Determine true Axis of object [3D environment]

Question

5.00/5 (1 vote)

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My question this time is to figure out how to properly place (create) a cylinder in space to exactly fit into a line (so the line is exactly in the center of the cylinder). Here is what I am working with:

http://i60.tinypic.com/2njxa95.png

As you can see, I have tried to create the cylinders from the axis X (1,0,0), Y(0,1,0), and Z(0,0,1).

Some gave a different result than others.

I have both start and end points of the line [(x,y,z) values], the angle of it (degrees/rad)

As for the cylinder, I am able to create it based off of radius, height, location in space, workplane x and z axis.

I am able to rotate the cylinder using a function .SetRotate(Axis, vPoint, deg)

Which works based off an axis, location (same used to create) and the angle in degrees.

I am using the same angle value I am obtaining from the line, and my guess is I must somehow figure out the correct axis (the same one as the line).

I am trying to achieve the following: http://i62.tinypic.com/n62aa8.png[^]

If you need more information please let me know. Thanks.

EDIT: My code that might help:

VB

Dim PickObj As New VISIPick
        Dim FaceList As New VISIList
        Dim db As New VISIDatabase
        Dim OldElList As New VISIList

        '* new var
        Dim mwp, mpw, matT, matR As New VISIMatrix
        Dim P2 As New VISIPoint
        Dim Axis As New VISIVector
        '---

        'PickObj.Filter = SEARCH_SEGM
        PickObj.Message = "Pick a Line"
        'PickObj.MoreElements = True
        If PickObj.Pick = False Then
            Exit Sub
        End If
        'PickObj.ClearSelection()

        FaceList.Init(5, LTYPE_FACE)

        db.WorkDBKey = PickObj.PickedKey
        db.GetElement()

        'Make element variable compatible with workplane - add to list
        '*FaceList.AddItem(db.WorkElement)

        '*WPL.Create(FaceList)
        'Dim mwp, mpw As New VISIMatrix

        WPL.GetDefault()
        WPL.CreateFromZAxis(PickObj.PickedPoint, WPL.ZAxis)
        WPL.WorkPlaneWorld(mwp, mpw)

        If WPL.LastError <> V_NOERROR Then
            MsgBox(WPL.LastError)
            Exit Sub
        End If

        'Display existence of workplane
        lblDebug.Text = "(" & WPL.Origin.X.ToString() & "," & WPL.Origin.Y.ToString() & "," & WPL.Origin.Z.ToString() & ")" & vbNewLine & _
            WPL.XAxis.CX.ToString() & " " & WPL.XAxis.CY.ToString() & " " & WPL.XAxis.CZ.ToString() & vbNewLine & _
              " " & WPL.YAxis.CX.ToString() & " " & WPL.YAxis.CY.ToString() & " " & WPL.YAxis.CZ.ToString() & vbNewLine & _
              " " & WPL.ZAxis.CX.ToString() & " " & WPL.ZAxis.CY.ToString() & " " & WPL.ZAxis.CZ.ToString()

        'MsgBox(WPL.XAxis.CX.ToString() & " " & WPL.XAxis.CY.ToString() & " " & WPL.XAxis.CZ.ToString() & vbNewLine & _
        '      " " & WPL.YAxis.CX.ToString() & " " & WPL.YAxis.CY.ToString() & " " & WPL.YAxis.CZ.ToString() & vbNewLine & _
        '      " " & WPL.ZAxis.CX.ToString() & " " & WPL.ZAxis.CY.ToString() & " " & WPL.ZAxis.CZ.ToString())

        Dim x, y, z, rad, deg As Double

        x = db.WorkElement.EndPoint.X - db.WorkElement.StartPoint.X
        y = db.WorkElement.EndPoint.Y - db.WorkElement.StartPoint.Y
        z = db.WorkElement.EndPoint.Z - db.WorkElement.StartPoint.Z

        rad = (Math.Asin(z / Math.Sqrt((x ^ 2) + (y ^ 2) + (z ^ 2)))).ToString()
        deg = (rad * (180 / Math.PI)).ToString()

        If (deg > 0) Then
            vPoint.Put(db.WorkElement.StartPoint.X, db.WorkElement.StartPoint.Y, db.WorkElement.StartPoint.Z)
        Else
            vPoint.Put(db.WorkElement.EndPoint.X, db.WorkElement.EndPoint.Y, db.WorkElement.EndPoint.Z)
        End If
        lblDeg.Text = deg.ToString()

        SolFac.CreateCylinder(0.006, db.WorkElement.Length, vPoint, WPL.XAxis, WPL.ZAxis)
        vList.Init(10, LTYPE_BODY)

        Axis.Put(1, 0, 0)

        If SolFac.LastError <> V_NOERROR Then
            MsgBox(SolFac.LastError)
        Else
            vList.AddItem(SolFac.Result)
            mwp.SetRotate(Axis, vPoint, deg) 'rotate a body based off an angle
            'matT.SetTranslate(vPoint, P2) ' move body from one point to another
            'mwp.Mul(matR, matT) 'apply both
            SolFac.WorkMatrix = mwp
            SolFac.ApplyMatrix(vList)
            Appl.UpdateSolidsOnScreen()
        End If

Posted 27-Jan-15 4:50am

jk0391

Updated 28-Jan-15 7:29am

v3

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Comments

Sergey Alexandrovich Kryukov 27-Jan-15 15:22pm

If you mean that your red ray marked with green line around it represents "true axis", this notion remains undefined. You need to give normal mathematical definition of this notion. Your mention of "center of the sphere" is confusing, because it's not clear which sphere, you never depict anything like sphere.
—SA

jk0391 28-Jan-15 13:30pm

Sorry, I meant to say CYLINDER and not SPHERE. My mistake there. I updated the question. Basically, I need to generate this cylinder so it wraps around the line, the line being exactly in the center.

Sergey Alexandrovich Kryukov 28-Jan-15 13:49pm

All right. Anyway, you need clearer explanation and mathematically-strict definition of what you want to achieve. You just need to add more text, in more precise terms, face it. You need to define what exactly you mean by "true axis". Sorry, I cannot promise the solution, but I am nearly sure that no one will give your the solution before you provide much stricter and more detailed formulation of the problem.
—SA

Kenneth Haugland 28-Jan-15 14:21pm

http://gamedev.stackexchange.com/questions/34105/finding-the-normal-from-one-3d-vector-line-to-any-point-on-another-3d-vector-lin

Than its just a matter of calculating the desired point.

[no name] 28-Jan-15 15:57pm

Sorry maybe a question because the leak of my noob english: Does it mean in easy words, if you rotate your cylinder and rotate also the same the 'line' the resulted positions of both objects are not more longer what you expect? If this is right, then think about the 'rotation center' of both objects.

jk0391 28-Jan-15 16:00pm

Hi, thanks for your reply. The line cannot be moved/rotated. The cylinder is what I am positioning so it is exactly aligned around the line in space. Perhaps trying to trace my code will give you the numbers/values you are looking for?

Fredrik Bornander 28-Jan-15 16:43pm

If you take a vector that is the direction of the red line, in your code x, y, z, and call it Vr, then take the vector that is the direction the cylinder extends in before being rotated to match the red line (lets say [0,1,0], or whatever your CreateCylinder call yields), call that Vc.
I think that if you then get the angle between those vectors, call it A, then you'll want to rotate the cylinder A radians around the axis that is the cross product of Vr and Vc.

jk0391 29-Jan-15 9:33am

Hard to follow with what you said, would you able to simplify this, possibly providing a formula with what I am working with? Thank you so much for replying.

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Fredrik Bornander · Accepted Answer · 2015-01-29T04:35:00

Solution 1

You have a red line defined by two points (in your code I think it's the vector from db.WorkElement.StartPoint to db.WorkElement.EndPoint), call that redLineDirection;

redLineDirection = normalize(db.WorkElement.EndPoint - db.WorkElement.StartPoint);

Then you have the direction in which the cylinder extends when you create it (I think this is along the positive Y-axis [0,1,0] in your case, but I am not sure), call that cylinderDirection, let this vector be a unit vector of length one.

Now figure out the angle between those vectors using the dot product[^], it will be something like

angle = arccos(dot(redLineDirection, cylinderDirection)));

No need to divide by the lengths as they're both of length one. Unit is radians.

At this point, you know how much to rotate the cylinder, angle, but you also need to figure out about which axis to do this.

Using the cross product[^] you'll be able to find this.

rotateAxis = cross(redLineDirection, cylinderDirection);

Call SetRotate with the new values;

mwp.SetRotate(rotateAxis, vPoint, angle); // might have to convert angle to degrees here.

I've not considered the translation of the cylinder as you seem to have that under control.

Hope this helps,
Fredrik

Posted 29-Jan-15 4:35am

Fredrik Bornander

Comments

jk0391 29-Jan-15 11:07am

Here is my code, see if it looks OK to you. Please ignore the commented code. Thank you again for helping me. I tried it and it did not work, I am thinking I need to adjust my CreateCylinder call (WPL axis values...)

Dim PickObj As New VISIPick
Dim FaceList As New VISIList
Dim db As New VISIDatabase
Dim OldElList As New VISIList

'* new var
Dim mwp, mpw, matT, matR As New VISIMatrix
Dim P2 As New VISIPoint
Dim Axis As New VISIVector
'---

'PickObj.Filter = SEARCH_SEGM
PickObj.Message = "Pick a Line"
'PickObj.MoreElements = True
If PickObj.Pick = False Then
Exit Sub
End If
'PickObj.ClearSelection()

FaceList.Init(5, LTYPE_FACE)

db.WorkDBKey = PickObj.PickedKey
db.GetElement()

'Make element variable compatible with workplane - add to list
'*FaceList.AddItem(db.WorkElement)

WPL.GetDefault()
WPL.CreateFromZAxis(PickObj.PickedPoint, WPL.ZAxis)
WPL.WorkPlaneWorld(mwp, mpw)

If WPL.LastError <> V_NOERROR Then
MsgBox(WPL.LastError)
Exit Sub
End If

Dim p As New VISIPoint
Dim pick As New VISIPick

p.Put(0, 0, 0)
pick.VectorPoint = p
pick.Filter = SEARCH_DIRECTION
pick.MoreElements = False
If (pick.Pick() = False) Then
pick.ClearSelection()
Exit Sub
End If
pick.ClearSelection()

'Display existence of workplane
lblDebug.Text = "(" & WPL.Origin.X.ToString() & "," & WPL.Origin.Y.ToString() & "," & WPL.Origin.Z.ToString() & ")" & vbNewLine & _
WPL.XAxis.CX.ToString() & " " & WPL.XAxis.CY.ToString() & " " & WPL.XAxis.CZ.ToString() & vbNewLine & _
" " & WPL.YAxis.CX.ToString() & " " & WPL.YAxis.CY.ToString() & " " & WPL.YAxis.CZ.ToString() & vbNewLine & _
" " & WPL.ZAxis.CX.ToString() & " " & WPL.ZAxis.CY.ToString() & " " & WPL.ZAxis.CZ.ToString()

Dim x, y, z, rad, deg As Double

x = db.WorkElement.EndPoint.X - db.WorkElement.StartPoint.X
y = db.WorkElement.EndPoint.Y - db.WorkElement.StartPoint.Y
z = db.WorkElement.EndPoint.Z - db.WorkElement.StartPoint.Z

rad = (Math.Asin(z / Math.Sqrt((x ^ 2) + (y ^ 2) + (z ^ 2)))).ToString()
deg = (rad * (180 / Math.PI)).ToString()

'WPL = Util.rotateWorkPlane(WPL, deg)

If (deg > 0) Then
vPoint.Put(db.WorkElement.StartPoint.X, db.WorkElement.StartPoint.Y, db.WorkElement.StartPoint.Z)
Else
vPoint.Put(db.WorkElement.EndPoint.X, db.WorkElement.EndPoint.Y, db.WorkElement.EndPoint.Z)
End If
lblDeg.Text = deg.ToString()

Dim redLine As New Vector3D(x, y, z)
redLine.Normalize()
Dim vectorD As New Vector3D(0, 1, 0)

Dim crossP As New Vector3D()
Dim angle As Double

angle = Math.Acos(Vector3D.DotProduct(redLine, vectorD))
angle = (angle * (180 / Math.PI))
crossP = Vector3D.CrossProduct(redLine, vectorD)
'--
'Dim v1 As New Vector3D(db.WorkElement.EndPoint.X, db.WorkElement.EndPoint.Y, db.WorkElement.EndPoint.Z)
'Dim v2 As New Vector3D(db.WorkElement.StartPoint.X, db.WorkElement.StartPoint.Y, db.WorkElement.StartPoint.Z)

'MsgBox(Vector3D.AngleBetween(v1, v2))
'--

'crossP = Vector3D.CrossProduct(vectorD, vectorN)
'angleBetween = Vector3D.AngleBetween(vectorD, vectorN)

'WPL.ZAxis.CX = pick.PickedVector.CX
'WPL.ZAxis.CY = pick.PickedVector.CY
'WPL.ZAxis.CZ = pick.PickedVector.CZ

SolFac.CreateCylinder(0.006, db.WorkElement.Length, vPoint, WPL.XAxis, WPL.ZAxis)
vList.Init(10, LTYPE_BODY)

Axis.Put(crossP.X, crossP.Y, crossP.Z)

'Axis = Util

Fredrik Bornander 30-Jan-15 7:59am

I can't read that code and tell you what's wrong, I don't know how all the used methods work.

jk0391 30-Jan-15 13:55pm

Sorry I know you can't compile it to test it yourself, I was just asking you to go over it because you already traced my code before to post the solution you proposed. Can you not trace it? Again, thank you for your time.

Fredrik Bornander 31-Jan-15 4:19am

Can you show me a image of what the result was, maybe I can deduce what went wrong from that.

jk0391 3-Feb-15 9:27am

Apologies for the delay. Here is my full code as I noticed it cut off before:

WPL.GetDefault()
WPL.CreateFromZAxis(PickObj.PickedPoint, WPL.ZAxis)
WPL.WorkPlaneWorld(mwp, mpw)

If WPL.LastError <> V_NOERROR Then
MsgBox(WPL.LastError)
Exit Sub
End If

Dim p As New VISIPoint
Dim pick As New VISIPick

p.Put(0, 0, 0)
pick.VectorPoint = p
pick.Filter = SEARCH_DIRECTION
pick.MoreElements = False
If (pick.Pick() = False) Then
pick.ClearSelection()
Exit Sub
End If
pick.ClearSelection()

'Display existence of workplane
lblDebug.Text = "(" & WPL.Origin.X.ToString() & "," & WPL.Origin.Y.ToString() & "," & WPL.Origin.Z.ToString() & ")" & vbNewLine & _
WPL.XAxis.CX.ToString() & " " & WPL.XAxis.CY.ToString() & " " & WPL.XAxis.CZ.ToString() & vbNewLine & _
" " & WPL.YAxis.CX.ToString() & " " & WPL.YAxis.CY.ToString() & " " & WPL.YAxis.CZ.ToString() & vbNewLine & _
" " & WPL.ZAxis.CX.ToString() & " " & WPL.ZAxis.CY.ToString() & " " & WPL.ZAxis.CZ.ToString()

Dim x, y, z, rad, deg As Double

x = db.WorkElement.EndPoint.X - db.WorkElement.StartPoint.X
y = db.WorkElement.EndPoint.Y - db.WorkElement.StartPoint.Y
z = db.WorkElement.EndPoint.Z - db.WorkElement.StartPoint.Z

rad = (Math.Asin(z / Math.Sqrt((x ^ 2) + (y ^ 2) + (z ^ 2)))).ToString()
deg = (rad * (180 / Math.PI)).ToString()

'WPL = Util.rotateWorkPlane(WPL, deg)

If (deg > 0) Then
vPoint.Put(db.WorkElement.StartPoint.X, db.WorkElement.StartPoint.Y, db.WorkElement.StartPoint.Z)
Else
vPoint.Put(db.WorkElement.EndPoint.X, db.WorkElement.EndPoint.Y, db.WorkElement.EndPoint.Z)
End If
lblDeg.Text = deg.ToString()

Dim redLine As New Vector3D(x, y, z)
redLine.Normalize()
Dim vectorD As New Vector3D(0, 1, 0)

Dim crossP As New Vector3D()
Dim angle As Double

angle = Math.Acos(Vector3D.DotProduct(redLine, vectorD))
angle = angle * (180 / Math.PI)
crossP = Vector3D.CrossProduct(redLine, vectorD)
'--
'Dim v1 As New Vector3D(db.WorkElement.EndPoint.X, db.WorkElement.EndPoint.Y, db.WorkElement.EndPoint.Z)
'Dim v2 As New Vector3D(db.WorkElement.StartPoint.X, db.WorkElement.StartPoint.Y, db.WorkElement.StartPoint.Z)

'MsgBox(Vector3D.AngleBetween(v1, v2))
'--

'crossP = Vector3D.CrossProduct(vectorD, vectorN)
'angleBetween = Vector3D.AngleBetween(vectorD, vectorN)

'WPL.ZAxis.CX = pick.PickedVector.CX
'WPL.ZAxis.CY = pick.PickedVector.CY
'WPL.ZAxis.CZ = pick.PickedVector.CZ

SolFac.CreateCylinder(0.006, db.WorkElement.Length, vPoint, WPL.XAxis, WPL.ZAxis)
vList.Init(10, LTYPE_BODY)

Axis.Put(crossP.X, crossP.Y, crossP.Z)

'Axis = Util.rotateVector(Axis, Axis, deg)

If SolFac.LastError <> V_NOERROR Then
MsgBox(SolFac.LastError)
Else
vList.AddItem(SolFac.Result)
mwp.SetRotate(Axis, vPoint, angle) 'rotate a body based off an angle
'matT.SetTranslate(vPoint, P2) ' move body from one point to another
'mwp.TransformVector(Axis)
'mwp.Mul(matR, matT) 'apply new changes
SolFac.WorkMatrix = mwp
SolFac.ApplyMatrix(vList)
'SolFac.RotateBodies(vList, Axis, vPoint, deg)
Appl.UpdateSolidsOnScreen()
End If

jk0391 3-Feb-15 9:30am

...and the picture you requested. Disregard the cube.

http://i58.tinypic.com/1zya8b4.png

Fredrik Bornander 3-Feb-15 10:45am

Can't figure out where that went wrong. But lets try this instead;
OrientationTest.zip (10.8 KB). This is a WPF app that replicates what you're trying to achieve. Look at that code, all in the MainWindow essentially and see if that helps. If you set up the WPF app to have the same input in terms of where the red line start and stops you should be able step through both and figure out where your values go wrong.

Really hope we'll get it right this time :)

jk0391 4-Feb-15 14:16pm

Fredrik, thanks so much for making this project. Very interesting to trace and compare. I believe it will still not work as the line I have can be anywhere in space, whereas yours must always originate from (0,0,0) which is not dynamic. This is a great study, though as it will help me tackle the project later on in the future. For now I am taking care of other projects. :(

Fredrik Bornander 4-Feb-15 17:21pm

Sorry I was too lazy putting that together. In addition to translate the cylinder along the distance between point a and b, you also need to translate it to point a to make sure it's in the correct place.
I've fixed that for you in this project;
OrientationTest.zip (10.9 KB)

Apologies for the mistake.