Page 54 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Lab on Computer Graphics

Notes The line drawing algorithm using the Digital Differential Analyses (DDA) method. Select any
two points on the pseudo screen with mouse clicks. The ‘ideal line’ is first drawn as thin blue
straight line between the two selected points. Determining suitable intermediate pixels using
the DDA algorithm enables the line to be drawn. Click ‘clear’ to refresh the screen, and to select
a new pair of points.
Line Equation

The Cartesiand slop-intercept equation for a straight line is:
y = mx + b (1)
with
m-> slope

b-> y intercept
The 2 end points of a line segment are specified at a position(x 1 , y 1 )
Determine the values for the slope m and y intercept b with the following calculation.

Here, slope m:
m = ( y 2 – y 1 ) / ( x 2 – x 1 )
m = Dy / Dx (2)
y intercept b
b = y 1 – mx 1 (3)

• Algorithms for displaying straight line based on this equation
• y interval Dy from the equation
m = Dy / Dx
Dy = m Dx (4)

Similarly x interval Dx from the equation
m = Dy / Dx
Dx = Dy /m (5)

3.3.1 Line DDA Algorithm
• The digital differential analyzer (DDA) is a scan conversion line algorithm based on
calculation either Dy or Dx.
• The line at unit intervals is one coordinate and determine corresponding integer values
nearest line for the other coordinate.
• Consider first a line with positive slope.
Step 1
If the slope is less than or equal to 1, the unit x intervals Dx = 1 and compute each successive
y values.
Dx = 1
m = Dy / Dx

m = ( y 2 – y 1 ) / 1
m = (y k + 1 – y k ) /1
y k + 1 = y k + m (6)

48 LOVELY PROFESSIONAL UNIVERSITY