ortho6.py

#
#import math
import matplotlib.pyplot as plt
def orthocenter_info(A, B, C):
    def line_equation(p1, p2):
        x1, y1 = p1
        x2, y2 = p2
        m = (y2 - y1) / (x2 - x1) if x2 != x1 else float('inf')
        b = y1 - m * x1 if m != float('inf') else None
        return m, b

    def perpendicular_line(point, m):
        x, y = point
        m_perp = -1 / m if m != 0 else float('inf')
        b_perp = y - m_perp * x if m_perp != float('inf') else None
        return (m_perp, b_perp)

    def intersection(m1, b1, m2, b2):
        if m1 == m2:
            return None  # Lines are parallel
        if m1 == float('inf'):
            x = b1
            y = m2 * x + b2
        elif m2 == float('inf'):
            x = b2
            y = m1 * x + b1
        else:
            x = (b2 - b1) / (m1 - m2)
            y = m1 * x + b1
        return (x, y)

    # Calculate equations of two altitudes. First get eqns of sides of triangle
    m_BC, b_BC = line_equation(B, C)
    m_AC, b_AC = line_equation(A, C)
    m_AB, b_AB = line_equation(A, B)

    m_A_perp, b_A_perp = perpendicular_line(A, m_BC)
    m_B_perp, b_B_perp = perpendicular_line(B, m_AC)
    m_C_perp, b_C_perp = perpendicular_line(C, m_AB)
    perp_lines = ( (m_BC,b_BC), (m_B_perp, b_B_perp),(m_C_perp, b_C_perp) )


    Afoot = intersection(m_A_perp,b_A_perp, m_BC,b_BC)

    Bfoot = intersection(m_B_perp,b_B_perp, m_AC,b_AC)

    Cfoot = intersection(m_C_perp,b_C_perp, m_AB,b_AB)

    feet = (Afoot,Bfoot,Cfoot)

    # Find the intersection of the two altitudes
    orthocenter = intersection(m_A_perp, b_A_perp, m_B_perp, b_B_perp)

    return orthocenter, perp_lines, feet

# Test the function
# vertexA = (0, 0)
# vertexB = (60, 10)
# vertexC = (30, 60)
#
# orthoInfo = orthocenter_info(vertexA, vertexB, vertexC)
# print("Result is: ",orthoInfo)
#
# orthocentrePoint, perpLines, altitudeFeet = orthoInfo
# orthcentrex, orthcentrey = orthocentrePoint
#
# fA,fB,fC = altitudeFeet
# fAx,fAy =fA
# fBx,fBy =fB
# fCx,fCy =fC
#
#
# fig, ax = plt.subplots(figsize=(6, 6))
# Ax,Ay = vertexA
# Bx,By = vertexB
# Cx,Cy = vertexC
# circle = plt.Circle((orthcentrex, orthcentrey), 0.5, fill=False, color='r')
# ax.add_artist(circle)
# ax.plot([Ax,Bx,Cx,Ax], [Ay,By,Cy,Ay], 'r-', linewidth=2) #this plots the triangle
# ax.plot([Ax,fAx], [Ay, fAy], 'r-', linewidth=1)
# ax.plot([Bx,fBx], [By, fBy], 'r-', linewidth=1)
# ax.plot([Cx,fCx], [Cy, fCy], 'r-', linewidth=1)
#
# plt.show()
#ortho5.py works ok 20/07/24