pyFindOddTriangle

# Given the coordinates of the points of a set of triangles, find the odd one out
# The triangles are of similar shapes, but different sizes and rotations
# One triangle is a mirror image
# Mike Kerry - August 2022
# [email protected]

import math
rad2deg = 180/math.pi


def get_length_and_slope(t, w, v):
    # Compute the length of one side of a triangle
    # and the bearing of the end point from the start point
    # t points to a triangle. w and v refer to 2 points of the triangle

    dx = t[v][0] - t[w][0]      # x-axis distance between points
    dy = t[v][1] - t[w][1]      # y-axis distance between points

    # math.hypot calculates a hypotoneuse    sqrt(dx*dx + dy*dy)
    lgth = math.hypot(dx, dy)

    # atan2 computes a bearing between 2 points, between -pi and +pi radians
    # given x and y axis distances dx and dy between the 2 points
    ang = rad2deg * math.atan2(dy, dx)
    return lgth, ang


a = [(3.0, 6.0), (3.0, 3.0), (7.0, 3.0)]
b = [(4.4, 3.2), (4.4, 5.0), (2.0, 5.0)]
c = [(3.0, 5.2), (5.4, 5.2), (5.4, 2.0)]
d = [(4.0, 1.0), (5.5, 1.0), (5.5, 3.0)]
arr = [a, b, c, d]


for j, tri in enumerate(arr):
    print("\nTRIANGLE: ", chr(ord('A') + j))       # TRIANGLE: A thru D
    # Assume the points of the triangle are labelled p, q and r
    # Hence the sides are pq, qr, and pr
    p, q, r = 0, 1, 2
    lenpq, slopepq = get_length_and_slope(tri, p, q)
    lenqr, slopeqr = get_length_and_slope(tri, q, r)
    lenpr, slopepr = get_length_and_slope(tri, p, r)
    circ = lenpq + lenqr + lenpr    # total circumference of triangle
    # for each side, compute its proportion of the overall circumference
    percentpq = lenpq * 100 / circ
    percentqr = lenqr * 100 / circ
    percentpr = lenpr * 100 / circ
    print(f"Percentages: {percentpq:.0f} {percentqr:.0f} {percentpr:.0f}")

    # compute the directed angle at point q (between sides pq and qr)
    angleq = slopeqr - slopepq
    print(f"Angle q: {angleq:.1f}")

# Results:
# TRIANGLE:  A
# Percentages: 25 33 42
# Angle q: 90.0
#
# TRIANGLE:  B
# Percentages: 25 33 42
# Angle q: 90.0
#
# TRIANGLE:  C
# Percentages: 25 33 42
# Angle q: -90.0
#
# TRIANGLE:  D
# Percentages: 25 33 42
# Angle q: 90.0

# From the above, we can see that triangle C is the odd one.
# Its angle 'q' is reversed compared to the other three triangles

print(math.pi)