Initial data commit

Task/Find-if-a-point-is-within-a-triangle/Python/find-if-a-point-is-within-a-triangle.py

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+""" find if point is in a triangle """
+
+from sympy.geometry import Point, Triangle
+
+def sign(pt1, pt2, pt3):
+    """ which side of plane cut by line (pt2, pt3) is pt1 on? """
+    return (pt1.x - pt3.x) * (pt2.y - pt3.y) - (pt2.x - pt3.x) * (pt1.y - pt3.y)
+
+
+def iswithin(point, pt1, pt2, pt3):
+    """
+    Determine if point is within triangle formed by points p1, p2, p3.
+    If so, the point will be on the same side of each of the half planes
+    defined by vectors p1p2, p2p3, and p3p1. zval is positive if outside,
+    negative if inside such a plane. All should be positive or all negative
+    if point is within the triangle.
+    """
+    zval1 = sign(point, pt1, pt2)
+    zval2 = sign(point, pt2, pt3)
+    zval3 = sign(point, pt3, pt1)
+    notanyneg = zval1 >= 0 and zval2 >= 0 and zval3 >= 0
+    notanypos = zval1 <= 0 and zval2 <= 0 and zval3 <= 0
+    return notanyneg or notanypos
+
+if __name__ == "__main__":
+    POINTS = [Point(0, 0)]
+    TRI = Triangle(Point(1.5, 2.4), Point(5.1, -3.1), Point(-3.8, 0.5))
+    for pnt in POINTS:
+        a, b, c = TRI.vertices
+        isornot = "is" if iswithin(pnt, a, b, c) else "is not"
+        print("Point", pnt, isornot, "within the triangle", TRI)