# CATIA V5 Macro - Useful Functions

## CATIA V5 Macro - Useful Functions

Unlock the full potential of Catia V5 with my comprehensive collection of useful VBA functions.

This web page provides a comprehensive set of helper functions for Catia V5, including functions to get point coordinates, normalize vectors, get plane equations and vectors, and determine the distance between two points.

Other functions allow you to determine whether two points are on the same side of a plane, get the vector of a line, and find the BrepName from a Catia Selection.

Additionally, you can use this web page to determine whether two lines are skew, intersecting or parallel, and to calculate the distance between two skew lines.

You can also calculate the DOT and CROSS products of two vectors, and obtain the inverse and determinant of an N x N matrix, as well as the Adjoint and Minor matrices.

For designers looking to work with curves, the page includes functions to approximate a curve using Cubic or Quadratic Bezier, and to sort vectors.

Other functions allow you to get the direction vector of a line, the normal vector of a plane containing two lines, and the distance between two lines.

The functions are designed to streamline your workflow and increase your productivity, allowing you to take your Catia V5 designs to the next level.

Create a Module in your project and paste the code below, name it Q

``````Public Type iPct
X As Double
Y As Double
Z As Double
End Type

Public Type iPlan
Ax As Double
By As Double
Cz As Double
Dt As Double
End Type

Public Enum iIntVal
Intersectie = 0  'Intersection
Paralele = 1
Oblice = 2  'Skew
End Enum

Public Type iIntersect
Result As iIntVal
Val As iPct
End Type``````

Create a new module and name it as you like, just paste the code below in it

``````Sub CATMain()
'From Star Treck :)
Dim Q As New clsGVI
Dim A As iPct
Dim B As iPct
Dim C As iPct
Dim D As iPct
'Point A and B are on one line
'Point C and D are on second line
A.X = 1: A.Y = 1: A.Z = 1
B.X = 3: B.Y = 3: B.Z = 1
C.X = 0: C.Y = 1: C.Z = 4
D.X = 0: D.Y = 3: D.Z = 3
Dim dist As Double
dist = Q.LineToLineDistance(A, B, C, D)
Debug.Print "The minimum distance between the two lines is " & dist
End Sub``````

Create a Class Module in the same project and rename it to clsGVI and paste the code below

``Const PI As Double = 3.14159265358979``

Catia V5 VBA function to get point coordinates

``````Public Function GetPointXYZ(MyPoint As Variant) As iPct
Dim Coord(2): Set GetPointXYZ = New iPct
MyPoint.GetCoordinates Coord
GetPointXYZ.X = Coord(0): GetPointXYZ.Y = Coord(1): GetPointXYZ.Z = Coord(2)
Erase Coord
End Function``````

Catia V5 VBA function to get point coordinates relative to an specified axis system

``````Public Function LCS(AxisSys As Variant, Point2Measure As iPct) As iPct
Dim AOrig(2): Dim Vx(2): Dim Vy(2): Dim Vz(2)
Dim iOrig As iPct: Dim iVx As iPct: Dim iVy As iPct: Dim iVz As iPct: Dim Diff As iPct
Set LCS = New iPct
AxisSys.GetOrigin AOrig: iOrig.X = AOrig(0): iOrig.Y = AOrig(1): iOrig.Z = AOrig(2)
AxisSys.GetXAxis Vx: iVx.X = Vx(0): iVx.Y = Vx(1): iVx.Z = Vx(2)
AxisSys.GetYAxis Vy: iVy.X = Vy(0): iVy.Y = Vy(1): iVy.Z = Vy(2)
AxisSys.GetZAxis Vz: iVz.X = Vz(0): iVz.Y = Vz(1): iVz.Z = Vz(2)
NormalizeVector iVx, iVx
NormalizeVector iVy, iVy
NormalizeVector iVz, iVz
Diff.X = Point2Measure.X - iOrig.X: Diff.Y = Point2Measure.Y - iOrig.Y: Diff.Z = Point2Measure.Z - iOrig.Z
LCS.X = DotProduct(Diff, iVx): LCS.Y = DotProduct(Diff, iVy): LCS.Z = DotProduct(Diff, iVz)
Set iOrig = Nothing: Set iVx = Nothing: Set iVy = Nothing: Set iVz = Nothing: Set Diff = Nothing
Erase AOrig: Erase Vx: Erase Vy: Erase Vz
End Function``````

Catia V5 VBA procedure to Normalize of a vector

``````Public Sub NormalizeVector(IVect As iPct, ByRef NVect As iPct)
Dim Mag As Double
Mag = Sqr(IVect.X ^ 2 + IVect.Y ^ 2 + IVect.Z ^ 2)
If Mag < 0.0000001 Then Call Err.Raise(1001, , "Zero length vector cannot be normalized")
NVect.X = IVect.X / Mag
NVect.Y = IVect.Y / Mag
NVect.Z = IVect.Z / Mag
End Sub``````

Catia V5 VBA function to get Plane Equation

``````Public Function PlaneEquation(PartOrigin As iPct, PlaneOrigin As iPct, FirstVector As iPct, SecondVector As iPct) As iPlan
Set PlaneEquation = New iPlan
PlaneEquation.Ax = PartOrigin.Y * (FirstVector.Z - SecondVector.Z) + FirstVector.Y * (SecondVector.Z - PartOrigin.Z) + SecondVector.Y * (PartOrigin.Z - FirstVector.Z)
PlaneEquation.By = PartOrigin.Z * (FirstVector.X - SecondVector.X) + FirstVector.Z * (SecondVector.X - PartOrigin.X) + SecondVector.Z * (PartOrigin.X - FirstVector.X)
PlaneEquation.Cz = PartOrigin.X * (FirstVector.Y - SecondVector.Y) + FirstVector.X * (SecondVector.Y - PartOrigin.Y) + SecondVector.X * (PartOrigin.Y - FirstVector.Y)
PlaneEquation.Dt = PlaneOrigin.X * (FirstVector.Y * SecondVector.Z - SecondVector.Y * FirstVector.Z) + FirstVector.X * (SecondVector.Y * PlaneOrigin.Z - PlaneOrigin.Y * _
SecondVector.Z) + SecondVector.X * (PlaneOrigin.Y * FirstVector.Z - FirstVector.Y * PlaneOrigin.Z)
End Function``````

Catia V5 VBA function to get plane vectors

``````Public Function GetPlaneVectors(MyPlane As Variant) As iPct()
Dim ArrRet() As iPct: ReDim ArrRet(1)
Dim V1(2): Dim V2(2)
MyPlane.GetFirstAxis V1: ArrRet(0).X = V1(0): ArrRet(0).Y = V1(1): ArrRet(0).Z = V1(2)
MyPlane.GetSecondAxis V2: ArrRet(1).X = V2(0): ArrRet(1).Y = V2(1): ArrRet(1).Z = V2(2)
GetPlaneVectors = ArrRet
Erase ArrRet: Erase V1: Erase V2
End Function``````

Catia V5 VBA function to get angle between two planes - Dihedral Angle

``````Public Function DihedralAngle(FirstPlane As iPlan, SecondPlane As iPlan) As Double
DihedralAngle = ArcCos(FirstPlane.Ax * SecondPlane.Ax + FirstPlane.By * SecondPlane.By + FirstPlane.Cz * SecondPlane.Cz / _
Sqr((FirstPlane.Ax ^ 2 + FirstPlane.By ^ 2 + FirstPlane.Cz ^ 2) * (SecondPlane.Ax ^ 2 + SecondPlane.By ^ 2 + SecondPlane.Cz ^ 2)))
End Function``````

Catia V5 VBA function to get ArcCos

``````Public Function ArcCos(Radians As Double) As Double
If Round(Radians, 8) = 1 Then ArcCos = 0: Exit Function
If Round(Radians, 8) = -1 Then ArcCos = PI: Exit Function
ArcCos = Atn(-Radians / Sqr(1 - Radians ^ 2)) + 2 * Atn(1)
End Function``````

Catia V5 VBA function to get ArcSin

``````Public Function ArcSin(Radians As Double) As Double
If (Sqr(1 - Radians ^ 2) <= 0.000000000001) And (Sqr(1 - Radians ^ 2) >= -0.000000000001) Then
ArcSin = PI / 2
Else
End If
End Function``````

Catia V5 VBA function to get distance between two points

``````Public Function P2PDist(FirstPoint As iPct, SecondPoint As iPct) As Double
Distance = Sqr((SecondPoint.X - FirstPoint.X) ^ 2 + (SecondPoint.Y - FirstPoint.Y) ^ 2 + (SecondPoint.Z - FirstPoint.Z) ^ 2)
End Function``````

Catia V5 VBA function to determine if two points on the same side of a plane

``````Public Function WhichSideOfPlane(Plane As iPlan, FirstPoint As iPct, SecondPoint As iPct) As Integer()
Dim ArrReturn() As Integer: ReDim ArrReturn(1)
ArrReturn(0) = Plane.Ax * FirstPoint.X + Plane.By * FirstPoint.Y + Plane.Cz * FirstPoint.Z - Plane.Dt
ArrReturn(1) = Plane.Ax * SecondPoint.X + Plane.By * SecondPoint.Y + Plane.Cz * SecondPoint.Z - Plane.Dt
WhichSideOfPlane = ArrReturn
Erase ArrReturn
End Function``````

Catia V5 VBA function to get the vector of line

``````Public Function GetLineVector(FirstPoint As iPct, SecondPoint As iPct) As iPct
Dim Dist As Double: Set GetLineVector = New iPct
Dist = P2PDist(FirstPoint, Seconpoint)
GetLineVector.X = (SecondPoint.X - FirstPoint.X) / Dist
GetLineVector.Y = (SecondPoint.Y - FirstPoint.Y) / Dist
GetLineVector.Z = (SecondPoint.Z - FirstPoint.Z) / Dist
End Function``````

Catia V5 VBA function to get BrepName from Catia Selection

``````Public Function GetBrep(MyBRepName As String) As String
MyBRepName = Replace(MyBRepName, "Selection_", "")
MyBRepName = Left(MyBRepName, InStrRev(MyBRepName, "));"))
MyBRepName = MyBRepName + ");WithPermanentBody;WithoutBuildError;WithSelectingFeatureSupport;MFBRepVersion_CXR15)"
'");WithTemporaryBody;WithoutBuildError;WithInitialFeatureSupport;MonoFond;MFBRepVersion _CXR14)"
GetBrep = MyBRepName
End Function``````

Catia V5 VBA function to determine if two lines are skew, intersecting or parallel

``````Public Function LLIntersect(A As iPct, B As iPct, C As iPct, D As iPct) As iIntersect
Dim M(3, 3) As Double
M(0, 0) = A.X: M(0, 1) = A.Y: M(0, 2) = A.Z: M(0, 3) = 1
M(1, 0) = B.X: M(1, 1) = B.Y: M(1, 2) = B.Z: M(1, 3) = 1
M(2, 0) = C.X: M(2, 1) = C.Y: M(2, 2) = C.Z: M(2, 3) = 1
M(3, 0) = D.X: M(3, 1) = D.Y: M(3, 2) = D.Z: M(3, 3) = 1
If GetDet(M) <> 0 Then Erase M: LLIntersect.Result = Oblice: Exit Function    'skew lines
Dim CxB() As Double: Dim AxB() As Double: ReDim CxB(2): ReDim AxB(2)
Dim Av(2) As Double: Dim Bv(2) As Double: Dim Cv(2) As Double
Av(0) = B.X - A.X: Av(1) = B.Y - A.Y: Av(2) = B.Z - A.Z
Bv(0) = D.X - C.X: Bv(1) = D.Y - C.Y: Bv(2) = D.Z - C.Z
Cv(0) = C.X - A.X: Cv(1) = C.Y - A.Y: Cv(2) = C.Z - A.Z
CxB = CrossProd(Cv, Bv): AxB = CrossProd(Av, Bv)
Dim s As Double
On Error GoTo paralelele
s = DotProd(CxB, AxB) / Abs(DotProd(AxB, AxB))
Dim iInter As iPct
iInter.X = A.X + Av(0) * s    'X coordinate of intersection
iInter.Y = A.Y + Av(1) * s    'Y coordinate of intersection
iInter.Z = A.Z + Av(2) * s    'Z coordinate of intersection
LLIntersect.Result = Intersectie    'intersecting lines
LLIntersect.Val = iInter
paralelele:
Erase CxB: Erase AxB: Erase Cv: Erase Bv: Erase Av
If Err.Number <> 0 Then LLIntersect.Result = PParalele: Err.Clear    'parallel lines
End Function``````

Catia V5 VBA function to get the distance between two skew lines

``````Public Function SkewLDist(A As iPct, B As iPct, C As iPct, D As iPct) As Double
Dim Av(2) As Double: Dim Bv(2) As Double: Dim Cv(2) As Double
Dim Det(2, 2) As Double
Av(0) = A.X - B.X: Av(1) = A.Y - B.Y: Av(2) = A.Z - B.Z
Bv(0) = C.X - A.X: Bv(1) = C.Y - A.Y: Bv(2) = C.Z - A.Z
Cv(0) = D.X - C.X: Cv(1) = D.Y - C.Y: Cv(2) = D.Z - C.Z
Det(0, 0) = DotProd(Cv, Cv): Det(0, 1) = DotProd(Cv, Av): Det(0, 2) = DotProd(Cv, Bv)
Det(1, 0) = DotProd(Cv, Av): Det(1, 1) = DotProd(Av, Av): Det(1, 2) = DotProd(Av, Bv)
Det(2, 0) = DotProd(Cv, Bv): Det(2, 1) = DotProd(Av, Bv): Det(2, 2) = DotProd(Bv, Bv)
Dim v As Double
v = GetDet(Det)
SkewLDist = Sqr(v / (Det(0, 0) * Det(1, 1) - Det(1, 0) ^ 2))
End Function``````

Catia V5 VBA function to get DOT product of two vectors - length must be 3

``````Public Function DotProd(V1() As Double, V2() As Double) As Double
DotProd = V1(0) * V2(0) + V1(1) * V2(1) + V1(2) * V2(2)
End Function``````

Catia V5 VBA function to get CROSS product of two vectors - length must be 3

``````Public Function CrossProd(V1() As Double, V2() As Double) As Double()
Dim Res() As Double
ReDim Res(2)
Res(0) = V1(1) * V2(2) - V1(2) * V2(1)
Res(1) = V1(2) * V2(0) - V1(0) * V2(2)
Res(2) = V1(0) * V2(1) - V1(1) * V2(0)
CrossProd = Res
Erase Res
End Function``````

Catia V5 VBA function to get inverse of an N x N matrix

``````Public Function GetInverse(M() As Double) As Double()
Dim RetVal() As Double: Dim Size As Integer
Dim Det As Double: Dim Adj() As Double
Dim i As Integer: Dim j As Integer
Size = UBound(M): Det = GetDet(M)
If Det <> 0 Then
ReDim RetVal(Size, Size)
For i = 0 To Size
For j = 0 To Size
RetVal(i, j) = Adj(i, j) / Det
Next
Next
GetInverse = RetVal
Erase RetVal
End If
End Function``````

Catia V5 VBA function to get Determinant of an N x N matrix

``````Public Function GetDet(M() As Double) As Double
Dim i As Integer: Dim j As Integer
Dim Size As Integer: Size = UBound(M): Dim RetVal As Double
If Size = 1 Then
RetVal = RetVal + M(0, 0) * M(1, 1) - M(0, 1) * M(1, 0)   'daca e deteminant 2x2
Else
For i = 0 To Size
RetVal = RetVal + ((-1) ^ i) * M(0, i) * GetDet(GetMinor(M, 0, i))    'daca e determinant NxN
Next
End If
GetDet = RetVal
End Function``````

Catia V5 VBA function to get Adjoint matrix - it is used to calculate inverse of an N x N matrix

``````Public Function GetAdjoint(M() As Double) As Double()
Dim i As Integer: Dim j As Integer
Dim Size As Integer: Size = UBound(M)
Dim RetVal() As Double: ReDim RV(Size, Size)
For i = 0 To Size
For j = 0 To Size
RetVal(j, i) = ((-1) ^ (i + j)) * GetDet(GetMinor(M, i, j))    'RetVal(i, j)=matricea cofactor; RetVal(j, i)= transpusa matricii cofactor
Next
Next
Erase RetVal
End Function``````

Catia V5 VBA function to get Minor matrix - it is used to calculate the determinant of an N x N matrix

``````Public Function GetMinor(Min() As Double, RemRow As Integer, RemCol As Integer) As Double()
Dim RetVal() As Double: Dim i As Integer: Dim j As Integer
Dim IdxC As Integer: Dim IdxR As Integer
Dim Size As Integer: IdxR = 0: Size = UBound(Min) - 1
ReDim RetVal(Size, Size) As Double
For i = 0 To Size + 1
If i <> RemRow Then
IdxC = 0
For j = 0 To Size + 1
If j <> RemCol Then
RetVal(IdxR, IdxC) = Min(i, j)
IdxC = IdxC + 1
End If
Next
IdxR = IdxR + 1
End If
Next
GetMinor = RetVal
Erase RetVal
End Function``````

Catia V5 VBA function to approximate a curve using Cubic Bezier curves

``````Public Function BSpline3(CollectionOfiPcts As Collection, Increment As Double) As Collection
Dim i As Double: Dim t As Double
Dim A As iPlan: Dim B As iPlan: Dim C As iPlan: Dim Point2Add As iPct
Set BSpline3 = New Collection
For i = 1 To CollectionOfiPcts.Count - 3
Set A = New iPlan: Set B = New iPlan: Set C = New iPlan
A.Ax = (-CollectionOfiPcts(i).X + 3 * CollectionOfiPcts(i + 1).X - 3 * CollectionOfiPcts(i + 2).X + CollectionOfiPcts(i + 3).X) / 6
A.By = (3 * CollectionOfiPcts(i).X - 6 * CollectionOfiPcts(i + 1).X + 3 * CollectionOfiPcts(i + 2).X) / 6
A.Cz = (-3 * CollectionOfiPcts(i).X + 3 * CollectionOfiPcts(i + 2).X) / 6
A.Dt = (CollectionOfiPcts(i).X + 4 * CollectionOfiPcts(i + 1).X + CollectionOfiPcts(i + 2).X) / 6
B.Ax = (-CollectionOfiPcts(i).Y + 3 * CollectionOfiPcts(i + 1).Y - 3 * CollectionOfiPcts(i + 2).Y + CollectionOfiPcts(i + 3).Y) / 6
B.By = (3 * CollectionOfiPcts(i).Y - 6 * CollectionOfiPcts(i + 1).Y + 3 * CollectionOfiPcts(i + 2).Y) / 6
B.Cz = (-3 * CollectionOfiPcts(i).Y + 3 * CollectionOfiPcts(i + 2).Y) / 6
B.Dt = (CollectionOfiPcts(i).Y + 4 * CollectionOfiPcts(i + 1).Y + CollectionOfiPcts(i + 2).Y) / 6
C.Ax = (-CollectionOfiPcts(i).Z + 3 * CollectionOfiPcts(i + 1).Z - 3 * CollectionOfiPcts(i + 2).Z + CollectionOfiPcts(i + 3).Z) / 6
C.By = (3 * CollectionOfiPcts(i).Z - 6 * CollectionOfiPcts(i + 1).Z + 3 * CollectionOfiPcts(i + 2).Z) / 6
C.Cz = (-3 * CollectionOfiPcts(i).Z + 3 * CollectionOfiPcts(i + 2).Z) / 6
C.Dt = (CollectionOfiPcts(i).Z + 4 * CollectionOfiPcts(i + 1).Z + CollectionOfiPcts(i + 2).Z) / 6
For t = 0 To 1 Step Increment
Point2Add.X = A.Dt + A.Cz * t + A.By * t ^ 2 + A.Ax * t ^ 3
Point2Add.Y = B.Dt + B.Cz * t + B.By * t ^ 2 + B.Ax * t ^ 3
Point2Add.Z = C.Dt + C.Cz * t + C.By * t ^ 2 + C.Ax * t ^ 3
Next
Set A = Nothing: Set B = Nothing: Set C = Nothing
Next
End Function``````

Catia V5 VBA function to approximate an curve using Quadratic Bezier curves

``````Public Function BSplineC(CollectionOfiPcts As Collection, Increment As Double) As Collection
Dim j As Double
Dim t As Double
Dim A As iPct: Dim B As iPct: Dim C As iPct: Dim Point2Add As iPct
Set BSplineC = New Collection
For j = 2 To CollectionOfiPcts.Count - 1
Set A = New iPct: Set B = New iPct: Set C = New iPct
A.X = (CollectionOfiPcts(j - 1).X - 2 * CollectionOfiPcts(j).X + CollectionOfiPcts(j + 1).X) / 2
A.Y = (-2 * CollectionOfiPcts(j - 1).X + 2 * CollectionOfiPcts(j).X) / 2
A.Z = (CollectionOfiPcts(j - 1).X + CollectionOfiPcts(j).X) / 2
B.X = (CollectionOfiPcts(j - 1).Y - 2 * CollectionOfiPcts(j).Y + CollectionOfiPcts(j + 1).Y) / 2
B.Y = (-2 * CollectionOfiPcts(j - 1).Y + 2 * CollectionOfiPcts(j).Y) / 2
B.Z = (CollectionOfiPcts(j - 1).Y + CollectionOfiPcts(j).Y) / 2
C.X = (CollectionOfiPcts(j - 1).Z - 2 * CollectionOfiPcts(j).Z + CollectionOfiPcts(j + 1).Z) / 2
C.Y = (-2 * CollectionOfiPcts(j - 1).Z + 2 * CollectionOfiPcts(j).Z) / 2
C.Z = (CollectionOfiPcts(j - 1).Z + CollectionOfiPcts(j).Z) / 2
For t = 0 To 1 Step Increment
Point2Add.X = A.Z + A.Y * t + A.X * t ^ 2
Point2Add.Y = B.Z + B.Y * t + B.X * t ^ 2
Point2Add.Z = C.Z + C.Y * t + C.X * t ^ 2
Next
Set A = Nothing: Set B = Nothing: Set C = Nothing
Next
End Function``````

Catia V5 VBA procedure to sort vectors

``````Public Sub SortVector(Array2Sort, Order As String)
Dim X As Integer
Dim Temp
Select Case Order
Case "A"
Sorted = False
Do While Not Sorted
Sorted = True
For X = 0 To UBound(Array2Sort) - 1
If Array2Sort(X) > Array2Sort(X + 1) Then
Temp = Array2Sort(X + 1)
Array2Sort(X + 1) = Array2Sort(X)
Array2Sort(X) = Temp
Sorted = False
End If
Next X
Loop
Case "D"
Sorted = False
Do While Not Sorted
Sorted = True
For X = 0 To UBound(Array2Sort) - 1
If Array2Sort(X) < Array2Sort(X + 1) Then
Temp = Array2Sort(X + 1)
Array2Sort(X + 1) = Array2Sort(X)
Array2Sort(X) = Temp
Sorted = False
End If
Next X
Loop
Case Else
MsgBox "Invalid parameter Value Order=A or D"
End Select
End Sub``````

Catia V5 VBA Function to get direction vector of a line

``````Public Function GetDirectionVector(FirstPoint As iPct, SecondPoint As iPct) As iPct
GetDirectionVector.X = FirstPoint.X - SecondPoint.X
GetDirectionVector.Y = FirstPoint.Y - SecondPoint.Y
GetDirectionVector.Z = FirstPoint.Z - SecondPoint.Z
End Function``````

Catia V5 VBA Function to get normal vector of a plane containing 2 lines

``````Public Function GetNormalVectorTwoLines(VectorA As iPct, VectorB As iPct) As iPct
GetNormalVectorTwoLines.X = VectorA.Y * VectorB.Z - VectorA.Z * VectorB.Y
GetNormalVectorTwoLines.Y = VectorA.Z * VectorB.X - VectorA.X * VectorB.Z
GetNormalVectorTwoLines.Z = VectorA.X * VectorB.Y - VectorA.Y * VectorB.X
End Function``````

Catia V5 VBA Function to get the distance between 2 lines

``````'Old function name has been changed for clarity
'Public Function LLDistance(PointA As Q.iPct, PointB As Q.iPct, PointC As Q.iPct, PointD As Q.iPct) As Double
Public Function LineToLineDistance(PointA As Q.iPct, PointB As Q.iPct, PointC As Q.iPct, PointD As Q.iPct) As Double
Dim v As Q.iPct
Dim w As Q.iPct
Dim nv As Q.iPct
Dim ux As Double, uy As Double, uz As Double
Dim dotProduct As Double
Dim nvLength As Double
' Calculate the direction vectors of each line
v = GetDirectionVector(PointA, PointB)
w = GetDirectionVector(PointC, PointD)
' Calculate the normal vector of the plane containing both lines
nv = GetNormalVectorTwoLines(v, w)
' Calculate the vector between the two points on the first line and the second line
ux = PointC.X - PointA.X: uy = PointC.Y - PointA.Y: uz = PointC.Z - PointA.Z
' Calculate the dot product of the vector between the two points and the normal vector of the plane
dotProduct = ux * nv.X + uy * nv.Y + uz * nv.Z
' Calculate the length of the normal vector of the plane
nvLength = Sqr(nv.X ^ 2 + nv.Y ^ 2 + nv.Z ^ 2)
' Divide the absolute value of the dot product by the length of the normal vector to get the minimum distance between the two lines
LLDistance = Abs(dotProduct) / nvLength
End Function``````
Const PI As Double = 3.14159265358979
'Get point coordinates
Public Function GetPointXYZ(MyPoint As Variant) As iPct
Dim Coord(2): Set GetPointXYZ = New iPct
MyPoint.GetCoordinates Coord
GetPointXYZ.X = Coord(0): GetPointXYZ.Y = Coord(1): GetPointXYZ.Z = Coord(2)
Erase Coord
End Function
'Get point coordinates from a specified axis system
Public Function LCS(AxisSys As Variant, Point2Measure As iPct) As iPct
Dim AOrig(2): Dim Vx(2): Dim Vy(2): Dim Vz(2)
Dim iOrig As iPct: Dim iVx As iPct: Dim iVy As iPct: Dim iVz As iPct: Dim Diff As iPct
Set LCS = New iPct
AxisSys.GetOrigin AOrig: iOrig.X = AOrig(0): iOrig.Y = AOrig(1): iOrig.Z = AOrig(2)
AxisSys.GetXAxis Vx: iVx.X = Vx(0): iVx.Y = Vx(1): iVx.Z = Vx(2)
AxisSys.GetYAxis Vy: iVy.X = Vy(0): iVy.Y = Vy(1): iVy.Z = Vy(2)
AxisSys.GetZAxis Vz: iVz.X = Vz(0): iVz.Y = Vz(1): iVz.Z = Vz(2)
NormalizeVector iVx, iVx
NormalizeVector iVy, iVy
NormalizeVector iVz, iVz
Diff.X = Point2Measure.X - iOrig.X: Diff.Y = Point2Measure.Y - iOrig.Y: Diff.Z = Point2Measure.Z - iOrig.Z
LCS.X = DotProduct(Diff, iVx): LCS.Y = DotProduct(Diff, iVy): LCS.Z = DotProduct(Diff, iVz)
Set iOrig = Nothing: Set iVx = Nothing: Set iVy = Nothing: Set iVz = Nothing: Set Diff = Nothing
Erase AOrig: Erase Vx: Erase Vy: Erase Vz
End Function
'Normalizaton of a vector
Public Sub NormalizeVector(IVect As iPct, ByRef NVect As iPct)
Dim Mag As Double
Mag = Sqr(IVect.X ^ 2 + IVect.Y ^ 2 + IVect.Z ^ 2)
If Mag < 0.0000001 Then Call Err.Raise(1001, , "Zero length vector cannot be normalized")
NVect.X = IVect.X / Mag
NVect.Y = IVect.Y / Mag
NVect.Z = IVect.Z / Mag
End Sub
'Get Plane Equation
Public Function PlaneEquation(PartOrigin As iPct, PlaneOrigin As iPct, FirstVector As iPct, SecondVector As iPct) As iPlan
Set PlaneEquation = New iPlan
PlaneEquation.Ax = PartOrigin.Y * (FirstVector.Z - SecondVector.Z) + FirstVector.Y * (SecondVector.Z - PartOrigin.Z) + SecondVector.Y * (PartOrigin.Z - FirstVector.Z)
PlaneEquation.By = PartOrigin.Z * (FirstVector.X - SecondVector.X) + FirstVector.Z * (SecondVector.X - PartOrigin.X) + SecondVector.Z * (PartOrigin.X - FirstVector.X)
PlaneEquation.Cz = PartOrigin.X * (FirstVector.Y - SecondVector.Y) + FirstVector.X * (SecondVector.Y - PartOrigin.Y) + SecondVector.X * (PartOrigin.Y - FirstVector.Y)
PlaneEquation.Dt = PlaneOrigin.X * (FirstVector.Y * SecondVector.Z - SecondVector.Y * FirstVector.Z) + FirstVector.X * (SecondVector.Y * PlaneOrigin.Z - PlaneOrigin.Y * _
SecondVector.Z) + SecondVector.X * (PlaneOrigin.Y * FirstVector.Z - FirstVector.Y * PlaneOrigin.Z)
End Function
'Get plane vectors
Public Function GetPlaneVectors(MyPlane As Variant) As iPct()
Dim ArrRet() As iPct: ReDim ArrRet(1)
Dim V1(2): Dim V2(2)
MyPlane.GetFirstAxis V1: ArrRet(0).X = V1(0): ArrRet(0).Y = V1(1): ArrRet(0).Z = V1(2)
MyPlane.GetSecondAxis V2: ArrRet(1).X = V2(0): ArrRet(1).Y = V2(1): ArrRet(1).Z = V2(2)
GetPlaneVectors = ArrRet
Erase ArrRet: Erase V1: Erase V2
End Function
'Get angle between two planes
Public Function DihedralAngle(FirstPlane As iPlan, SecondPlane As iPlan) As Double
DihedralAngle = ArcCos(FirstPlane.Ax * SecondPlane.Ax + FirstPlane.By * SecondPlane.By + FirstPlane.Cz * SecondPlane.Cz / _
Sqr((FirstPlane.Ax ^ 2 + FirstPlane.By ^ 2 + FirstPlane.Cz ^ 2) * (SecondPlane.Ax ^ 2 + SecondPlane.By ^ 2 + SecondPlane.Cz ^ 2)))
End Function
'Nothing to comment
Public Function ArcCos(Radians As Double) As Double
If Round(Radians, 8) = 1 Then ArcCos = 0: Exit Function
If Round(Radians, 8) = -1 Then ArcCos = PI: Exit Function
ArcCos = Atn(-Radians / Sqr(1 - Radians ^ 2)) + 2 * Atn(1)
End Function
'Nothing to comment
Public Function ArcSin(Radians As Double) As Double
If (Sqr(1 - Radians ^ 2) <= 0.000000000001) And (Sqr(1 - Radians ^ 2) >= -0.000000000001) Then
ArcSin = PI / 2
Else
End If
End Function
'Get distance between two points
Public Function P2PDist(FirstPoint As iPct, SecondPoint As iPct) As Double
Distance = Sqr((SecondPoint.X - FirstPoint.X) ^ 2 + (SecondPoint.Y - FirstPoint.Y) ^ 2 + (SecondPoint.Z - FirstPoint.Z) ^ 2)
End Function
'Are two points on the same side of the plane?
Public Function WhichSideOfPlane(Plane As iPlan, FirstPoint As iPct, SecondPoint As iPct) As Integer()
Dim ArrReturn() As Integer: ReDim ArrReturn(1)
ArrReturn(0) = Plane.Ax * FirstPoint.X + Plane.By * FirstPoint.Y + Plane.Cz * FirstPoint.Z - Plane.Dt
ArrReturn(1) = Plane.Ax * SecondPoint.X + Plane.By * SecondPoint.Y + Plane.Cz * SecondPoint.Z - Plane.Dt
WhichSideOfPlane = ArrReturn
Erase ArrReturn
End Function
'Get the vector of a line
Public Function GetLineVector(FirstPoint As iPct, SecondPoint As iPct) As iPct
Dim Dist As Double: Set GetLineVector = New iPct
Dist = P2PDist(FirstPoint, Seconpoint)
GetLineVector.X = (SecondPoint.X - FirstPoint.X) / Dist
GetLineVector.Y = (SecondPoint.Y - FirstPoint.Y) / Dist
GetLineVector.Z = (SecondPoint.Z - FirstPoint.Z) / Dist
End Function
'How to Get BREPNAME FROM CATIA
Public Function GetBrep(MyBRepName As String) As String
MyBRepName = Replace(MyBRepName, "Selection_", "")
MyBRepName = Left(MyBRepName, InStrRev(MyBRepName, "));"))
MyBRepName = MyBRepName + ");WithPermanentBody;WithoutBuildError;WithSelectingFeatureSupport;MFBRepVersion_CXR15)"
'");WithTemporaryBody;WithoutBuildError;WithInitialFeatureSupport;MonoFond;MFBRepVersion _CXR14)"
GetBrep = MyBRepName
End Function
'Determine if two lines are skew, intersecting or parallel
Public Function LLIntersect(A As iPct, B As iPct, C As iPct, D As iPct) As iIntersect
Dim M(3, 3) As Double
M(0, 0) = A.X: M(0, 1) = A.Y: M(0, 2) = A.Z: M(0, 3) = 1
M(1, 0) = B.X: M(1, 1) = B.Y: M(1, 2) = B.Z: M(1, 3) = 1
M(2, 0) = C.X: M(2, 1) = C.Y: M(2, 2) = C.Z: M(2, 3) = 1
M(3, 0) = D.X: M(3, 1) = D.Y: M(3, 2) = D.Z: M(3, 3) = 1
If GetDet(M) <> 0 Then Erase M: LLIntersect.Result = Oblice: Exit Function    'skew lines
Dim CxB() As Double: Dim AxB() As Double: ReDim CxB(2): ReDim AxB(2)
Dim Av(2) As Double: Dim Bv(2) As Double: Dim Cv(2) As Double
Av(0) = B.X - A.X: Av(1) = B.Y - A.Y: Av(2) = B.Z - A.Z
Bv(0) = D.X - C.X: Bv(1) = D.Y - C.Y: Bv(2) = D.Z - C.Z
Cv(0) = C.X - A.X: Cv(1) = C.Y - A.Y: Cv(2) = C.Z - A.Z
CxB = CrossProd(Cv, Bv): AxB = CrossProd(Av, Bv)
Dim s As Double
On Error GoTo paralelele
s = DotProd(CxB, AxB) / Abs(DotProd(AxB, AxB))
Dim iInter As iPct
iInter.X = A.X + Av(0) * s    'X coordinate of intersection
iInter.Y = A.Y + Av(1) * s    'Y coordinate of intersection
iInter.Z = A.Z + Av(2) * s    'Z coordinate of intersection
LLIntersect.Result = Intersectie    'intersecting lines
LLIntersect.Val = iInter
paralelele:
Erase CxB: Erase AxB: Erase Cv: Erase Bv: Erase Av
If Err.Number <> 0 Then LLIntersect.Result = PParalele: Err.Clear    'parallel lines
End Function
'Get the distance between two skew lines
Public Function SkewLDist(A As iPct, B As iPct, C As iPct, D As iPct) As Double
Dim Av(2) As Double: Dim Bv(2) As Double: Dim Cv(2) As Double
Dim Det(2, 2) As Double
Av(0) = A.X - B.X: Av(1) = A.Y - B.Y: Av(2) = A.Z - B.Z
Bv(0) = C.X - A.X: Bv(1) = C.Y - A.Y: Bv(2) = C.Z - A.Z
Cv(0) = D.X - C.X: Cv(1) = D.Y - C.Y: Cv(2) = D.Z - C.Z
Det(0, 0) = DotProd(Cv, Cv): Det(0, 1) = DotProd(Cv, Av): Det(0, 2) = DotProd(Cv, Bv)
Det(1, 0) = DotProd(Cv, Av): Det(1, 1) = DotProd(Av, Av): Det(1, 2) = DotProd(Av, Bv)
Det(2, 0) = DotProd(Cv, Bv): Det(2, 1) = DotProd(Av, Bv): Det(2, 2) = DotProd(Bv, Bv)
Dim v As Double
v = GetDet(Det)
SkewLDist = Sqr(v / (Det(0, 0) * Det(1, 1) - Det(1, 0) ^ 2))
End Function
'Get DOT product of two vectors - lenght must be 3
Public Function DotProd(V1() As Double, V2() As Double) As Double
DotProd = V1(0) * V2(0) + V1(1) * V2(1) + V1(2) * V2(2)
End Function
'Get CROSS product of two vectors - lenght must be 3
Public Function CrossProd(V1() As Double, V2() As Double) As Double()
Dim Res() As Double
ReDim Res(2)
Res(0) = V1(1) * V2(2) - V1(2) * V2(1)
Res(1) = V1(2) * V2(0) - V1(0) * V2(2)
Res(2) = V1(0) * V2(1) - V1(1) * V2(0)
CrossProd = Res
Erase Res
End Function
'Get inverse of an NxN matrix
Public Function GetInverse(M() As Double) As Double()
Dim RetVal() As Double: Dim Size As Integer
Dim Det As Double: Dim Adj() As Double
Dim i As Integer: Dim j As Integer
Size = UBound(M): Det = GetDet(M)
If Det <> 0 Then
ReDim RetVal(Size, Size)
For i = 0 To Size
For j = 0 To Size
RetVal(i, j) = Adj(i, j) / Det
Next
Next
GetInverse = RetVal
Erase RetVal
End If
End Function
'Get Determinant of an NxN matrix
Public Function GetDet(M() As Double) As Double
Dim i As Integer: Dim j As Integer
Dim Size As Integer: Size = UBound(M): Dim RetVal As Double
If Size = 1 Then
RetVal = RetVal + M(0, 0) * M(1, 1) - M(0, 1) * M(1, 0)   'daca e deteminant 2x2
Else
For i = 0 To Size
RetVal = RetVal + ((-1) ^ i) * M(0, i) * GetDet(GetMinor(M, 0, i))    'daca e determinant NxN
Next
End If
GetDet = RetVal
End Function
'Get Adjoint matrix - it is used to calculate the inverse of an NxN matrix
Public Function GetAdjoint(M() As Double) As Double()
Dim i As Integer: Dim j As Integer
Dim Size As Integer: Size = UBound(M)
Dim RetVal() As Double: ReDim RV(Size, Size)
For i = 0 To Size
For j = 0 To Size
RetVal(j, i) = ((-1) ^ (i + j)) * GetDet(GetMinor(M, i, j))    'RetVal(i, j)=matricea cofactor; RetVal(j, i)= transpusa matricii cofactor
Next
Next
Erase RetVal
End Function
'Get Minor matrix - it is used to calculate the determinant of an NxN matrix
Public Function GetMinor(Min() As Double, RemRow As Integer, RemCol As Integer) As Double()
Dim RetVal() As Double: Dim i As Integer: Dim j As Integer
Dim IdxC As Integer: Dim IdxR As Integer
Dim Size As Integer: IdxR = 0: Size = UBound(Min) - 1
ReDim RetVal(Size, Size) As Double
For i = 0 To Size + 1
If i <> RemRow Then
IdxC = 0
For j = 0 To Size + 1
If j <> RemCol Then
RetVal(IdxR, IdxC) = Min(i, j)
IdxC = IdxC + 1
End If
Next
IdxR = IdxR + 1
End If
Next
GetMinor = RetVal
Erase RetVal
End Function
'How to aproximate an curve using Cubic Bezier curves
Public Function BSpline3(CollectionOfiPcts As Collection, Increment As Double) As Collection
Dim i As Double: Dim t As Double
Dim A As iPlan: Dim B As iPlan: Dim C As iPlan: Dim Point2Add As iPct
Set BSpline3 = New Collection
For i = 1 To CollectionOfiPcts.Count - 3
Set A = New iPlan: Set B = New iPlan: Set C = New iPlan
A.Ax = (-CollectionOfiPcts(i).X + 3 * CollectionOfiPcts(i + 1).X - 3 * CollectionOfiPcts(i + 2).X + CollectionOfiPcts(i + 3).X) / 6
A.By = (3 * CollectionOfiPcts(i).X - 6 * CollectionOfiPcts(i + 1).X + 3 * CollectionOfiPcts(i + 2).X) / 6
A.Cz = (-3 * CollectionOfiPcts(i).X + 3 * CollectionOfiPcts(i + 2).X) / 6
A.Dt = (CollectionOfiPcts(i).X + 4 * CollectionOfiPcts(i + 1).X + CollectionOfiPcts(i + 2).X) / 6
B.Ax = (-CollectionOfiPcts(i).Y + 3 * CollectionOfiPcts(i + 1).Y - 3 * CollectionOfiPcts(i + 2).Y + CollectionOfiPcts(i + 3).Y) / 6
B.By = (3 * CollectionOfiPcts(i).Y - 6 * CollectionOfiPcts(i + 1).Y + 3 * CollectionOfiPcts(i + 2).Y) / 6
B.Cz = (-3 * CollectionOfiPcts(i).Y + 3 * CollectionOfiPcts(i + 2).Y) / 6
B.Dt = (CollectionOfiPcts(i).Y + 4 * CollectionOfiPcts(i + 1).Y + CollectionOfiPcts(i + 2).Y) / 6
C.Ax = (-CollectionOfiPcts(i).Z + 3 * CollectionOfiPcts(i + 1).Z - 3 * CollectionOfiPcts(i + 2).Z + CollectionOfiPcts(i + 3).Z) / 6
C.By = (3 * CollectionOfiPcts(i).Z - 6 * CollectionOfiPcts(i + 1).Z + 3 * CollectionOfiPcts(i + 2).Z) / 6
C.Cz = (-3 * CollectionOfiPcts(i).Z + 3 * CollectionOfiPcts(i + 2).Z) / 6
C.Dt = (CollectionOfiPcts(i).Z + 4 * CollectionOfiPcts(i + 1).Z + CollectionOfiPcts(i + 2).Z) / 6
For t = 0 To 1 Step Increment
Point2Add.X = A.Dt + A.Cz * t + A.By * t ^ 2 + A.Ax * t ^ 3
Point2Add.Y = B.Dt + B.Cz * t + B.By * t ^ 2 + B.Ax * t ^ 3
Point2Add.Z = C.Dt + C.Cz * t + C.By * t ^ 2 + C.Ax * t ^ 3
Next
Set A = Nothing: Set B = Nothing: Set C = Nothing
Next
End Function
'How to aproximate an curve using Quadratic Bezier curves
Public Function BSplineC(CollectionOfiPcts As Collection, Increment As Double) As Collection
Dim j As Double
Dim t As Double
Dim A As iPct: Dim B As iPct: Dim C As iPct: Dim Point2Add As iPct
Set BSplineC = New Collection
For j = 2 To CollectionOfiPcts.Count - 1
Set A = New iPct: Set B = New iPct: Set C = New iPct
A.X = (CollectionOfiPcts(j - 1).X - 2 * CollectionOfiPcts(j).X + CollectionOfiPcts(j + 1).X) / 2
A.Y = (-2 * CollectionOfiPcts(j - 1).X + 2 * CollectionOfiPcts(j).X) / 2
A.Z = (CollectionOfiPcts(j - 1).X + CollectionOfiPcts(j).X) / 2
B.X = (CollectionOfiPcts(j - 1).Y - 2 * CollectionOfiPcts(j).Y + CollectionOfiPcts(j + 1).Y) / 2
B.Y = (-2 * CollectionOfiPcts(j - 1).Y + 2 * CollectionOfiPcts(j).Y) / 2
B.Z = (CollectionOfiPcts(j - 1).Y + CollectionOfiPcts(j).Y) / 2
C.X = (CollectionOfiPcts(j - 1).Z - 2 * CollectionOfiPcts(j).Z + CollectionOfiPcts(j + 1).Z) / 2
C.Y = (-2 * CollectionOfiPcts(j - 1).Z + 2 * CollectionOfiPcts(j).Z) / 2
C.Z = (CollectionOfiPcts(j - 1).Z + CollectionOfiPcts(j).Z) / 2
For t = 0 To 1 Step Increment
Point2Add.X = A.Z + A.Y * t + A.X * t ^ 2
Point2Add.Y = B.Z + B.Y * t + B.X * t ^ 2
Point2Add.Z = C.Z + C.Y * t + C.X * t ^ 2
Next
Set A = Nothing: Set B = Nothing: Set C = Nothing
Next
End Function
'Vector sorting
Public Sub SortVector(Array2Sort, Order As String)
Dim X As Integer
Dim Temp
Select Case Order
Case "A"
Sorted = False
Do While Not Sorted
Sorted = True
For X = 0 To UBound(Array2Sort) - 1
If Array2Sort(X) > Array2Sort(X + 1) Then
Temp = Array2Sort(X + 1)
Array2Sort(X + 1) = Array2Sort(X)
Array2Sort(X) = Temp
Sorted = False
End If
Next X
Loop
Case "D"
Sorted = False
Do While Not Sorted
Sorted = True
For X = 0 To UBound(Array2Sort) - 1
If Array2Sort(X) < Array2Sort(X + 1) Then
Temp = Array2Sort(X + 1)
Array2Sort(X + 1) = Array2Sort(X)
Array2Sort(X) = Temp
Sorted = False
End If
Next X
Loop
Case Else
MsgBox "Invalid parameter Value Order=A or D"
End Select
End Sub