 Author Topic: Math - 3D Solid Challenge  (Read 6902 times)

0 Members and 1 Guest are viewing this topic. Re: Math - 3D Solid Challenge
« Reply #15 on: January 29, 2008, 04:53:37 PM »
Thats what I thought, but google didn't even know
Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second Re: Math - 3D Solid Challenge
« Reply #16 on: January 29, 2008, 04:53:58 PM »
what about the fact that the centerlines are off of the center of the upper part?
Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second

Cathy

• Bull Frog
• Posts: 251 Re: Math - 3D Solid Challenge
« Reply #17 on: January 29, 2008, 05:04:44 PM »
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? Re: Math - 3D Solid Challenge
« Reply #18 on: January 29, 2008, 05:08:15 PM »
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
Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second Re: Math - 3D Solid Challenge
« Reply #19 on: January 29, 2008, 05:15:56 PM »
>>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.
Forth is like the Tao: it is a Way, and is realized when followed.
Its fragility is its strength; its simplicity is its direction - Michael Ham

Lao Tzu: To attain knowledge, add things
every day; to obtain wisdom, remove things every day. Re: Math - 3D Solid Challenge
« Reply #20 on: January 29, 2008, 05:22:00 PM »
thanks
Everyone has a photographic memory, Some just don't have film.
They say money can't buy happiness, but it can buy Bacon and that's a close second

Bryco

• Water Moccasin
• Posts: 1849 Re: Math - 3D Solid Challenge
« Reply #21 on: January 30, 2008, 10:55:23 AM »
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.

Code: [Select]
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 Re: Math - 3D Solid Challenge
« Reply #22 on: January 30, 2008, 05:44:32 PM »
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?
Forth is like the Tao: it is a Way, and is realized when followed.
Its fragility is its strength; its simplicity is its direction - Michael Ham

Lao Tzu: To attain knowledge, add things
every day; to obtain wisdom, remove things every day.

Bryco

• Water Moccasin
• Posts: 1849 Re: Math - 3D Solid Challenge
« Reply #23 on: January 30, 2008, 08:07:38 PM »
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" Re: Math - 3D Solid Challenge
« Reply #24 on: January 30, 2008, 08:12:53 PM »
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).
Forth is like the Tao: it is a Way, and is realized when followed.
Its fragility is its strength; its simplicity is its direction - Michael Ham

Lao Tzu: To attain knowledge, add things
every day; to obtain wisdom, remove things every day. Re: Math - 3D Solid Challenge
« Reply #25 on: January 30, 2008, 08:36:21 PM »
It's even easier, I just noticed that ent's have a Mirror3d method. that may help.
Forth is like the Tao: it is a Way, and is realized when followed.
Its fragility is its strength; its simplicity is its direction - Michael Ham

Lao Tzu: To attain knowledge, add things
every day; to obtain wisdom, remove things every day. Re: Math - 3D Solid Challenge
« Reply #26 on: January 30, 2008, 09:52:48 PM »
This is what I'm thinking -
Forth is like the Tao: it is a Way, and is realized when followed.
Its fragility is its strength; its simplicity is its direction - Michael Ham

Lao Tzu: To attain knowledge, add things
every day; to obtain wisdom, remove things every day.

Bryco

• Water Moccasin
• Posts: 1849 Re: Math - 3D Solid Challenge
« Reply #27 on: January 31, 2008, 12:27:43 AM »
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.
Code: [Select]
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 cross-product 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

Bryco

• Water Moccasin
• Posts: 1849 Re: Math - 3D Solid Challenge
« Reply #28 on: January 31, 2008, 12:39:12 AM »
Test dwg.

SEANT

• Bull Frog
• Posts: 324 Re: Math - 3D Solid Challenge
« Reply #29 on: January 31, 2008, 07:02:10 AM »
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 non-aligned 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

Sean Tessier