Draw a line using the Midpoint algorithm where the starting point is (32, 35) and the ending point is (41, 41).

Theory: The Mid-Point line plotting algorithm was introduced by “Pitway and Van Aken.” It is an incremental line drawing algorithm. In this algorithm, we perform incremental calculations. The calculations are based on the previous step to find the value of the next point. We perform the same process for each step.

The Midpoint Line Algorithm is designed for efficiency and simplicity when drawing lines on a pixel grid. It avoids the need for floating-point calculations or trigonometric functions, making it suitable for real-time graphics.

The decision parameter P is crucial in determining whether the next pixel should move horizontally (x) or diagonally (x and y) based on the relative positions of the endpoint and the line. When P is positive or zero, it means the midpoint is above or on the actual line, so we move diagonally. When P is negative, it means the midpoint is below the actual line, so we move horizontally.

By following this process, the algorithm efficiently plots the points that best approximate the line between the given start and end points, making it a preferred choice for line drawing in computer graphics.

Input:

• Starting point (x1, y1) and ending point (x2, y2) of the line.

Output:

• A set of pixel coordinates (x, y) approximating the line between (x1, y1) and (x2, y2).

Algorithm:

1. Initialize variables:

• x to x1, y to y1.

• Calculate differences: dx = x2 - x1, dy = y2 - y1.

• Calculate the decision parameter P: P = 2 * dy - dx.

2. Plot the starting point (x, y).

3. Loop:

• While x < x2, update the pixel coordinates and P:

• If P < 0, increment x by 1, update P.

• If P ≥ 0, increment both x and y by 1, update P.

4. Continue looping until x ≥ x2.

5. The line is complete.

The algorithm efficiently draws lines by considering the relationship between the decision parameter P and the line's slope, avoiding complex calculations like floating-point or trigonometric operations.

```
import matplotlib.pyplot as plt
print("Enter the value of x1")
x1 = int(input())
print("Enter the value of x2")
x2 = int(input())
print("Enter the value of y1")
y1 = int(input())
print("Enter the value of y2")
y2 = int(input())
dx = x2 - x1
dy = y2 - y1
dy2 = dy * 2
dk = dy2 - dx
dd1 = dy - dx
dd2 = 2 * dd1
if abs(dx) > abs(dy):
steps = abs(dx)
else:
steps = abs(dy)
xincrement = dx / steps
yincrement = dy / steps
xcoordinate = []
ycoordinate = []
i = 0
while i < steps:
i += 1
if dk < 0:
x1 = x1 + 1
y1 = y1
dk = dk + (2 * dy)
print("x1: ", x1, "y1:", y1)
xcoordinate.append(x1)
ycoordinate.append(y1)
else:
x1 = x1 + 1
y1 = y1 + 1
dk = dk + dd2
print("x1: ", x1, "y1:", y1)
xcoordinate.append(x1)
ycoordinate.append(y1)
plt.plot(xcoordinate, ycoordinate)
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.title("Mid Point Algorithm")
plt.show()
```

This Python code implements the Midpoint Line Drawing Algorithm, which is used to draw a straight line on a graphical display. Here's a explanation of the code:

Import the matplotlib.pyplot library for plotting.

Get user input for the coordinates of two points (x1, y1) and (x2, y2) to define the line.

Calculate the differences between the x-coordinates (dx) and y-coordinates (dy) of the two points, as well as the values dy2, dk, dd1, dd2, and steps.

Initialize empty lists xcoordinate and ycoordinate to store the coordinates of points on the line.

Use a loop that iterates steps times, where steps is determined by the steeper of the two slopes (dx or dy). This loop calculates and appends the coordinates of points along the line using the Midpoint Algorithm.

Within the loop, it checks the value of dk. If dk is less than 0, it updates the coordinates (x1, y1) and adjusts dk. If dk is greater than or equal to 0, it updates the coordinates (x1, y1) and adjusts dk.

It prints the updated coordinates (x1, y1) within each iteration of the loop.

After calculating all the points, it plots the line using plt.plot and labels the X and Y axes, and sets the plot title.

Finally, it displays the plot using plt.show().

This code essentially draws a line between two user-defined points using the Midpoint Line Drawing Algorithm and visualizes it using matplotlib.

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