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Consider line function f(x,y) = 3x - 2y-6+Z, where Z is your student number mod 3. a) By using DDA algorithm, b) By using Bresenham algorithm, Show your steps and find the pixels to be colored between x = -1 and x=(4+Z).

User Ryan Doom
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Answer:

To use the DDA algorithm, we need to determine the slope of the line and the increments for x and y. The slope of the line is given by:

m = (y2 - y1)/(x2 - x1)

In this case, we can rewrite the equation of the line as:

f(x,y) = 3x - 2y + (3-n) (where n is your student number mod 3)

Let's take two points on the line:

P1 = (-1, f(-1,y1)) and P2 = (4+n, f(4+n,y2))

where y1 and y2 are arbitrary values that we will choose later.

The coordinates of P1 are:

x1 = -1 y1 = (3*(-1) - 2y1 + (3-n)) / 2 = (-2y1 + n - 3) / 2

Similarly, the coordinates of P2 are:

x2 = 4 + n y2 = (3*(4+n) - 2y2 + (3-n)) / 2 = (3n - 2*y2 + 15) / 2

The slope of the line is:

m = (y2 - y1)/(x2 - x1) = (3n - 2y2 + 15 - n + 2*y1 - 3) / (4 + n - (-1))

Simplifying this expression, we get:

m = (n - 2y2 + 3y1 + 12) / (n + 5)

Now, we need to determine the increments for x and y. Since we are going from left to right, the increment for x is 1. We can then use the equation of the line to find the corresponding value of y for each value of x.

Starting from P1, we have:

x = -1 y = y1

For each subsequent value of x, we can increment y by:

y += m

And round to the nearest integer to get the pixel value. We repeat this process until we reach x = 4+n.

To use the Bresenham algorithm, we need to choose two points on the line such that the absolute value of the slope is less than or equal to 1. We can use the same points as before and rearrange the equation of the line as:

-2y = (3 - n) - 3

Step-by-step explanation:

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