Smooth transformation of an arch to line

Hello everyone,

My problem is to create a set of curves with the same lenght that are gradual transformations of an arc into a straight line with the same start point as the arc.

I have the start point, direction and by function (R*Pi) the lenght of the resulting line and starting arch. The problem to solve is how to get the iterations inbetween (the white curves in the image).

If any one could help me with a way to formulate a function to do this I'd be ever so happy. It is a bit trickier that you might think.

Cheers,

Eric

Attachments:

BlendArctoLine.jpg, 46 KB

Replies to This Discussion

Permalink Reply by Giulio Piacentino on June 7, 2010 at 5:08am

Hi Eric,

could this be a method?

- Giulio
________________________
giulio@mcneel.com
McNeel Europe, Barcelona

Attachments:

arc-unroll.ghx, 105 KB

Permalink Reply by Giulio Piacentino on June 7, 2010 at 5:15am

Same, for Grasshopper 6.59. (There is no scripting involved)

Attachments:

arc-unroll-6-59.ghx, 104 KB

Permalink Reply by Eric Werner on June 7, 2010 at 7:17am

Thank you so much Giulio for you quick and elegant solution! I made it into a function for anyone else that might need it.

Private Sub RunScript(ByVal angle As Double, ByVal length As Double, ByVal sPt As On3dPoint, ByRef crv As Object)

' function for straightening an arc into a line

If angle = 0 Then

Dim ePt As New on3dpoint(spt.x, spt.y + length, spt.z)
crv = New OnLine(sPt, ePt)

Else

Dim division As Double = length / angle

Dim Origin As New On3dpoint(spt.x + division, spt.y, spt.z) '
Dim xAxis As New On3dVector(-1, 0, 0)
Dim yAxis As New On3dVector(0, 1, 0)

Dim Plane As New OnPlane(Origin, xAxis, yAxis)

crv = New Onarc(plane, division, angle)

End If

End Sub

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