Add Generalized Bresenham Line Algorithm (all octants) for Hacktoberfest

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()