Computer graphics

[aayush_005]

Computer graphics is the creation and manipulation of pictures with the aid of computer. There are two types of computer graphics.

 Interactive computer graphics
 Non-interactive graphics or passive computer graphics

Interactive computer graphics:

The computer graphics in which the observer has some control over the image by providing him with an input device so that he can signal his request to computer. Example: Video games.

Interactive computer graphics involves two way communication between computer and user. The user gives signals to computer through the input device and computer can modify the displayed picture accordingly. In this way we maintain conversation or dialogue with the computer.

Non-interactive computer graphics:

The computer graphics in which the observer has no control over the image. Example: Titles shown on TV.

Applications of Graphics:

Computers have become powerful tool for the rapid and
economical production of pictures. Computer graphics are used in several
areas such as
 Science
 Engineering
 Medicine
 Business
 Industry
 Government
 Art
 Entertainment
 Advertising
 Education and training




Computer aided design:

A major use of computer graphics is in design process particularly for engineering and architectural systems. Computer aided design referred as CAD methods are now routinely used in the design of buildings, automobiles, aircraft, space craft and textiles etc.,

 Useful for testing performance of a vehicle.
 System in virtual reality environments.
 Realistic renderings of design process.
 Realistic 3D renderings of building designs.

Presentation Graphics:

Presentation graphics used to produce illustration for reports or generate 35mm slides etc., These graphics are commonly used to summarize and economic data for research reports, managerial reports, consumer information bulletins etc.,
Example: bar charts, line graphs and pie charts.

Computer art:

Computer graphics methods are widely used in both fine art and commercial art applications. Artists uses variety of computer methods including special purpose hardware, paint brush programs etc.,

Entertainment:

Computer graphics methods are now commonly used in making motion pictures, music videos and television shows. Sometimes graphics are displayed by themselves i.e., computer animation and sometimes graphics objects are combined with the actors and live scenes.

Education and training:

Computer generated models of physical, financial and economic systems are often used as educational aids. For some training applications special system are designed.



Visualization:

Producing graphical representations for scientific, engineering and medical data sets and processes is generally referred to as scientific visualization. For commerce, industry and other non-scientific areas data sets and processes is generally referred to as business visualization.

Image processing:

Image processing apply techniques to modify or interpret existing pictures such as photographs and TV scans. Two principal applications of image processing are
1. Improving picture quality
2. Machine perception of visual information as used in robotics.

Uses: 1. To enhance the quality of a picture.
2. In medical applications such as in tomography operations.

Combination of image processing and computer graphics is used to design artificial limbs to plan and practice surgery generally referred as computer aided surgery.

Graphical User Interfaces (GUI):

The software packages provide a graphical interface. This provides a window manager that allows a user to display multiple window areas. Each window contains a different process that can contain graphical or non-graphical displays. To make a particular window active, we simply click in that window using an interactive pointing device. Interfaces also display menus and icons for fast selections for fast selection of processing operations.
Icons:
An icon is graphical symbol that is designed to looks like the processing operation it represents. The icons can take up less screen space and they can be understood more quickly.


Vector:
A vector has a single direction and a length. A vector may be denoted as [Dx, Dy], where Dx indicates how far to move along the x-axis direction and Dy indicates how far to move along the y-axis direction.

The vectors have no fixed position in space. They tell us that how far and what direction to move, but they do not tell us where to start. The vector is useful since it closely parallels the manner in which a pen draws lines on paper or an electron beam draws lines on a cathode ray tube. The command to the pen may be to move so far from its current position in a given direction.

The two vectors may be added by adding their respective components.
V1+V2 = [Dx1, Dy1] + [Dx2, Dy2]
= [Dx1 + Dx2 , Dy1 + Dy2]

Suppose we start at some point A. the first vector moves the pen from point A to point B; the second, from point B to point C. the right-hand side of the above equation produces a single vector which will move the pen directly from point A to point C.
We can also multiply a vector by a number by multiplying each of its components.
nV = n[Dx, Dy] = [nDx, nDy]
If we multiply a vector by the reciprocal of its length, the result is a vector with length equal to 1. Such vectors are called Unit vectors.

Raster:
The raster-scan display differs from the random-scan line-drawing display mainly in how displayed data are represented. A display file for a line-drawing display contains only information about lines and characters to be drawn; the void areas of the screen are ignored.
The raster-scan display controls the intensity of each dot, or pixel, in a rectangular matrix, or raster, of dots that covers the entire screen. Raster-scan implies in addition that the image is scanned onto the screen surface in a raster sequence, that is, as a succession of equidistant scan lines, each scan line made up of pixels.

Raster-scan displays owe their increase in popularity to two causes. The first of these is the need for greater realism in pictures, especially in application involving three-dimensional objects. While applications for these high-quality displayed images have been increasing, the cost of raster-scan display equipment has been decreasing, a second reason for wider acceptance of raster-scan graphics.

Lines:
We can specify a point with an ordered pair of numbers (x, y), where x is the horizontal distance from the origin and y is the vertical distance from the origin. . Two points will specify a line. Lines are described by equations such that if a point (x, y) satisfies the equations, then the point is on the line.

If the two points used to specify a line are (x1, y1) and (x2, y2), then an equation for the line is given by
y – y1 / x – x1 = y2 – y1 / x2 – x1

This says that the slope between any point on the line and (x1, y1) is the same as the slope between (x1, y1) and (x2, y2). There are many equivalent forms for this equation. Multiplying by the denominators gives the form
(x – x1) (y2 – y1) = (y – y1) (x2 – x1)
A little more algebra solving for y gives
y = mx + c
Where m = (y2 – y1) / (x2 – x1)

This is called the slope-intercept form of the line. The slope m is the change in height divided by the change in width for two points on the line. The intercept b is the height at which the line crosses the y-axis. This can be seen by noting that the point (0, b) satisfies the equation of the line.


Line Segment:

Our equations for lines specify all points in a given direction. Let’s consider only those points on a line which lie between two endpoints p1 and p2. This is called a line segment. A line segment may be specified bytes two endpoints. From these endpoints we can determine the equation of the line. From this equation and the endpoints we can decide if any point is or is not on the segment.
If the endpoints p1 = (x1, y1) and p2 = (x2, y2) and these yield equation y = mx + b, then another point p3 = (x3, y3) lies on the segment if

1. y3 = mx3 + b,
2. min (x1, x2) <= x3 <= max (x1, x2),
3. min (y1, y2) <= y3 <= max (y1, y2).

Here the notation min(x1, x2) means the smallest of x1 and x2 & the notation max(x1, x2) means the larger of two numbers.


Midpoint:
The midpoint of a line segment half way between the endpoints of a segment. It will have an x-coordinate half way between the x-coordinates of the endpoints, and a y-coordinate half way between the y-coordinates of the endpoints. Therefore, the midpoint is
(Xm, Ym) = [(x1+x2)/2, (y1+y2)/2]

Distance:

Distance between two points:
Consider two points (X1,Y1) and (X2, Y2) then the distance between these two points is determined by the formula D=((X2-X1)2 + (Y2-Y1)2)1/2

Distance between a point and a line:
We have a point (X0, Y0) and a line rx+sy+t=0, where r, s, t were chosen to satisfy the equation r2+s2=1. The line which is perpendicular to the given line and contains the given point is –sx+ry+(sx0+ry0). We can determine the intersection point of the original line and this perpendicular. i.e.,(s(sx0-ry0)-rt, -st-r(sx0-ry0)).

Then the distance between the above intersection point and the given point is nothing but the distance between the point and the line.

L= ({x0-[s(sx0-ry0)-rt]}2 + {y0-[-st-r(sx0-ry0)]}2)1/2. This will reduced to the form L=|rx0+sy0+t|. i.e., it is just the magnitude of the value obtained by substituting the coordinates of the point into the expression for the line. When the expression is zero, the point is on the line, while other values give the distance of the point from the line.