TheSwamp
Code Red => VB(A) => Topic started by: CmdrDuh on January 29, 2008, 10:02:40 AM

Anybody up for a 3D math challenge? What I need to do is locate 3 blocks in 3D Space, and Connect them with 2 pieces of 3d "pipe" Should be easy enough with the math, its the connecting Im having problems with.

The blocks needed are here as well

Now here is the challenge, Write a routine, preferable in VBA to accommodate varying C.L. to C.L. (centerline to centerline) heights. the picture shown is a 6 foot separation

Do the angles of the 'T' pieces remain the same? this means the centre of the 2 bottom pieces will vary then yes?
If this is the case you need to create 2 vectors from the pipes, scale them to suit the changed height between the centres.
I'll knock up a quick piccy when I get to work and make sure we're on the same page.

The hard part is the inverse matrix in vba for extruding the pipes.

The angle is always 30degrees b/t the 2 down pipes, the 2 bottom pieces would then have to move to accomodate the height difference. Also, the blocks I posted can be edited if we need to move the insertion points. After playing with it today, I ended p moving the ins pt to be more inline with the down pipe. The problem I ran into was the Vpart at the top. The center of the Vpipes does not go through the center of the top piece, so I am having trouble figuring out how to calc where to go. Maybe Im just over looking something simple.

Bryco, I was thinking of using hardcoded numbers from the ins pt of the top piece to get to the location of the pipe start, and then doing the TAN calc based on CL to CL distance to do the extrusion. Or Im totally in left field

99.999999% of the time the UCS will be world, and that .0000001% of the time, It wont work anyway.

I was thinking of drawing lines from start to end point for the pipes, and extruding a circle w/ the normal set to the line, the length calced. Similiar to the horizontal and vertical extrusions you helped me with about a year ago

Here's the math part anyway (I think :) )

IRT pipe extrusions, draw the circle/s, translate to point and set normal to line direction as Duh said and extrude the length of the line. Some calc's would also be need to located the 'actual' sp and ep of the pipe as it won't be the full length of the line.
To derive the cot and csc use these 
csc = 1/sinA
cot = 1/tanA
plug 'em in and away you go ;)

Mick, here is a pic showing the lower pieces moving inward to accomodate the shorter distance.

Good, that makes it easy then.
The length of the line to pnt1 in my piccy = 1/sinA x H
pnt1.x = 1/tanA x H
pnt1.y = H
IRT to anything other than wcs, always do the modeling in wcs then xform into place, it's a lot easier.

IRT ?

In Regards To :)

Thats what I thought, but google didn't even know

what about the fact that the centerlines are off of the center of the upper part?

Would putting some workpoints in your blocks help with some of this? Like a point where the CLs cross, points where the pipes connect?
IRT  odd I always use WRT (with respect to). Is that just a difference is Aussie English and American English? Or is just a difference in disciplines?

I was thinking of calcing the workpoint in code, and then moving down and to the left/right from there to start the line. If you look at the first pic, you can see some cross's inside the pipe, that is the start/stop point for the vertical anlge of pipe

>>what about the fact that the centerlines are off of the center of the upper part?
The angle is still the same so I'd translate the pipe 11/16 to the left and the bottom T the amount of the offset from insert point to the left, repeat on right side.
I'd have a go at this but I'm busy with something else at the moment but here's the steps I would take using the math I posted earlier 
Calc the pipe lengths and pnt1 on the left side
Insert the top pipe at origin
Insert the left bottom T at pnt1 and translate it the offset amount to the left
Extrude the pipe, translate it to the origin and the angle then translate it left the top T offset amount
(and along the line a bit if needed to clear cross pipe as it's shorter than the actual line length)
Copy and mirror over top T c.l. for right side.
If I get time later I'll code something up.

thanks

I had some success with below code.
To the apex bock I added 2 regions on defpoints that are positiioned where you have the lines.
These regions are copied from the block itself then tranlated to the blockrefs position.
Then extruded.
Sub Cmd()
Dim Ent As AcadEntity
Dim B As AcadBlock
Dim Br As AcadBlockReference
Dim P, m, Ret
Dim Ms As AcadBlock
Dim Obj(0) As Object
Dim C1 As AcadCircle, C2 As AcadCircle
Dim R1 As AcadRegion
Dim sBlock As String
Dim Dist As Double, Ht As Double
Dim Util As AcadUtility
Set Util = ThisDrawing.Utility
Set Ms = ThisDrawing.ModelSpace
sBlock = "5020760"
Util.GetEntity Ent, P, "Pick the 5020"
If Not TypeOf Ent Is AcadBlockReference Then Exit Sub
If Not Ent.Name = sBlock Then Exit Sub
Set Br = Ent
Set B = ThisDrawing.Blocks(sBlock)
For Each Ent In B
If TypeOf Ent Is AcadRegion Then
Set Obj(0) = Ent
Ret = ThisDrawing.CopyObjects(Obj, Ms)
Set R1 = Ret(0)
R1.Layer = "0"
R1.Color = 2
Exit For
End If
Next Ent
Dist = Util.GetDistance(, "Centerline distance")
If Dist < 17.0855 Then
MsgBox ("Distance must be larger than 17")
Exit Sub
End If
Ht = (Dist  17.0855) / Cos(15 / 180 * PI) + 4
m = BlockRefMatrix(Br)
m = InverseMatrix(m)
R1.TransformBy (m)
Dim Tube As Acad3DSolid
Set Tube = Ms.AddExtrudedSolid(R1, Ht, 0)
End Sub
Function BlockRefMatrix(oBref As AcadBlockReference) As Variant
Dim V, m(3, 3) As Double, M1, M2
Dim j As Integer
Dim X, Y, Z, ins
Dim Rot As Double
Rot = oBref.Rotation
Z = oBref.Normal
V = GetOcsFromNormal(Z)
X = V(0): Y = V(1)
PrintP X
PrintP Y
ins = oBref.InsertionPoint
M1 = RotZ(Rot)
For j = 0 To 2
m(0, j) = X(j)
m(1, j) = Y(j)
m(2, j) = Z(j)
Next j
m(0, 3) = ins(0): m(1, 3) = ins(1): m(2, 3) = ins(2)
m(3, 3) = 1
'PrintM M
If Rot = 0 Then
BlockRefMatrix = m
Else
M2 = M4xM4(m, M1)
PrintM M2
BlockRefMatrix = M2
End If
End Function

I had some success with below code.
To the apex bock I added 2 regions on defpoints that are positiioned where you have the lines.
These regions are copied from the block itself then tranlated to the blockrefs position.
Then extruded.
Great idea Bryco! saves quite a bit of matrix mojo. Perhaps you can put the other bottom blocks in as well as nested in the correct alignment then just translate it along the line vector the given amount after calc'ing with the new height?

I haven't done much coding for the creation and editing of 3d objects so I tried a circle first, only to find a cylinder doesn't follow a path.
So yes the region saves a bit of matricising (Pres. Bush speak).
After an hour I thought I would have the hard part whooped but alas the correct matrix is eluding me for the funky blocks. (Dang it). Works for the blocks rotated in the same plane.
Mick, I think straight vector math will establish the insertion point of the other blocks and when that is translated using the same magical matrix David can say "Bob's me uncle"

Do you mean to rotate the bottom T or to mirror it?
To create a mirror matrix you should be able to just negate some the vectors for axes and translation and transformBy.
If you are mirroring over the y axis, negate the x vector for example.
if it's the rotation of the blocks perhaps setting them up in the block drg in the correct location/orientation for simple insert (create a block for left and right say).

It's even easier, I just noticed that ent's have a Mirror3d method. that may help.

This is what I'm thinking 

This works, finally. David the last part is mirror3d as Mick suggests.
Transpose rather than inverse threw for a while as usual (More brains reqd.)
There is a weird variety of math used here, but they all relate to normals somewhere.
Option Explicit
Const PI As Double = 3.14159265358979
Sub Dav()
Dim Ent As AcadEntity
Dim B As AcadBlock
Dim Br As AcadBlockReference
Dim P, M, M1, Ret
Dim Ms As AcadBlock
Dim Obj(0) As Object
Dim C1 As AcadCircle, C2 As AcadCircle
Dim R1 As AcadRegion
Dim sBlock As String
Dim Dist As Double, Ht As Double
Dim Util As AcadUtility
Dim Zero(2) As Double
Set Util = ThisDrawing.Utility
Set Ms = ThisDrawing.ModelSpace
sBlock = "5020760"
Util.GetEntity Ent, P, "Pick the 5020"
If Not TypeOf Ent Is AcadBlockReference Then Exit Sub
If Not Ent.Name = sBlock Then Exit Sub
Set Br = Ent
Set B = ThisDrawing.Blocks(sBlock)
For Each Ent In B
If TypeOf Ent Is AcadRegion Then
Set Obj(0) = Ent
Ret = ThisDrawing.CopyObjects(Obj, Ms)
Set R1 = Ret(0)
R1.Layer = "0"
R1.color = 2
Exit For
End If
Next Ent
Dist = Util.GetDistance(, "Centerline distance")
If Dist < 17.0855 Then
MsgBox ("Distance must be larger than 17")
Exit Sub
End If
Ht = (Dist  17.0855) / Cos(15 / 180 * PI) + 4
M = BlockRefMatrix(Br)
M1 = Transpose(M)
R1.TransformBy (M1)
Dim Tube As Acad3DSolid
Set Tube = Ms.AddExtrudedSolid(R1, Ht, 0)
R1.Delete
Dim width As Double
Dim inspt(2) As Double
Dim Br2 As AcadBlockReference
width = (Tan(15 / 180 * PI) * (Dist  17.0855)) + 4.0682
inspt(1) = width: inspt(2) = Dist
P = TransformPt2(M1, inspt)
Set Br2 = Ms.InsertBlock(Zero, "5141714", 1, 1, 1, 0)
Br2.Normal = Br.Normal
Br2.Rotation = Br.Rotation
Br2.Move Zero, P
End Sub
Function BlockRefMatrix(oBref As AcadBlockReference) As Variant
Dim V, M(3, 3) As Double, M1, M2
Dim j As Integer
Dim X, Y, Z, ins
Dim Rot As Double
Rot = oBref.Rotation
Z = oBref.Normal
V = GetOcsFromNormal(Z)
X = V(0): Y = V(1)
ins = oBref.InsertionPoint
M1 = RotZ(Rot)
For j = 0 To 2
M(0, j) = X(j)
M(1, j) = Y(j)
M(2, j) = Z(j)
M(3, j) = ins(j)
Next j
M(3, 3) = 1
If Rot = 0 Then
BlockRefMatrix = M
Else
M2 = M4xM4(M, M1)
BlockRefMatrix = M2
End If
End Function
Function Transpose(Matrix As Variant) As Variant
Dim iCnt As Integer, jCnt As Integer
Dim transMat(0 To 3, 0 To 3) As Double
Dim I As Integer, j As Integer
iCnt = UBound(Matrix, 1)
jCnt = UBound(Matrix, 2)
For I = 0 To iCnt
For j = 0 To jCnt
transMat(I, j) = Matrix(j, I)
Next j
Next I
Transpose = transMat
End Function
Function TransformPt2(M As Variant, P1 As Variant) As Variant
Dim I As Integer
Dim X As Double, Y As Double, Z As Double, d As Double
Dim P(3) As Double
Dim P2(2) As Double
For I = 0 To 2
P(I) = P1(I)
Next
P(3) = 1
For I = 0 To 3
X = X + P(I) * M(0, I)
Y = Y + P(I) * M(1, I)
Z = Z + P(I) * M(2, I)
d = d + P(I) * M(3, I)
Next
P2(0) = X: P2(1) = Y: P2(2) = Z
TransformPt2 = P2
End Function
Function GetOcsFromNormal(N As Variant) As Variant
'Arbitrary Axis Algorithm in dxf help
'N is the normal vector.
'Wy is the world Y axis, which is always (0,1,0).
'Wz is the world Z axis, which is always (0,0,1).
Dim Wy(2) As Double
Dim Wz(2) As Double
Dim Nx As Double, Ny As Double
Dim Ax, Ay, Ocs(1) As Variant
N = NormaliseVector(N)
Wy(0) = 0: Wy(1) = 1: Wy(2) = 0
Wz(0) = 0: Wz(1) = 0: Wz(2) = 1
Nx = N(0): Ny = N(1)
If (Abs(Nx) < 1 / 64) And (Abs(Ny) < 1 / 64) Then
'Ax = Wy X N (where “X” is the crossproduct operator).
Ax = Crossproduct(Wy, N)
Else
Ax = Crossproduct(Wz, N)
End If
Ocs(0) = Ax
Ay = Crossproduct(N, Ax)
Ocs(1) = Ay
GetOcsFromNormal = Ocs
End Function
Function RotZ(Ang As Double) As Variant
'Rotate by an angle around the z axis
Dim M
Dim CosAng As Double, sinAng As Double
CosAng = Cos(Ang): sinAng = Sin(Ang)
M = IDMatrix
M(0, 0) = CosAng
M(0, 1) = sinAng
M(1, 0) = sinAng
M(1, 1) = CosAng
RotZ = M
End Function
Function M4xM4(M1, M2) As Variant
'Matrix x matrix
Dim M(3, 3) As Double
Dim I As Integer, j As Integer
Dim k As Integer
Dim Sum As Double
For I = 0 To 3
For j = 0 To 3
For k = 0 To 3
Sum = Sum + M1(k, j) * M2(I, k)
Next k
M(I, j) = Sum
Sum = 0
Next j
Next I
M4xM4 = M
End Function
Function NormaliseVector(V As Variant) As Variant
Dim Unit As Double
Dim Vn(2) As Double
Unit = Sqr(V(0) * V(0) + V(1) * V(1) + V(2) * V(2))
Vn(0) = V(0) / Unit: Vn(1) = V(1) / Unit: Vn(2) = V(2) / Unit
NormaliseVector = Vn
End Function
Function Crossproduct(A, B) As Variant
Dim Ax As Double, Ay As Double, Az As Double
Dim Bx As Double, By As Double, Bz As Double
Dim Unit As Double
Dim c(2) As Double
'get CrossProduct
Ax = A(0): Ay = A(1): Az = A(2)
Bx = B(0): By = B(1): Bz = B(2)
c(0) = Ay * Bz  Az * By
c(1) = Az * Bx  Ax * Bz
c(2) = Ax * By  Ay * Bx
'Convert to unit normal
Unit = Sqr(c(0) * c(0) + c(1) * c(1) + c(2) * c(2))
c(0) = c(0) / Unit: c(1) = c(1) / Unit: c(2) = c(2) / Unit
Crossproduct = c
End Function
Function IDMatrix()
Dim M(3, 3) As Double
Dim I As Integer, j As Integer
M(0, 0) = 1
M(1, 1) = 1
M(2, 2) = 1
M(3, 3) = 1
IDMatrix = M
End Function

Test dwg.

Excellent work once again gentlemen. A word of caution; if you persist in this development of “one click design creation”, managers may do the work themselves and figure they need CAD techs no longer. :)
Bryco, I see you’ve expanded the scope of the project to include “other’world’ly” alignments – certainly a welcome inclusion for those of us with chaotic structures. The one recommendation I would make for dealing with these nonaligned setups, like the block in CmdrduhTest.dwg @ (99.9462, 265.5402, 0.4912), is to switch order of operation from:
Br2.Normal = Br.Normal
Br2.Rotation = Br.Rotation
To:
Br2.Rotation = Br.Rotation
Br2.Normal = Br.Normal

thanks Sean, re the rotation,normal is there a set of circumstances where that is necessary?

I should mention that I'm still using 2004 and may be missing some code changes of the later AutoCAD releases.
The example I refered to does not align exactly unless those lines are switched. This example also cause my setup problems.

Cool, it has no probs in 2008, in 2004 it needs to be written as you say.
There's a mystery.

I suppose it is sensible to expect the VBA 3d interface to change with so much extra going on in 2007/2008. Still, I’ve got to wonder if the boys at Autodesk just like to keep us guessing. They certainly like to keep us upgrading.
Once again, nice job.

CmdrDuhdid it do what you wanted?

I have been gone for 2 days getting my eyes tested. So I haven't had a chance to try it yet. Monday I intend to try it. I'll definetly let you know!!!
Thanks

Well while it's monday, it is the third monday that has passed.
A bit rude mate.

Sorry Bryco, I haven't had time to do any programming at work lately. This week Im home with sick kids, and I have the flu.

Sorry Bryco, I haven't had time to do any programming at work lately. This week Im home with sick kids, and I have the flu.
Get well soon (all of you).

Rum and limes David .. rum for you, limes for the kids :)

Get well all.

Rum and limes David
Irie Mon 8) :)

Well I sent the kids back to school today, and Im back at work, so lets see how that bit of code worked. :)

Rum and limes David .. rum for you, limes for the kids :)
Just what the Dr. ordered :)

That is awesome! I just need to work out the mirror part, but that was way cool. Bryco, I am definetly going to have to study the matrix stuff more, because that was hard core

>> I am definitely going to have to study the matrix stuff
Yep, once you understand vectors and matrices (which are just groups/lists of vectors) you can do pretty much anything you like in 3 dimensions ;)

Glad you like it, David.
C# has all that right at your fingertips but I wonder how difficult it would be to use them without understanding them.
I just wrote a mirror jig for C# and almost laughed when I figured out the jig needed was a rotation jig.
You mirror it once then rotate it where you want (kinda sorta)