怎样画两个圆的公切线？

bird168 发表于 2007-4-23 20:42:00

现在已知两个圆，怎样通过程序画这两个圆的公切线？

bird168 发表于 2007-4-24 22:15:00

木有人知道吗？

mccad 发表于 2007-4-25 03:49:00

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 发表于 2007-4-25 09:30:00

本帖最后由作者于 2007-4-25 18:28:15 编辑 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 发表于 2007-4-25 10:31:00

' 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 FunctionPrivate 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 发表于 2007-4-25 18:30:00

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 发表于 2007-4-25 18:59:00

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。

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怎样画两个圆的公切线？