怎样画两个圆的公切线？

bird168

现在已知两个圆，怎样通过程序画这两个圆的公切线？

bird168

木有人知道吗？

mccad

只要知道几何做法就没有问题。

几何做法：

在大圆圆心上画一个圆，半径为大圆半径减小圆的半径。然后从小圆圆心画直线与刚画的圆相切，然后把该直线向外偏一段距离，距离是小圆的半径。

而从程序上来做，则可以通过角度来计算该直线的圆心位置以及角度。

bird168

楼上的是一种方法，可是从已知一点画一个圆的切线，从几何方法上讲也很麻烦。我在想可不可不以通过设置捕捉来画呢？

比如，在cad中正常的画两个圆的公切线可以用这样的方法：

1 先画两个圆
2 命令 L 回车,命令 TAN回车,在第一个圆画一点,命令TAN,在第二个圆画一点.就是公切线

希望大家帮我想想办法，如何把上面的命令转成程序来实现？

我现在初步认为用sendcommand方法，不过不知道该如何通过程序指定两个圆的点呢？

iq0050

' 返回值为是否存在切线,lines为切线集合
Public Function LinesTangentToTwoCircles(circle0 As Circle2D, circle1 As Circle2D, lines As Collection) As Boolean
  Dim w As Vector2D
  w.x = circle1.center.x - circle0.center.x
  w.y = circle1.center.y - cricle0.center.y
  Dim wLenSqr As Double
  wLenSqr = w.x * w.x + w.y * w.y
  Dim rSum As Double
  rSum = circle0.radius + circle1.radius
  If wLenSqr <= rSum * rSum Then
    LinesTangentToTwoCircles = False
    Exit Function
  End If
 
  Const epsilon = 0.00001
  Dim rDiff As Double
  rDiff = circle1.radius - circle0.radius
  If Abs(rDiff) >= epsilon Then
    Dim R0sqr As Double, R1sqr As Double, c0 As Double, c1 As Double, c2 As Double, dircr As Double
    R0sqr = circle0.radius * circle0.radius
    R1sqr = circle1.radius * circle1.radius
    c0 = -R0sqr
    c1 = 2# * R0sqr
    c2 = circle1.radius * circle1.radius - R0sqr
    Dim invc2 As Double
    invc2 = 1# / c2
    discr = Sqr(Abs(c1 * c1 - 4# * c0 * c2))
    Dim s As Double, oms As Double, a As Double
    s = -0.5 * (c1 + discr) * invc2
   
    Dim Line1 As New Line2D
    Line1.p.x = circle0.center.x + s * w.x
    Line1.p.y = circle0.center.y + s * w.y
   
    Dim Line2 As New Line2D
    Line2.p.x = Line1.p.x
    Line2.p.y = Line1.p.y
    If s >= 0.5 Then
      a = Sqr(Abs(wLenSqr - R0sqr / (s * s)))
    Else
      oms = 1# - s
      a = Sqr(Abs(wLenSqr = R1sqr / (oms * oms)))
    End If
    GetDirections w, a, Line1.direction, Line2.direction
   
    Dim Line3 As New Line2D
    s = -0.5 * (c1 - discr) * invc2
    Line3.p.x = circle0.center.x + s * w.x
    Line3.p.y = circle0.center.y + s * w.y
   
    Dim Line4 As New Line2D
    Line4.p.x = Line3.p.x
    Line4.p.y = Line3.p.y
   
    If s >= 0.5 Then
      a = Sqr(Abs(wLenSqr - R0sqr / (s * s)))
    Else
      oms = 1# - s
      a = Sqr(Abs(wLenSqr - R1sqr / (oms * oms)))
    End If
    GetDirections w, a, Line3.direction, Line4.direction
  Else
    Dim mid As Point2D
    mid.x = 0.5 * (circle0.center.x + circle1.center.x)
    mid.y = 0.5 * (circle0.center.y + circle1.center.y)
   
    a = Sqr(Abs(wLenSqr - 4# * circle0.radius * circle0.radius))
    GetDirections w, a, Line1.direction, Line2.direction
    Line1.p.x = mid.x
    Line1.p.y = mid.y
    Line2.p.x = mid.x
    Line2.p.y = mid.y
   
    Dim invwlen As Double
    invwlen = 1# / Sqr(wLenSqr)
    w.x = w.x * invwlen
    w.y = w.y * invwlen
   
    Line3.p.x = mid.x + circle0.radius * w.y
    Line3.p.y = mid.y - circle0.radius * w.x
    Line3.direction.x = w.x
    Line3.direction.y = w.y
    Line4.p.x = mid.x - circle0.radius * w.y
    Line4.p.y = mid.y - circle0.radius * w.x
    Liner.direction.x = w.x
    Line4.direction.y = w.y
  End If
  lines.Add Line1
  lines.Add Line2
  lines.Add Line3
  lines.Add Line4
  LinesTangentToTwoCircles = True
End Function

Private Sub GetDirections(w As Vector2D, a As Double, dir0 As Vector2D, dir1 As Vector2D)
  Dim aSqr As Double
  aSqr = a * a
  Dim wxSqr As Double
  wxSqr = w.x * w.x
  Dim wySqr As Double
  wySqr = w.y * w.y
  Dim c2 As Double, invc2 As Double
  c2 = wxSqr + wySqr
  invc2 = 1# / c2
  Dim c0 As Double, c1 As Double, discr As Double, invwx As Double, invwy As Double
  If Abs(w.x) >= Abs(w.y) Then
    c0 = aSqr - wxSqr
    c1 = -2# * a * w.y
    discr = Sqr(Abs(c1 * c1 - 4# * c0 * c2))
    invwx = 1# / w.x
    dir0.y = -0.5 * (c1 + discr) * invc2
    dir0.x = (a - w.y * dir0.y) * invwx
    dir1.y = -0.5 * (c1 - discr) * invc2
    dir1.x = (a - w.y * dir1.y) * invwx
  Else
    c0 = aSqr - wySqr
    c1 = -2# * a * w.x
    discr = Sqr(Abs(c1 * c1 - 4# * c0 * c2))
    invwy = 1# / w.y
    dir0.x = -0.5 * (c1 + discr) * invc2
    dir0.y = (a - w.x * dir0.x) * invwy
    dir1.x = -0.5 * (c1 - discr) * invc2
    dir1.y = (a - w.x * dir1.x) * invwy
  End If
End Sub

bird168

谢谢5楼的程序。

不过还是想大家帮我想想我在4楼说的那个方法，个人认为如果成功将会是最简单的一种方法。

bird168

哈哈，搞定了

acad.ActiveDocument.SendCommand “line tan 100,180,0 tan 340,100,0 ”

只要在不同的圆上各取一个点作为输入参数就可以了。