Created
July 18, 2024 22:07
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Checks if points are in a triangle and draws it
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| import math | |
| import matplotlib.pyplot as plt | |
| def distance(x1, y1, x2, y2): | |
| return math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2) | |
| def is_triangle_non_degenerate(ax, ay, bx, by, cx, cy): | |
| # Calculate the lengths of the sides | |
| ab = distance(ax, ay, bx, by) | |
| bc = distance(bx, by, cx, cy) | |
| ca = distance(cx, cy, ax, ay) | |
| # Check the triangle inequality theorem | |
| return ab + bc > ca and ab + ca > bc and bc + ca > ab | |
| def is_point_in_triangle(px, py, ax, ay, bx, by, cx, cy): | |
| # Use the sign of areas method to check if the point is inside the triangle | |
| def sign(x1, y1, x2, y2, x3, y3): | |
| return (x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3) | |
| b1 = sign(px, py, ax, ay, bx, by) < 0.0 | |
| b2 = sign(px, py, bx, by, cx, cy) < 0.0 | |
| b3 = sign(px, py, cx, cy, ax, ay) < 0.0 | |
| return b1 == b2 == b3 | |
| # Function to check both points p and q | |
| def check_points_in_triangle(ax, ay, bx, by, cx, cy, px, py, qx, qy): | |
| # Check if the triangle is non-degenerate | |
| if not is_triangle_non_degenerate(ax, ay, bx, by, cx, cy): | |
| return 0 | |
| # Check if point p is in the triangle | |
| p_in_triangle = is_point_in_triangle(px, py, ax, ay, bx, by, cx, cy) | |
| # Check if point q is in the triangle | |
| q_in_triangle = is_point_in_triangle(qx, qy, ax, ay, bx, by, cx, cy) | |
| if p_in_triangle and q_in_triangle: | |
| return 3 | |
| elif p_in_triangle: | |
| return 2 | |
| elif q_in_triangle: | |
| return 1 | |
| else: | |
| return 4 | |
| # Example usage | |
| ax, ay = 0, 0 | |
| bx, by = 5, 0 | |
| cx, cy = 0, 5 | |
| px, py = 1, 1 | |
| qx, qy = 6, 6 | |
| result = check_points_in_triangle(ax, ay, bx, by, cx, cy, px, py, qx, qy) | |
| # Plotting the triangle and points | |
| plt.figure() | |
| plt.plot([ax, bx], [ay, by], 'k-') | |
| plt.plot([bx, cx], [by, cy], 'k-') | |
| plt.plot([cx, ax], [cy, ay], 'k-') | |
| plt.scatter([ax, bx, cx], [ay, by, cy], color='blue', label='Triangle vertices') | |
| plt.scatter(px, py, color='green' if result in [2, 3] else 'red', label='Point p') | |
| plt.scatter(qx, qy, color='green' if result in [1, 3] else 'red', label='Point q') | |
| plt.legend() | |
| plt.xlabel('x') | |
| plt.ylabel('y') | |
| plt.title('Triangle and Points p and q') | |
| plt.grid(True) | |
| plt.show() |
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