.

The figure below shows the internal organization of a video controller. It consists of raster-scan generator, x and y address registers and pixel value register. The raster-scan generator produces deflection signals that generate the raster scan. The raster scan generator also controls the x and y address registers which in turn define the memory location to be accessed next. Frarne buffer locations, and the corresponding screen positions, are referenced in Cartesian coordinates. For many graphics monitors, the coordinate origin is defined at the lower left screen corner. The screen surface is then represented as the first quadrant of a two-dimensional system, with positive x values increasing to the right and positive y values increasing from bottom to top. (On some personal computers, the coordinate origin is referenced at the upper left comer of the screen, so the y values are inverted.) Scan lines are then labeled from y, at the top of the screen to 0 at the bottom. Along each scan line, screen pixel positions are labeled from 0 to xmax. During each fetch the pixel value is read and is used to control the intensity of the CRT beam.

Simple organization of Video Controller

C) Color tables

In color displays, 24- bits per pixel are commonly used, where 8-bits represent 256 levels for each color. Here it is necessary to read 24-bits for each pixel from frame buffer. This is very time consuming. To avoid this video controller uses look up table (LUT) to store many entries of pixel values in RGB format. With this facility, now it is necessary only to read index to the look up table from the frame buffer for each pixel. This index specifies the one of the entries in the look-up table. The specified entry in the loop up table is then used to control the intensity or color of the CRT.

Usually, look-up table has 256 entries. Therefore, the index to the look-up table has 8-bits and hence for each pixel, the frame buffer has to store 8-bits per pixel instead of 24 bits. Figure below shows the organization of a color (Video) look-up table.

Organization of a Video look-up table

There are several advantages in storing color codes in a lookup table. Use of a color table can provide a "reasonable" number of simultaneous colors without requiring Iarge frame buffers. For most applications, 256 or 512 different colors are sufficient for a single picture. Also, table entries can be changed at any time, allowing a user to be able to experiment easily with different color combinations in a design, scene, or graph without changing the attribute settings for the graphics data structure. In visualization and image-processing applications, color tables are convenient means for setting color thresholds so that all pixel values above or below a specified threshold can be set to the same color. For these reasons, some systems provide both capabilities for color-code storage, so that a user can elect either to use color tables or to store color codes directly in the frame buffer.

4. Describe the following:

A) Basic Concepts in Line Drawing

B) Digital Differential Analyzer Algorithm

C) Bresenham’s Line Drawing Algorithm

Ans –

A) Basic Concepts in Line Drawing

Before discussing specific line drawing algorithms it is useful to note the general requirements for such algorithms. These requirements specify the desired characteristics of line.

· The line should appear as a straight line and it should start and end accurately.

· The line should be displayed with constant brightness along its length independent of its length and orientation.

· The line should be drawn rapidly.

Let us see the different lines drawn in Fig.3.5.

a) Vertical and horizontal lines b) 450 line

c) Lines with other orientation

As shown in Figure a horizontal and vertical lines are straight and have same width. The 450 line is straight but its width is not constant. On the other hand, the line with any other orientation is neither straight nor has same width. Such cases are due to the finite resolution of display and we have to accept approximate pixels in such situations, shown in Fig.3.5 (c).

The brightness of the line is dependent on the orientation of the line. We can observe that the effective spacing between pixels for the 450 line is greater than for the vertical and horizontal lines. This will make the vertical and horizontal lines appear brighter than the 450 line. Complex calculations are required to provide equal brightness along lines of varying length and orientation. Therefore, to draw line rapidly some compromises are made such as

· Calculate only an approximate line length.

· Reduce the calculations using simple integer arithmetic

· Implement the result in hardware or firmware

B) DDA Line Algorithm

1. Read the line end points (x1,y1 ) and (x2,y2) such that they are not equal.

[if equal then plot that point and exit]

2. ∆x = and ∆y =

3. If then

Length=

else

Length=

end if

4. = (x2-x1)/length

= (y2-y1)/length

This makes either or equal to 1 because the length is either | x2-x1| or |y2-y1|, the incremental value for either x or y is 1.

5. x = x1+0.5 * sign( )

y = y1+0.5*sign( )

[Here the sign function makes the algorithm worl in all quadrant. It returns –1, 0,1 depending on whether its argument is <0, =0, >0 respectively. The factor 0.5 makes it possible to round the values in the integer function rather than truncating them]

6. i=1 [begins the loop, in this loop points are plotted]

7. while(i length)

{

Plot (Integer(x), Integer(y))

x= x+∆x

y= y+∆y

i=i+1

}

8. stop

C) Bressenham’s Line Drawing Algorithm

Bresenham’s line algorithm uses only integer addition and subtraction and multiplication by 2, and we know that the computer can perform the operations of integer addition and subtraction very rapidly. The computer is also time-efficient when performing integer multiplication by powers of 2. Therefore, it is an efficient method for scan-converting straight lines.

The basic principle of Bresenham’s line algorithm is to select the optimum raster locations to represent a straight line. To accomplish this, the algorithm always increments either x or y by one unit depending on the slope of line. The increment in the other variable is determined by examining the distance between the actual line location and the nearest pixel. This distance is called decision variable or the error. This is illustrated in the Figure below..

As shown in the Figure above the line does not pass through all raster points (pixels). It passes through raster point (0,0) and subsequently crosses three pixels. It is seen that the intercept of line with the line x=1 is closer to the line y=0,i.e. pixel(1,0) than to the line y=1 i.e. pixel (1,1). Hence, in this case, the raster point at (1,0) better represents the path of the line that at (1,1). The intercept, of the line with the line x=2 is close to the line y=1, i.e. pixel (2,1) than to the line y=0,i.e. pixel(2.0). Hence the raster point at (2,1) better represents the path of the line, as shown in the Figure above.

In mathematical term error or decision variable is defined as

e=DB-DA Or DA-DB

Let us define e= DB-DA. Now if e>0, then it implies that DB>DA, i.e., the pixel above the line is closer to the true line. If DB < DA (i.e.<0) then we can say that the pixel below the line is closer to the true line. Thus by checking only the sign of error term it is possible to determine the better pixel to represent the line path.

The error term is initially set as e=2∆y-∆x

Where ∆y=y2-y1, and ∆x=x2-x1

Then according to value of e following actions are taken.

while (e≥0)

{

y=y+1

e=e-2*∆x

}

x=x+1

e=e+2*∆y

When e≥0, error is initialized with e=e – 2∆x. This is continued till error is negative. In each iteration y is incremented by 1. When e<0, error is initialized to e=e + 2∆y. In both the cases x is incremented by 1. Let us see the Bresenham’s line drawing algorithm.

Bresenham’s Line Algorithm

1. Read the line end points (x1, y1) and (x2, y2) such that they are not equal.

[if equal then plot that line and exit]

2. ∆x = and ∆y =

3. [initialize starting point]

x = x1

y = y1

4. e = 2 * ∆y – ∆x

[ Initialize value of decision variable or error to compensate for non zero intercepts]

5. i = 1 [initialize counter]

6. Plot (x, y)

7. while (e >0)

{

y = y+1

e = e-2 * ∆x

}

x = x+1

e = e+2 * ∆y

8. i = i+1

9. if ( i ∆x) then go to step 6

10. stop