Task: Total circles area







Python: from collections import namedtuple

Circle = namedtuple("Circle", "x y r")

circles = [
    Circle( 1.6417233788,  1.6121789534, 0.0848270516),
    Circle(-1.4944608174,  1.2077959613, 1.1039549836),
    Circle( 0.6110294452, -0.6907087527, 0.9089162485),
    Circle( 0.3844862411,  0.2923344616, 0.2375743054),
    Circle(-0.2495892950, -0.3832854473, 1.0845181219),
    Circle( 1.7813504266,  1.6178237031, 0.8162655711),
    Circle(-0.1985249206, -0.8343333301, 0.0538864941),
    Circle(-1.7011985145, -0.1263820964, 0.4776976918),
    Circle(-0.4319462812,  1.4104420482, 0.7886291537),
    Circle( 0.2178372997, -0.9499557344, 0.0357871187),
    Circle(-0.6294854565, -1.3078893852, 0.7653357688),
    Circle( 1.7952608455,  0.6281269104, 0.2727652452),
    Circle( 1.4168575317,  1.0683357171, 1.1016025378),
    Circle( 1.4637371396,  0.9463877418, 1.1846214562),
    Circle(-0.5263668798,  1.7315156631, 1.4428514068),
    Circle(-1.2197352481,  0.9144146579, 1.0727263474),
    Circle(-0.1389358881,  0.1092805780, 0.7350208828),
    Circle( 1.5293954595,  0.0030278255, 1.2472867347),
    Circle(-0.5258728625,  1.3782633069, 1.3495508831),
    Circle(-0.1403562064,  0.2437382535, 1.3804956588),
    Circle( 0.8055826339, -0.0482092025, 0.3327165165),
    Circle(-0.6311979224,  0.7184578971, 0.2491045282),
    Circle( 1.4685857879, -0.8347049536, 1.3670667538),
    Circle(-0.6855727502,  1.6465021616, 1.0593087096),
    Circle( 0.0152957411,  0.0638919221, 0.9771215985)]

def main():
    
    x_min = min(c.x - c.r for c in circles)
    x_max = max(c.x + c.r for c in circles)
    y_min = min(c.y - c.r for c in circles)
    y_max = max(c.y + c.r for c in circles)

    box_side = 500

    dx = (x_max - x_min) / box_side
    dy = (y_max - y_min) / box_side

    count = 0

    for r in xrange(box_side):
        y = y_min + r * dy
        for c in xrange(box_side):
            x = x_min + c * dx
            if any((x-circle.x)**2 + (y-circle.y)**2 <= (circle.r ** 2)
                   for circle in circles):
                count += 1

    print "Approximated area:", count * dx * dy

main()


VB: Public c As Variant
Public pi As Double
Dim arclists() As Variant
Public Enum circles_
    xc = 0
    yc
    rc
End Enum
Public Enum arclists_
    rho
    x_
    y_
    i_
End Enum
Public Enum shoelace_axis
    u = 0
    v
End Enum
Private Sub give_a_list_of_circles()
    c = Array(Array(1.6417233788, 1.6121789534, 0.0848270516), _
    Array(-1.4944608174, 1.2077959613, 1.1039549836), _
    Array(0.6110294452, -0.6907087527, 0.9089162485), _
    Array(0.3844862411, 0.2923344616, 0.2375743054), _
    Array(-0.249589295, -0.3832854473, 1.0845181219), _
    Array(1.7813504266, 1.6178237031, 0.8162655711), _
    Array(-0.1985249206, -0.8343333301, 0.0538864941), _
    Array(-1.7011985145, -0.1263820964, 0.4776976918), _
    Array(-0.4319462812, 1.4104420482, 0.7886291537), _
    Array(0.2178372997, -0.9499557344, 0.0357871187), _
    Array(-0.6294854565, -1.3078893852, 0.7653357688), _
    Array(1.7952608455, 0.6281269104, 0.2727652452), _
    Array(1.4168575317, 1.0683357171, 1.1016025378), _
    Array(1.4637371396, 0.9463877418, 1.1846214562), _
    Array(-0.5263668798, 1.7315156631, 1.4428514068), _
    Array(-1.2197352481, 0.9144146579, 1.0727263474), _
    Array(-0.1389358881, 0.109280578, 0.7350208828), _
    Array(1.5293954595, 0.0030278255, 1.2472867347), _
    Array(-0.5258728625, 1.3782633069, 1.3495508831), _
    Array(-0.1403562064, 0.2437382535, 1.3804956588), _
    Array(0.8055826339, -0.0482092025, 0.3327165165), _
    Array(-0.6311979224, 0.7184578971, 0.2491045282), _
    Array(1.4685857879, -0.8347049536, 1.3670667538), _
    Array(-0.6855727502, 1.6465021616, 1.0593087096), _
    Array(0.0152957411, 0.0638919221, 0.9771215985))
    pi = WorksheetFunction.pi()
End Sub
Private Function shoelace(s As Collection) As Double
    
    
    
    
    
    
    Dim t As Double
    If s.Count > 2 Then
        s.Add s(1)
        For i = 1 To s.Count - 1
            t = t + s(i + 1)(u) * s(i)(v) - s(i)(u) * s(i + 1)(v)
        Next i
    End If
    shoelace = t / 2
End Function
Private Sub arc_sub(acol As Collection, f0 As Double, u0 As Double, v0 As Double, _
    f1 As Double, u1 As Double, v1 As Double, this As Integer, j As Integer)
    
    
    If acol.Count = 0 Then Exit Sub 
    Debug.Assert acol.Count Mod 2 = 0
    Debug.Assert f0 <> f1
    If f1 = pi Or f1 + pi < 5E-16 Then f1 = -f1
    If f0 = pi Or f0 + pi < 5E-16 Then f0 = -f0
    If f0 < f1 Then
        
        
        
        If f1 < acol(1)(rho) Or f0 > acol(acol.Count)(rho) Then Exit Sub 
        i = acol.Count + 1
        start = 1
        Do
            i = i - 1
        Loop Until f1 > acol(i)(rho)
        If i Mod 2 = start Then
            acol.Add Array(f1, u1, v1, j), after:=i
        End If
        i = 0
        Do
            i = i + 1
        Loop Until f0 < acol(i)(rho)
        If i Mod 2 = 1 - start Then
            acol.Add Array(f0, u0, v0, j), before:=i
            i = i + 1
        End If
        Do While acol(i)(rho) < f1
            acol.Remove i
            If i > acol.Count Then Exit Do
        Loop
    Else
        start = 1
        If f0 > acol(1)(rho) Then
            i = acol.Count + 1
            Do
                i = i - 1
            Loop While f0 < acol(i)(0)
            If f0 = pi Then
                acol.Add Array(f0, u0, v0, j), before:=i
            Else
                If i Mod 2 = start Then
                    acol.Add Array(f0, u0, v0, j), after:=i
                End If
            End If
        End If
        If f1 <= acol(acol.Count)(rho) Then
            i = 0
            Do
                i = i + 1
            Loop While f1 > acol(i)(rho)
            If f1 + pi < 5E-16 Then
                acol.Add Array(f1, u1, v1, j), after:=i
            Else
                If i Mod 2 = 1 - start Then
                    acol.Add Array(f1, u1, v1, j), before:=i
                End If
            End If
        End If
        Do While acol(acol.Count)(rho) > f0 Or acol(acol.Count)(i_) = -1
            acol.Remove acol.Count
            If acol.Count = 0 Then Exit Do
        Loop
        If acol.Count > 0 Then
            Do While acol(1)(rho) < f1 Or (f1 = -pi And acol(1)(i_) = this)
                acol.Remove 1
                If acol.Count = 0 Then Exit Do
            Loop
        End If
    End If
End Sub
Private Sub circle_cross()
    ReDim arclists(LBound(c) To UBound(c))
    Dim alpha As Double, beta As Double
    Dim x3 As Double, x4 As Double, y3 As Double, y4 As Double
    Dim i As Integer, j As Integer
    For i = LBound(c) To UBound(c)
        Dim arccol As New Collection
        
        
        
        
        
        
        
        
        
        arccol.Add Array(-pi, c(i)(xc) - c(i)(r), c(i)(yc), i)
        arccol.Add Array(pi, c(i)(xc) - c(i)(r), c(i)(yc), -1)
        For j = LBound(c) To UBound(c)
            If i <> j Then
                x0 = c(i)(xc)
                y0 = c(i)(yc)
                r0 = c(i)(rc)
                x1 = c(j)(xc)
                y1 = c(j)(yc)
                r1 = c(j)(rc)
                d = Sqr((x0 - x1) ^ 2 + (y0 - y1) ^ 2)
                
                If d >= r0 + r1 Or d <= Abs(r0 - r1) Then
                    
                Else
                    a = (r0 ^ 2 - r1 ^ 2 + d ^ 2) / (2 * d)
                    h = Sqr(r0 ^ 2 - a ^ 2)
                    x2 = x0 + a * (x1 - x0) / d
                    y2 = y0 + a * (y1 - y0) / d
                    x3 = x2 + h * (y1 - y0) / d
                    y3 = y2 - h * (x1 - x0) / d
                    alpha = WorksheetFunction.Atan2(x3 - x0, y3 - y0)
                    x4 = x2 - h * (y1 - y0) / d
                    y4 = y2 + h * (x1 - x0) / d
                    beta = WorksheetFunction.Atan2(x4 - x0, y4 - y0)
                    
                    
                    
                    
                    arc_sub arccol, alpha, x3, y3, beta, x4, y4, i, j
                End If
            End If
        Next j
        Set arclists(i) = arccol
        Set arccol = Nothing
    Next i
End Sub
Private Sub make_path()
    Dim pathcol As New Collection, arcsum As Double
    i0 = UBound(arclists)
    finished = False
    Do While True
        arcsum = 0
        Do While arclists(i0).Count = 0
            i0 = i0 - 1
        Loop
        j0 = arclists(i0).Count
        next_i = i0
        next_j = j0
        Do While True
            x = arclists(next_i)(next_j)(x_)
            y = arclists(next_i)(next_j)(y_)
            pathcol.Add Array(x, y)
            prev_i = next_i
            prev_j = next_j
            If arclists(next_i)(next_j - 1)(i_) = next_i Then
                
                next_j = arclists(next_i).Count - 1
                If next_j = 1 Then Exit Do 
            Else
                next_j = next_j - 1
            End If
            
            r = c(next_i)(rc)
            a1 = arclists(next_i)(prev_j)(rho)
            a2 = arclists(next_i)(next_j)(rho)
            If a1 > a2 Then
                alpha = a1 - a2
            Else
                alpha = 2 * pi - a2 + a1
            End If
            arcsum = arcsum + r * r * (alpha - Sin(alpha)) / 2
            
            next_i = arclists(next_i)(next_j)(i_)
            next_j = arclists(next_i).Count
            If next_j = 0 Then Exit Do 
            Do While arclists(next_i)(next_j)(i_) <> prev_i
                
                next_j = next_j - 1
            Loop
            If next_i = i0 And next_j = j0 Then
                finished = True
                Exit Do
            End If
        Loop
        If finished Then Exit Do
        i0 = i0 - 1
        Set pathcol = Nothing
    Loop
    Debug.Print shoelace(pathcol) + arcsum
End Sub
Public Sub total_circles()
    give_a_list_of_circles
    circle_cross
    make_path
End Sub