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Saturday, 15 February 2014

Computer Graphics Notes- Lab 11 - Line Drawing

LINE DRAWING

Basic Concepts of Line Drawing

Before discussing specific line drawing algorithms it is useful to note the general requirements for such algorithms.
●      The line should appear as a straight line.
 








Vertical and             Line with other orientation
horizontal lines

Horizontal and vertical lines are straight and have same width. The line with any other orientation is neither straight nor has same width. In this case we have to accept approximate pixels in such situations.

Rasterization of straight lines.



Rasterization yields uneven brightness: Horizontal and vertical lines appear brighter than the 45° lines.
For fixing so, we would need:
1. Calculation of square roots (increasing CPU time)
2. Multiple brigthness levels



=
Compromise:
1. Calculate only an approximate line
2. Use integer arithmetic
3. Use incremental methods

Line should terminate accurately.


Unless they are plotted correctly, they may terminate at the wrong place.
•       Line should have constant density.
To maintain constant density dots should be equally spaced.
•       The line should be drawn rapidly.
This implies that we have to draw line using minimum of computation.


Pixel plotting
Nine pixels are there in 3 rows and columns. Pixels are designated by the location of their centers in the pixel grid.



Line - Drawing Algorithm
The Cartesian slope - intercept equation for a straight line is
y = m   x + b
with m representing the 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). We can determine values for the slope m and y intercept b with the following calculations:
                                           y2  -  y1
m = ---------------
                                           x2 - x1

For any given x interval ∆x along a line, we can compute the corresponding y interval ∆y as
y = m x
Similarly, we can obtain the x interval ∆x corresponding to a specified ∆y as
           ∆y
∆x = ----------
            m


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