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DVR & Dr. HS MIC College of Technology
**Course:
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B.Tech
**Specialization:
**Computer Science Engineering**Views:
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**16 days ago**

UNIT I - 2D PRIMITIVES
Output primitives – Line, Circle and Ellipse drawing algorithms - Attributes of
output primitives – Two dimensional Geometric transformation - Two dimensional
viewing – Line, Polygon, Curve and Text clipping algorithms
Introduction
A picture is completely specified by the set of intensities for the pixel positions in the
display. Shapes and colors of the objects can be described internally with pixel arrays
into the frame buffer or with the set of the basic geometric – structure such as straight
line segments and polygon color areas. To describe structure of basic object is referred to
as output primitives.
Each output primitive is specified with input co-ordinate data and other information about
the way that objects is to be displayed. Additional output primitives that can be used to
constant a picture include circles and other conic sections, quadric surfaces, Spline curves
and surfaces, polygon floor areas and character string.
Points and Lines
Point plotting is accomplished by converting a single coordinate position furnished by
an application program into appropriate operations for the output device. With a CRT
monitor, for example, the electron beam is turned on to illuminate the screen phosphor at
the selected location
Line drawing is accomplished by calculating intermediate positions along the line path
between two specified end points positions. An output device is then directed to fill in
these positions between the end points
Digital devices display a straight line segment by plotting discrete points between the two
end points. Discrete coordinate positions along the line path are calculated from the
equation of the line. For a raster video display, the line color (intensity) is then loaded
into the frame buffer at the corresponding pixel coordinates. Reading from the frame
buffer, the video controller then plots “the screen pixels”.
Pixel positions are referenced according to scan-line number and column number (pixel
position across a scan line). Scan lines are numbered consecutively from 0, starting at the
bottom of the screen; and pixel columns are numbered from 0, left to right across each
scan line
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Figure : Pixel Postions reference by scan line number and column number
To load an intensity value into the frame buffer at a position corresponding to column x
along scan line y,
setpixel (x, y)
To retrieve the current frame buffer intensity setting for a specified location we use a low
level function
getpixel (x, y)
Line Drawing Algorithms
Digital Differential Analyzer (DDA) Algorithm
Bresenham’s Line Algorithm
Parallel Line Algorithm
The Cartesian slope-intercept equation for a straight line is
y=m.x+b
(1)
Where m as slope of the line and b as the y intercept
Given that the two endpoints of a line segment are specified at positions (x1,y1) and
(x2,y2) as in figure we can determine the values for the slope m and y intercept b with the
following calculations
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Figure : Line Path between endpoint positions (x1,y1) and (x2,y2)
m = ∆y / ∆x = y2-y1 / x2 - x1
(2)
b= y1 - m . x1
(3)
For any given x interval ∆x along a line, we can compute the corresponding y interval
∆y
∆y= m ∆x
(4)
We can obtain the x interval ∆x corresponding to a specified ∆y as
∆ x = ∆ y/m
(5)
For lines with slope magnitudes |m| < 1, ∆x can be set proportional to a small
horizontal deflection voltage and the corresponding vertical deflection is then set
proportional to ∆y as calculated from Eq (4).
For lines whose slopes have magnitudes |m | >1 , ∆y can be set proportional to a small
vertical deflection voltage with the corresponding horizontal deflection voltage set
proportional to ∆x, calculated from Eq (5)
For lines with m = 1,
are equal.
∆x = ∆y and the horizontal and vertical deflections voltage
Figure : Straight line Segment with five sampling positions along the x axis between x1 and x2
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Digital Differential Analyzer (DDA) Algortihm
The digital differential analyzer (DDA) is a scan-conversion line algorithm based on
calculation either ∆y or ∆x
The line at unit intervals in one coordinate and determine corresponding integer values
nearest the line path for the other coordinate.
A line with positive slop, if the slope is less than or equal to 1, at unit x intervals (∆x=1)
and compute each successive y values as
yk+1 = yk + m
(6)
Subscript k takes integer values starting from 1 for the first point and increases by 1 until
the final endpoint is reached. m can be any real number between 0 and 1 and, the
calculated y values must be rounded to the nearest integer
For lines with a positive slope greater than 1 we reverse the roles of x and y, (∆y=1) and
calculate each succeeding x value as
xk+1 = xk + (1/m)
(7)
Equation (6) and (7) are based on the assumption that lines are to be processed from the
left endpoint to the right endpoint.
If this processing is reversed, ∆x=-1 that the starting endpoint is at the right
yk+1 = yk – m
(8)
When the slope is greater than 1 and ∆y = -1 with
xk+1 = xk-1(1/m)
(9)
If the absolute value of the slope is less than 1 and the start endpoint is at the left, we set
∆x = 1 and calculate y values with Eq. (6)
When the start endpoint is at the right (for the same slope), we set ∆x = -1 and obtain y
positions from Eq. (8). Similarly, when the absolute value of a negative slope is greater
than 1, we use ∆y = -1 and Eq. (9) or we use ∆y = 1 and Eq. (7).
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