Page 29 - Computer Graphics

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Line Drawing Algorithms

Slope-intercept equation for a straight line
y=mx+c
Where m represents the slope of the line and c as the y intercept

Given that the two endpoints of a line segment are steadied at positions (x1 , y1)
and (x2 , y2)

Determine the values of the slope m and y intercept c with the help of this formula
c=y1 - m.x1 > m= (y2-y1) (x2-x1)

1. slope magnitudes m < 1 dx can be set proportional to a small horizontal
deflection voltage
2. slope magnitudes m > 1 dy can be set proportional to a small vertical
deflection voltage
3. slope magnitudes m = 1 , dx=dy can be set proportional to a horizontal and
vertical deflection voltage equal

x1
x2

x1 x2

Digital differential analyser algorithm (DDA)
The digital differential analyser (DDA) is a scan-conversion line algorithm based
on calculating either dy , (dy = dx/m) or dx , (dx = dy/m) using We sample the
line at unit in terrals in one coordinate and determine corresponding integer
values nearest the line path for the other coordinate.

1. Slope is less than or equal to 1 (m≥1), we sample at unit x intervals (dx =

1) and compute each successive y value.
Yk+1 = Yk+ m
2. Subscript k takes integer values starting from 1, for the first point, and

increases by 1 until the final endpoint is reached.
3. m can be any real number between 0 to 1.
4. y values must be rounded to the net integer.

1. When slope is greater than 1 (m > 1) .
2. Then calculate each succeeding x value

Xk+1 = Xk + 1/m