Unfold Function.ipynb

Kernel: SageMath (stable)

def PlotFigures(Figure, FigSize):
    Plot = []
    P = Figure.columns()
    Plot = Plot + [line([ [P[i][0], P[i][1]], [P[i+1][0], P[i+1][1]] ], color='blue') for i in [0..len(P)-2]]
    show(sum(Plot), axes=False, aspect_ratio=1, figsize=FigSize)

def Vectorize(figure):
    C = figure.columns()
    vectorList = []
    for i in [0..len(C)-2]:
        vectorList = vectorList + [vector(C[i+1]-C[i])]
    return vectorList

def Cross(a,b):
    c = vector([a[1]*b[2]-a[2]*b[1], -a[0]*b[2]+a[2]*b[0], a[0]*b[1]-a[1]*b[0]])
    return c

def CheckConvex(figure):
    C = figure.columns()
    V = Vectorize(figure)
    L = len(C)
    CrossResults = []
    for i in [0..L-2]:
        a = V[i % (L-1)]              #vector([V[i][0], V[i][1], 0])
        b = V[(i+1) % (L-1)]          #vector([V[(i+1) % L-2][0], V[(i+1)% L-2][1],0])
        c = Cross(a,b)[2]
        if c == 0:
            CrossResults = CrossResults + [m]
        else:
            m = abs(c)/c
            CrossResults = CrossResults + [m]
    for j in [1..len(CrossResults)-1]:
        if CrossResults[0] == CrossResults[j] or CrossResults[j] == 0:
            Test = True
        else:
            Test = False
            break
    return Test

def FlipPoint(Adjacent1, point, Adjacent2):
    X_1 = Adjacent1[0]
    Y_1 = Adjacent1[1]
    X_2 = Adjacent2[0]
    Y_2 = Adjacent2[1]
    a = point[0]
    b = point[1]
    if (X_2 == X_1) and (Y_2 != Y_1):
        print 'A'
        c = a + 2*(X_2-a)
        d = b
    else:
        if (Y_2 == Y_1) and (X_2 != X_1):
            print 'B'
            c = a
            d = b + 2*(Y_2 - b)
        else:
            if (Y_2 == Y_1) and (X_2 == X_1):  # the two adjacents should never be equal because flipping point should always be after a case like that
                print 'you know what this means'
                c = 0
                d = 0
            else:
                print 'C'
                m = (Y_2-Y_1)/(X_2-X_1)
                c = (m*X_1-Y_1+(a/m)+b)/(m+(1/m))
                d =(-1/m)*(c-a)+b
    return vector([c,d,1])

def Unfold(Figure):
    n = 0
    L = len(Vectorize(Figure))     # number of vectors from point to point in order = number of vertices
    M = L                          # mod number
    NewFigure = copy(Figure)
    V = Vectorize(NewFigure)
    a = V[0]
    b = V[1]
    c = Cross(a,b)[2]
    while c == 0:
        n = n+1
        a = V[n]
        b = V[n+1]
        c = Cross(a,b)[2]
    s = abs(c)/c
    while CheckConvex(NewFigure) == False:
        n=n+1
        V = Vectorize(NewFigure)
        a = V[n % M]
        b = V[(n+1) % M]
        c = Cross(a,b)[2]
        if c == 0:
            m = 0
        else:
            m = abs(c)/c
        show(m)
        if m != s and m != 0:
            NewFigure[:,(n % M)] = FlipPoint(NewFigure.columns()[n % M], NewFigure.columns()[(n+1) % M], NewFigure.columns()[(n+2) % M])
            print 'something'
    return NewFigure

twist = column_matrix([
        [0,0,1],
        [1,1,1],
        [1,0,1],
        [0,1,1],
        [0,0,1]
    ])

PlotFigures(twist,4)

PlotFigures(Unfold(twist),4)

B
something

B
something

C
something

A
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

C
something

WARNING: Some output was deleted.

CheckConvex(NewFigure)

show(twist)