BaseballSeam.rvb

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' BaseballSeam.rvb -- May 2012
' If this code works, it was written by Dale Fugier.
' If not, I don't know who wrote it.
' Works with Rhino 4.0 and Rhino 5.0.
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Option Explicit

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' Baseball
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Sub BaseballSeam()

	Dim a : a = 0.4
	Dim n : n = 40
  
	Dim t0 : t0 = 0.0
	Dim t1 : t1 = 4.0 * Rhino.PI
  
	Dim pts()
	ReDim pts(n)
  
	Dim u0 : u0 = 0
	Dim u1 : u1 = UBound(pts)

	Dim i, t, x
	For i = u0 To u1
		x = NormalizedAt(u0, u1, i)
		t = ParameterAt(t0, t1, x)
		pts(i) = PointAt(a, t)
		Rhino.Print Rhino.Pt2Str(pts(x))
	Next

	Call Rhino.AddInterpCurve(pts, 3, 3)

End Sub

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' PointAt
' Evaluates an ellipse at a parmeter
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Function PointAt(a, t)
	Dim p, pt(2)
	p = Rhino.PI
	pt(0) = Sin(p / 2 - (p / 2 - a) * Cos(t)) * Cos(t / 2 + a * Sin(2 * t))
	pt(1) = Sin(p / 2 - (p / 2 - a) * Cos(t)) * Sin(t / 2 + a * Sin(2 * t))
	pt(2) = Cos(p / 2 - (p / 2 - a) * Cos(t))
	PointAt = pt
End Function

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' ParameterAt
' Converts a normalized parameter to an interval value
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Function ParameterAt(t0, t1, x)
	ParameterAt = (1.0 - x) * t0 + x * t1
End Function

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' NormalizedAt
' Converts an interval value to a normalized parameter
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Function NormalizedAt(t0, t1, t)
	Dim x : x = t0
	If (t0 <> t1) Then
		If (t = t1) Then
			x = 1.0
		Else
			x = (t - t0) / (t1 - t0)
		End If
	End If
	NormalizedAt = x
End Function