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Hallo zusammen,

ich arbeite mich gerade in die Transformationen beim Inventor ein. Gibt es noch andere Beispiele?

http://forums.autodesk.com/t5/net/getting-blocs-amp-solids-rotation-angle-in-3d-space/td-p/3140470

Solution

There is no direct way to get these angles via API. However, it should be possible to get them via the 4x4 homogeneous transformation matrix.

t11  t12  t13  tx
t21  t22  t23  ty
t31  t32  t33  tz
0      0      0    1

tx, ty, and tz represent the translations along x, y, and z directions.

From the values of other elements of the matrix, one can get the Eulerian/ Cardanian angles.

Public Function Acos(value) As Double
    Acos = Math.Atn(-value / Math.Sqr(-value * value + 1)) + 2 * Math.Atn(1)
End Function

Sub CalculateRotationAngles(ByVal oMatrix As Inventor.Matrix, ByRef aRotAngles() As Double)
    Const PI = 3.14159265358979
    Const TODEGREES As Double = 180 / PI

    Dim dB As Double
    Dim dC As Double
    Dim dNumer As Double
    Dim dDenom As Double
    Dim dAcosValue As Double
       
    Dim oRotate As Inventor.Matrix
    Dim oAxis As Inventor.Vector
    Dim oCenter As Inventor.Point
   
    Set oRotate = ThisApplication.TransientGeometry.CreateMatrix
    Set oAxis = ThisApplication.TransientGeometry.CreateVector
    Set oCenter = ThisApplication.TransientGeometry.CreatePoint

    oCenter.X = 0
    oCenter.Y = 0
    oCenter.Z = 0

    '
    ' Choose aRotAngles[0] about x which transforms axes[2] onto the x-z plane
    '
    dB = oMatrix.Cell(2, 3)
    dC = oMatrix.Cell(3, 3)

    dNumer = dC
    dDenom = Sqr(dB * dB + dC * dC)

    ' Make sure we can do the division.  If not, then axes[2] is already in the x-z plane
    If (Abs(dDenom) <= 0.000001) Then
        aRotAngles(0) = 0#
    Else
        If (dNumer / dDenom >= 1#) Then
            dAcosValue = 0#
        Else
            If (dNumer / dDenom <= -1#) Then
                dAcosValue = PI
            Else
                dAcosValue = Acos(dNumer / dDenom)
            End If
        End If
   
        aRotAngles(0) = Sgn(dB) * dAcosValue
        oAxis.X = 1
        oAxis.Y = 0
        oAxis.Z = 0
 
        Call oRotate.SetToRotation(aRotAngles(0), oAxis, oCenter)
        Call oMatrix.PreMultiplyBy(oRotate)
    End If

    '
    ' Choose aRotAngles[1] about y which transforms axes[3] onto the z axis
    '
    If (oMatrix.Cell(3, 3) >= 1#) Then
        dAcosValue = 0#
    Else
        If (oMatrix.Cell(3, 3) <= -1#) Then
            dAcosValue = PI
        Else
            dAcosValue = Acos(oMatrix.Cell(3, 3))
        End If
    End If

    aRotAngles(1) = Math.Sgn(-oMatrix.Cell(1, 3)) * dAcosValue
    oAxis.X = 0
    oAxis.Y = 1
    oAxis.Z = 0
    Call oRotate.SetToRotation(aRotAngles(1), oAxis, oCenter)
    Call oMatrix.PreMultiplyBy(oRotate)

    '
    ' Choose aRotAngles[2] about z which transforms axes[0] onto the x axis
    '
    If (oMatrix.Cell(1, 1) >= 1#) Then
        dAcosValue = 0#
    Else
        If (oMatrix.Cell(1, 1) <= -1#) Then
            dAcosValue = PI
        Else
            dAcosValue = Acos(oMatrix.Cell(1, 1))
        End If
    End If

    aRotAngles(2) = Math.Sgn(-oMatrix.Cell(2, 1)) * dAcosValue

    'if you want to get the result in degrees
    aRotAngles(0) = aRotAngles(0) * TODEGREES
    aRotAngles(1) = aRotAngles(1) * TODEGREES
    aRotAngles(2) = aRotAngles(2) * TODEGREES
End Sub

This code example is based on the theory from http://kwon3d.com/theory/euler/euler_angles.html

http://modthemachine.typepad.com/files/mathgeometry.pdf

http://aucache.autodesk.com/au2011/sessions/5840/class_handouts/v1_MA5840_Ekins.pdf

http://www.geometrictools.com/Source/Mathematics.html

Vielen Dank

Georg

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