[triangle centers] calculate different center points for a triangle. #geometry #python

20240529_triangle.py

def H(z,a,b,l):
    '''
    from https://codegolf.stackexchange.com/questions/11767/the-centers-of-a-triangle

     1 - Incenter
     2 - Centroid
     3 - Circumcenter
     4 - Orthocenter
     5 - Equation of Euler Line
        (if the Euler Line is vertical, output the `x` value of the line
        (e.g. output `5` if the equation of the line is `x = 5`))
    '''
    c=complex
    T=lambda A,B: abs(c(*A)-c(*B))
    d=T(z,a)
    e=T(z,b)
    f=T(a,b)
    g=[((a[0]+b[0])/2,(a[1]+b[1])/2)
        for a,b in[[a,b],[z,a],[b,z]]
    ]
    E=(z[0]+a[0]+b[0])/3
    F=(z[1]+a[1]+b[1])/3
    m=lambda f:[(a,0) if (b[1][0]-b[0][0])==0 else (a,-1/((b[1][1]-b[0][1])/(b[1][0]-b[0][0])))if(b[1][1]-b[0][1])else''for a,b in zip(f,[[a,b],[z,a],[b,z]])]
    i=[u for u in m(g)if u!='']
    C=i[0][1]
    D=i[0][0][1]-(C*i[0][0][0])
    A=i[1][1]
    B=i[1][0][1]-(A*i[1][0][0])
    G=(B-D)/(C-A)
    H=C*G+D
    j=[u for u in m([z,b,a])if u!='']
    C=j[0][1]
    D=j[0][0][1]-(C*j[0][0][0])
    A=j[1][1]
    B=j[1][0][1]-(A*j[1][0][0])
    I=(B-D)/(C-A)
    J=C*I+D
    K,L=[((d*b[o])+(e*a[o])+(f*z[o]))/sum([d,e,f]) for o in [0,1]]
    a=(H-J)/(G-I) if (G-I) else ''
    b=H-(a*G) if a!=''else G
    print(['',(K,L),(E,F),(G,H),(I,J),[b,'%sx+%s'%(a,b)][a!='']][l])
    return (I,J)