Digital Project教程

Sub CATMain() Dim partDocument1 As PartDocument Set partDocument1 = CATIA.ActiveDocument Dim part1 As Part Set part1 = partDocument1.Part Dim hybridBodies1 As HybridBodies Set hybridBodies1 = part1.HybridBodies Dim hybridBody1 As HybridBody Set hybridBody1 = hybridBodies1.Item("Geometrical Set.1") Dim sketches1 As Sketches Set sketches1 = hybridBody1.HybridSketches Dim sketch1 As Sketch Set sketch1 = sketches1.Item("Sketch.1")
plotShell 0, 0, 0, 100, 8, factory2D1
sketch1.CloseEdition part1.InWorkObject = hybridBody1 part1.Update End Sub ‘end of Sub CATMain()
Sub plotShell(ByVal xCoord As Double, ByVal yCoord As Double, _ ByVal sAngle As Double, ByVal iniDia As Double, _ ByVal fOrder As Integer, ByRef facUsed As Factory2D) Dim fibArr() As Integer ReDim fibArr(fOrder) Dim plotpoint() ReDim plotpoint(fOrder, 6) getFibNumber fOrder, fibArr 1,0 0,0 For i = 1 To fOrder If i = 1 Then 'starting point x coordinate plotpoint(i, 1) = xCoord 'starting point y coordinate plotpoint(i, 2) = yCoord Else plotpoint(i, 1) = plotpoint(i - 1, 5) plotpoint(i, 2) = plotpoint(i - 1, 6) End If 1,-1
Combining Transformations
• Rotation with arbitrary point
– Translation*rotation*translation
x* x cos y sin x0 (cos 1) y0 sin y* x sin y cos x0 sin y0 (cos 1)
Transformation
• • • • • Scale Translation 2 Dimensional Rotation Reflection Combining Transformations
Scale
(x, y, 0) >> (sx, sy, 0)
T sI
sy
y
s 0 0 T 0 s 0 0 0 s
x sx
1 0 0 I 0 1 0 0 0 1
P * x
s 0 0 y 0 0 s 0 sx sy 0 0 0 s
Scale
P * x
sx 0 y 0 0
0 sy 0
0 s x s y 0 0 x y sz
0 0 0 0 1 0 0 1
T
my
1 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1
Combining Transformations
• Rotation with arbitrary point
x*, y* r θ α y0 x0, y0 x,y
part1.InWorkObject = sketch1 Dim factory2D1 As Factory2D Set factory2D1 = sketch1.OpenEdition() Dim geometricElements1 As GeometricElements Set geometricElements1 = sketch1.GeometricElements Dim axis2D1 As Axis2D Set axis2D1 = geometricElements1.Item("AbsoluteAxis") Dim line2D1 As Line2D Set line2D1 = axis2D1.GetItem("HDirection") line2D1.ReportName = 1 Dim line2D2 As Line2D Set line2D2 = axis2D1.GetItem("VDirection") line2D2.ReportName = 2
If θ = 90° then,
x* y x0 y0 y* x x0 y0
Draw Fibonacci Arcs
CATMain plotShell
getFibNumber
drawArc
Dim fibArr() As Integer Dim plotpoint(fOrder, 6)
• Product AB of m by n matrix A and n by p matrix is an m by p matrix C with the element defined by
Cij Aik Bkj
k 1 n
i 1, m;
j i, p
A11 A12 A13 B11 B12 A A22 A23 B21 B22 21 A31 A32 A33 B31 B32 A11B11 A12 B21 A13 B31 A11B12 A12 B22 A13 B32 A21B11 A22 B21 A23 B31 A21B12 A22 B22 A23 B32 A31B11 A32 B21 A33 B31 A31B12 A32 B22 A33 B32
x0
Combining Transformations
• Rotation with arbitrary point
x *
y * x
cos y sin
sin cos
ห้องสมุดไป่ตู้
x*, y* r θ α y0 θ x0, y0 x,y
x0
Combining Transformations
cos z sin z 0 0
x*, y*
sin z cos z 0 0
0 0 0 0 1 0 0 1
Rotate θ
r θ α x,y
Combining Transformations
• Rotation with arbitrary point
Function getFibNumber(ByVal fOrder As Integer, ByRef fArray() As Integer) If fOrder = 1 Then fArray(fOrder) = 1 ElseIf fOrder = 2 Then fArray(fOrder) = 1 Else fArray(fOrder) = getFibNumber(fOrder - 1, fArray) + _ getFibNumber(fOrder - 2, fArray) End If getFibNumber = fArray(fOrder) End Function
4 by 3 matrix
Row matrix
Sum & Scalar multiplication
• Sum
– Given m-by-n matrices A and B, their sum A + B is the mby-n matrix computed by adding corresponding elements
1 0 0 x0
x*, y* r θ x,y Translate x0, y0 α
0 1 0 y0
0 0 0 0 1 0 0 1
Combining Transformations
• Rotation with arbitrary point
– Translation*rotation*translation


Translation
• Move (x, y, 0) to (x+Δx, y+Δy, 0)
P * x x
y y 0
P x
y 0 1
0 0 0 0 1 0 0 1
0 1 0 1 P * x y 0 1 0 0 x y x x y y 0 1
• Rotation with arbitrary point
1 0 0 x0
x,y α y0 x0, y0 Translate -x0, -y0 x0
0 1 0 y0
0 0 0 0 1 0 0 1
Combining Transformations
• Rotation with arbitrary point
Parametric Design using Digital Project
11. Recap (Transformation & VBScript / VBA)