Add Generalized Bresenham Line Algorithm (all octants) for Hacktoberfest

Author: devdandekar24

graphics/bresenham_line_generalized.py

@@ -0,0 +1,64 @@
+"""
+Generalized Bresenham's Line Drawing Algorithm
+----------------------------------------------
+
+Handles all possible line slopes and directions.
+
+Reference:
+https://www.geeksforgeeks.org/dsa/bresenhams-line-generation-algorithm/
+
+>>> generalized_bresenham_line((0, 0), (5, 3))
+[(0, 0), (1, 1), (2, 1), (3, 2), (4, 2), (5, 3)]
+>>> generalized_bresenham_line((5, 5), (2, 3))
+[(5, 5), (4, 4), (3, 4), (2, 3)]
+"""
+
+import matplotlib.pyplot as plt
+
+
+def generalized_bresenham_line(
+    p1: tuple[int, int], p2: tuple[int, int]
+) -> list[tuple[int, int]]:
+    x1, y1 = p1
+    x2, y2 = p2
+    dx = abs(x2 - x1)
+    dy = abs(y2 - y1)
+    sx = 1 if x1 < x2 else -1
+    sy = 1 if y1 < y2 else -1
+    err = dx - dy
+
+    points = []
+
+    while True:
+        points.append((x1, y1))
+        if x1 == x2 and y1 == y2:
+            break
+        e2 = 2 * err
+        if e2 > -dy:
+            err -= dy
+            x1 += sx
+        if e2 < dx:
+            err += dx
+            y1 += sy
+
+    return points
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    x1 = int(input("Enter x1: "))
+    y1 = int(input("Enter y1: "))
+    x2 = int(input("Enter x2: "))
+    y2 = int(input("Enter y2: "))
+
+    points = generalized_bresenham_line((x1, y1), (x2, y2))
+    print("Generated points:", points)
+
+    xs, ys = zip(*points)
+    plt.plot(xs, ys, marker="o")
+    plt.title("Generalized Bresenham's Line Algorithm (All Slopes)")
+    plt.grid()
+    plt.show()