x,y绕x0,y0任意角度算法

兰州人

要求:

  中心点为x0,y0.求x,y绕x0,y0旋转任意角度的坐标

  方程

  设旋转角度为A，(x,y)变换之后的坐标为(x',y')，那么：
  x'=(x-x0)*cosA-(y-y0)*sinA+x0
  y'=(x-x0)*sinA+(y-y0)*cosA+y0

程序

 
Sub ls()
  Dim P0(0 To 2) As Double, pp(0 To 2) As Double
  P0(0) = 0: P0(1) = 0
  x = 10: y = 0
  Alfa = 30 * Pi / 180
  pp(0) = (x - P0(0)) * Cos(Alfa) - (y - P0(1)) * Sin(Alfa) + P0(0)
  pp(1) = (x - P0(0)) * Sin(Alfa) + (y - P0(1)) * Cos(Alfa) + P0(1)
  Dim objLine As AcadLine
  Set objLine = ThisDrawing.ModelSpace.AddLine(pp, P0)

End Sub
Function Pi()
  Pi = 4 * Atn(1)
End Function

 

兰州人

带功能函数

Type ReturnPoint
  X As Double
  Y As Double
  Z As Double
End Type

Sub lss()
  Dim p2(0 To 2) As Double, p1(0 To 2) As Double
  Dim objLine As AcadLine

  Dim pXY As Variant, P0 As Variant
  Dim pp As ReturnPoint
  pXY = Array(2, 2, 0)
  P0 = Array(0, 0, 0)
 
  pp = RotatingAroundTheZAxis(P0, pXY, 30)
  For ii = 0 To 2
    p1(ii) = P0(ii)
  Next ii
  p2(0) = pp.X: p2(1) = pp.Y: p2(2) = pp.Z
  Set objLine = ThisDrawing.ModelSpace.AddLine(p1, p2)
''
  pYZ = Array(0, 2, 2)
  P0 = Array(0, 0, 0)
 
  pp = RotatingAroundTheXAxis(P0, pYZ, 30)
  For ii = 0 To 2
    p1(ii) = P0(ii)
  Next ii
  p2(0) = pp.X: p2(1) = pp.Y: p2(2) = pp.Z
  Set objLine = ThisDrawing.ModelSpace.AddLine(p1, p2)
''
  pYZ = Array(2, 0, 2)
  P0 = Array(0, 0, 0)
 
  pp = RotatingAroundTheYAxis(P0, pYZ, 30)
  For ii = 0 To 2
    p1(ii) = P0(ii)
  Next ii
  p2(0) = pp.X: p2(1) = pp.Y: p2(2) = pp.Z
  Set objLine = ThisDrawing.ModelSpace.AddLine(p1, p2)

End Sub

Function RotatingAroundTheXAxis(P0 As Variant, pXY As Variant, Gama As Double) As ReturnPoint
  zz = pXY(2): yy = pXY(1)
  z0 = P0(2): y0 = P0(1)
  Gama = Gama * Pi / 180
  With RotatingAroundTheXAxis
    .X = pXY(0)
    .Y = (yy - y0) * Cos(Gama) - (zz - z0) * Sin(Gama) + y0
    .Z = (yy - y0) * Sin(Gama) + (zz - z0) * Cos(Gama) + z0
  End With
End Function

Function RotatingAroundTheYAxis(P0 As Variant, pXY As Variant, Belta As Double) As ReturnPoint
  xx = pXY(0): zz = pXY(2)
  x0 = P0(0): z0 = P0(2)
  Belta = Belta * Pi / 180
  With RotatingAroundTheYAxis
 
    .X = (xx - x0) * Cos(Belta) - (zz - z0) * Sin(Belta) + x0
    .Y = pXY(1)
    .Z = (xx - x0) * Sin(Belta) + (zz - z0) * Cos(Belta) + z0
   
  End With
End Function

Function RotatingAroundTheZAxis(P0 As Variant, pXY As Variant, Alfa As Double) As ReturnPoint
  xx = pXY(0): yy = pXY(1)
  x0 = P0(0): y0 = P0(1)
  Alfa = Alfa * Pi / 180
  With RotatingAroundTheZAxis
    .X = (xx - x0) * Cos(Alfa) - (yy - y0) * Sin(Alfa) + x0
    .Y = (xx - x0) * Sin(Alfa) + (yy - y0) * Cos(Alfa) + y0
    .Z = pXY(2)
  End With
End Function

Function Pi()
  Pi = 4 * Atn(1)
End Function