求圆弧与圆弧的交点

lgx9612 · 发表于 2014-8-29 21:52:00

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本帖最后由 lgx9612 于 2014-8-31 18:15 编辑

求圆弧与圆弧的交点（附:两个圆弧都是给定参数而定的，图中并没有这此图素，是虚拟的，此程序用来计算用）

(defun inters_arc&arc (c1-centerpoint c1-rad r1-start-ang r1-end-ang c2-centerpoint c2-rad r2-start-ang r2-end-ang
/ return_result_lgx p-point-1 p-point-2 dist-c1_c2 cosa_lgx inarc1 inarc2 interangle-lgx)
;;;原创,编写:刘国新
;;;求圆弧与圆弧的交点
;;;使用方法如下
;;;(inters_arc&arc (cdr (assoc 10 (setq arc (entget (car (entsel "请选择圆弧1\n"))))))
;;;(cdr (assoc 40 arc))(cdr (assoc 50 arc))(cdr (assoc 51 arc))
;;;(cdr (assoc 10 (setq arc (entget (car (entsel "请选择圆弧2\n"))))))
;;;(cdr (assoc 40 arc))(cdr (assoc 50 arc))(cdr (assoc 51 arc)))
(setq return_result_lgx nil)
(if (or (= c1-centerpoint nil)(= c2-centerpoint nil)(= c1-rad nil)(<= c1-rad 0)(= c2-rad nil)(<= c2-rad 0))
(setq return_result_lgx nil)
(progn
(if (= r1-start-ang nil)
(setq r1-start-ang 0.0)
)
(if (= r1-end-ang nil)
(setq r1-end-ang 0.0)
)
(if (= r2-start-ang nil)
(setq r2-start-ang 0.0)
)
(if (= r2-end-ang nil)
(setq r2-end-ang 0.0)
)
(setq r1-start-ang (atof (angtos r1-start-ang 0 8)))
(setq r1-end-ang (atof (angtos r1-end-ang 0 8)))
(if (and (= r1-end-ang 0.0)(= r1-start-ang 0.0))
(setq r1-end-ang 360.0)
)
(setq r2-start-ang (atof (angtos r2-start-ang 0 8)))
(setq r2-end-ang (atof (angtos r2-end-ang 0 8)))
(if (and (= r2-end-ang 0.0)(= r2-start-ang 0.0))
(setq r2-end-ang 360.0)
)
(if (or (> (distance c1-centerpoint c2-centerpoint)(+ c1-rad c2-rad))(< (distance c1-centerpoint c2-centerpoint)(abs (- c1-rad c2-rad)))
(= (distance c1-centerpoint c2-centerpoint) 0.0))
(progn
(setq p-point-1 nil)
(setq p-point-2 nil)
)
(if (or (equal (distance c1-centerpoint c2-centerpoint)(+ c1-rad c2-rad) 0.005)(equal (distance c1-centerpoint c2-centerpoint)(abs (- c1-rad c2-rad)) 0.005))
(progn
(if (> c1-rad c2-rad)
(progn
(setq p-point-1 (polar c1-centerpoint (angle c1-centerpoint c2-centerpoint) c1-rad))
(setq p-point-2 nil)
)
(progn
(setq p-point-1 (polar c2-centerpoint (angle c2-centerpoint c1-centerpoint) c2-rad))
(setq p-point-2 nil)
)
)
)
(progn
(setq dist-c1_c2 (distance c1-centerpoint c2-centerpoint))
(if (< (max dist-c1_c2 c1-rad c2-rad)(- (+ dist-c1_c2 c1-rad c2-rad) (max dist-c1_c2 c1-rad c2-rad)))
(if (or (= dist-c1_c2 0) (= c1-rad 0) (= c2-rad 0))
(princ "\n请输入正确的数值!\n")
(progn
(setq cosa_lgx (/ (- (+ (* (max c1-rad c2-rad) (max c1-rad c2-rad))(* dist-c1_c2 dist-c1_c2))(* (min c1-rad c2-rad) (min c1-rad c2-rad)))
(* (max c1-rad c2-rad) dist-c1_c2 2)))
(setq cosa_lgx (- (/ pi 2.0) (atan (/ cosa_lgx (sqrt (- 1.0 (* cosa_lgx cosa_lgx)))))))
)
)
(princ "\n请输入正确的数值!\n")
)
(if (> c1-rad c2-rad)
(progn
(setq p-point-1 (polar c1-centerpoint (+ (angle c1-centerpoint c2-centerpoint) cosa_lgx) c1-rad))
(setq p-point-2 (polar c1-centerpoint (- (angle c1-centerpoint c2-centerpoint) cosa_lgx) c1-rad))
)
(progn
(setq p-point-1 (polar c2-centerpoint (+ (angle c2-centerpoint c1-centerpoint) cosa_lgx) c2-rad))
(setq p-point-2 (polar c2-centerpoint (- (angle c2-centerpoint c1-centerpoint) cosa_lgx) c2-rad))
)
)
)
)
)
(progn
(if (/= p-point-1 nil)
(progn
(setq inarc1 0)
(setq inarc2 0)
(setq interangle-lgx (atof (angtos (angle c1-centerpoint p-point-1) 0 8)))
(if (< r1-end-ang r1-start-ang)
(if (or (<= interangle-lgx r1-end-ang)(>= interangle-lgx r1-start-ang))
(setq inarc1 1)
)
(if (and (>= interangle-lgx r1-start-ang)(<= interangle-lgx r1-end-ang))
(setq inarc1 1)
)
)
(if (= inarc1 1)
(progn
(setq interangle-lgx (atof (angtos (angle c2-centerpoint p-point-1) 0 8)))
(if (< r2-end-ang r2-start-ang)
(if (or (<= interangle-lgx r2-end-ang)(>= interangle-lgx r2-start-ang))
(setq inarc2 1)
)
(if (and (>= interangle-lgx r2-start-ang)(<= interangle-lgx r2-end-ang))
(setq inarc2 1)
)
)
)
)
(if (and (= inarc1 1)(= inarc2 1))
(setq return_result_lgx (list 1 p-point-1))
)
)
)
(if (/= p-point-2 nil)
(progn
(setq inarc1 0)
(setq inarc2 0)
(setq interangle-lgx (atof (angtos (angle c1-centerpoint p-point-2) 0 8)))
(if (< r1-end-ang r1-start-ang)
(if (or (<= interangle-lgx r1-end-ang)(>= interangle-lgx r1-start-ang))
(setq inarc1 1)
)
(if (and (>= interangle-lgx r1-start-ang)(<= interangle-lgx r1-end-ang))
(setq inarc1 1)
)
)
(if (= inarc1 1)
(progn
(setq interangle-lgx (atof (angtos (angle c2-centerpoint p-point-2) 0 8)))
(if (< r2-end-ang r2-start-ang)
(if (or (<= interangle-lgx r2-end-ang)(>= interangle-lgx r2-start-ang))
(setq inarc2 1)
)
(if (and (>= interangle-lgx r2-start-ang)(<= interangle-lgx r2-end-ang))
(setq inarc2 1)
)
)
)
)
(if (and (= inarc1 1)(= inarc2 1))
(if (= return_result_lgx nil)
(setq return_result_lgx (list 1 p-point-2))
(setq return_result_lgx (list 2 (cadr return_result_lgx) p-point-2))
)
)
)
)
)
)
)
(princ)
return_result_lgx
)

(defun inters_arc&arc (c1-centerpoint c1-rad r1-start-ang r1-end-ang c2-centerpoint c2-rad r2-start-ang r2-end-ang 
      / return_result_lgx p-point-1 p-point-2 dist-c1_c2 cosa_lgx inarc1 inarc2 interangle-lgx) 
;;;原创,编写:刘国新 
;;;求圆弧与圆弧的交点 
;;;使用方法如下 
;;;(inters_arc&arc (cdr (assoc 10 (setq arc (entget (car (entsel "请选择圆弧1\n")))))) 
;;;(cdr (assoc 40 arc))(cdr (assoc 50 arc))(cdr (assoc 51 arc)) 
;;;(cdr (assoc 10 (setq arc (entget (car (entsel "请选择圆弧2\n")))))) 
;;;(cdr (assoc 40 arc))(cdr (assoc 50 arc))(cdr (assoc 51 arc))) 
(setq return_result_lgx nil)   
(if (or (= c1-centerpoint nil)(= c2-centerpoint nil)(= c1-rad nil)(<= c1-rad 0)(= c2-rad nil)(<= c2-rad 0)) 
(setq return_result_lgx nil) 
(progn 
(if (= r1-start-ang nil) 
(setq r1-start-ang 0.0) 
) 
(if (= r1-end-ang nil) 
(setq r1-end-ang 0.0) 
) 
(if (= r2-start-ang nil) 
(setq r2-start-ang 0.0) 
) 
(if (= r2-end-ang nil) 
(setq r2-end-ang 0.0) 
) 
(setq r1-start-ang (atof (angtos r1-start-ang 0 8))) 
(setq r1-end-ang (atof (angtos r1-end-ang 0 8))) 
(if (and (= r1-end-ang 0.0)(= r1-start-ang 0.0)) 
(setq r1-end-ang 360.0) 
) 
(setq r2-start-ang (atof (angtos r2-start-ang 0 8))) 
(setq r2-end-ang (atof (angtos r2-end-ang 0 8))) 
(if (and (= r2-end-ang 0.0)(= r2-start-ang 0.0)) 
(setq r2-end-ang 360.0) 
) 
(if (or (> (distance c1-centerpoint c2-centerpoint)(+ c1-rad c2-rad))(< (distance c1-centerpoint c2-centerpoint)(abs (- c1-rad c2-rad))) 
  (= (distance c1-centerpoint c2-centerpoint) 0.0)) 
(progn 
(setq p-point-1 nil) 
(setq p-point-2 nil) 
) 
(if (or (equal (distance c1-centerpoint c2-centerpoint)(+ c1-rad c2-rad) 0.005)(equal (distance c1-centerpoint c2-centerpoint)(abs (- c1-rad c2-rad)) 0.005)) 
(progn 
(if (> c1-rad c2-rad) 
(progn 
(setq p-point-1 (polar c1-centerpoint (angle c1-centerpoint c2-centerpoint) c1-rad)) 
(setq p-point-2 nil) 
) 
(progn 
(setq p-point-1 (polar c2-centerpoint (angle c2-centerpoint c1-centerpoint) c2-rad)) 
(setq p-point-2 nil) 
) 
) 
) 
(progn 
(setq dist-c1_c2 (distance c1-centerpoint c2-centerpoint)) 
(if (< (max dist-c1_c2 c1-rad c2-rad)(- (+ dist-c1_c2 c1-rad c2-rad) (max dist-c1_c2 c1-rad c2-rad))) 
(if (or (= dist-c1_c2 0) (= c1-rad 0) (= c2-rad 0)) 
(princ "\n请输入正确的数值!\n") 
(progn 
(setq cosa_lgx (/ (- (+ (* (max c1-rad c2-rad) (max c1-rad c2-rad))(* dist-c1_c2 dist-c1_c2))(* (min c1-rad c2-rad) (min c1-rad c2-rad))) 
                (* (max c1-rad c2-rad) dist-c1_c2 2))) 
(setq cosa_lgx (- (/ pi 2.0) (atan (/ cosa_lgx (sqrt (- 1.0 (* cosa_lgx cosa_lgx))))))) 
) 
) 
(princ "\n请输入正确的数值!\n") 
) 
(if (> c1-rad c2-rad) 
(progn 
(setq p-point-1 (polar c1-centerpoint (+ (angle c1-centerpoint c2-centerpoint) cosa_lgx) c1-rad)) 
(setq p-point-2 (polar c1-centerpoint (- (angle c1-centerpoint c2-centerpoint) cosa_lgx) c1-rad)) 
) 
(progn 
(setq p-point-1 (polar c2-centerpoint (+ (angle c2-centerpoint c1-centerpoint) cosa_lgx) c2-rad)) 
(setq p-point-2 (polar c2-centerpoint (- (angle c2-centerpoint c1-centerpoint) cosa_lgx) c2-rad)) 
) 
) 
) 
) 
) 
(progn 
(if (/= p-point-1 nil) 
(progn 
(setq inarc1 0) 
(setq inarc2 0) 
(setq interangle-lgx (atof (angtos (angle c1-centerpoint p-point-1) 0 8))) 
(if (< r1-end-ang r1-start-ang) 
(if (or (<= interangle-lgx r1-end-ang)(>= interangle-lgx r1-start-ang)) 
(setq inarc1 1) 
) 
(if (and (>= interangle-lgx r1-start-ang)(<= interangle-lgx r1-end-ang)) 
(setq inarc1 1) 
) 
) 
(if (= inarc1 1) 
(progn 
(setq interangle-lgx (atof (angtos (angle c2-centerpoint p-point-1) 0 8))) 
(if (< r2-end-ang r2-start-ang) 
(if (or (<= interangle-lgx r2-end-ang)(>= interangle-lgx r2-start-ang)) 
(setq inarc2 1) 
) 
(if (and (>= interangle-lgx r2-start-ang)(<= interangle-lgx r2-end-ang)) 
(setq inarc2 1) 
) 
) 
) 
) 
(if (and (= inarc1 1)(= inarc2 1)) 
(setq return_result_lgx (list 1 p-point-1)) 
) 
) 
) 
(if (/= p-point-2 nil) 
(progn 
(setq inarc1 0) 
(setq inarc2 0) 
(setq interangle-lgx (atof (angtos (angle c1-centerpoint p-point-2) 0 8))) 
(if (< r1-end-ang r1-start-ang) 
(if (or (<= interangle-lgx r1-end-ang)(>= interangle-lgx r1-start-ang)) 
(setq inarc1 1) 
) 
(if (and (>= interangle-lgx r1-start-ang)(<= interangle-lgx r1-end-ang)) 
(setq inarc1 1) 
) 
) 
(if (= inarc1 1) 
(progn 
(setq interangle-lgx (atof (angtos (angle c2-centerpoint p-point-2) 0 8))) 
(if (< r2-end-ang r2-start-ang) 
(if (or (<= interangle-lgx r2-end-ang)(>= interangle-lgx r2-start-ang)) 
(setq inarc2 1) 
) 
(if (and (>= interangle-lgx r2-start-ang)(<= interangle-lgx r2-end-ang)) 
(setq inarc2 1) 
) 
) 
) 
) 
(if (and (= inarc1 1)(= inarc2 1)) 
(if (= return_result_lgx nil) 
(setq return_result_lgx (list 1 p-point-2)) 
(setq return_result_lgx (list 2 (cadr return_result_lgx) p-point-2)) 
) 
) 
) 
) 
) 
) 
) 
(princ) 
return_result_lgx 
)

newer · 发表于 2014-8-29 22:02:36

纯数学方法？

zxq0220 · 发表于 2014-8-30 07:46:29

newer 发表于 2014-8-29 22:02
纯数学方法？

可用了AutoCAD选择的功能。说明有实体存在才能计算。

lgx9612 · 发表于 2014-8-30 08:19:00

newer 发表于 2014-8-29 22:02
纯数学方法？

是三角函数.

ynhh · 发表于 2014-8-30 10:03:08

你数学功力好啊
这一类的交点有一个或两个
你又如何判断啊

ysq101 · 发表于 2014-8-30 11:20:17

好像之前看过谁的贴
用VL函数写的
很简结啊
不过楼主的数学功底好得不得了啊

lgx9612 · 发表于 2014-8-30 13:25:25

ysq101 发表于 2014-8-30 11:20
好像之前看过谁的贴
用VL函数写的
很简结啊

你应该说的是vla-intersectwith函数吧,这个不需要计算，将ename转为vla-object就可以得到交点的，但我现在的前提是两个圆弧都没有图，只有参数（虚拟两个圆弧来计算是否有交点）. 我的程序是用在如:我有已知的两个圆弧，但如果将两个圆弧都偏大或偏小一个距离后求他们是否有相交，有多少个交点?

lgx9612 · 发表于 2014-8-30 13:35:16

ynhh 发表于 2014-8-30 10:03
你数学功力好啊
这一类的交点有一个或两个
你又如何判断啊

分别判断交点是否在圆弧的起始角与终止角之间

st788796 · 发表于 2014-8-30 13:40:16

lgx9612 发表于 2014-8-30 13:35
分别判断交点是否在圆弧的起始角与终止角之间

节省的时间可以用来研究其他的

(defun arc&arc (a1c a1r a1san a1ean a2c a2r a2san a2ean / arc1 arc2 pts
ptl ms)
(setq ms (vla-get-modelspace
(vla-get-activedocument (vlax-get-acad-object))
)
arc1 (vlax-invoke ms 'AddArc a1c a1r a1san a1ean)
arc2 (vlax-invoke ms 'AddArc a2c a2r a2san a2ean)
)
(if (setq pts (vlax-invoke arc1 'IntersectWith arc2 0))
(if (= (length pts) 3)
(setq ptl pts)
(setq ptl (list (list (car pts) (cadr pts) (caddr pts))
(cdddr pts)
)
)
)
)
(mapcar 'vla-delete (list arc1 arc2))
ptl
)

lgx9612 · 发表于 2014-8-30 13:49:01

st788796 发表于 2014-8-30 13:40
节省的时间可以用来研究其他的

受教，谢谢!

newer · 发表于 2014-8-30 13:49:17

lgx9612 发表于 2014-8-30 13:25
你应该说的是vla-intersectwith函数吧,这个不需要计算，将ename转为vla-object就可以得到交点的， ...

你可以根据参数生成两个临时的实体，求交后，再删除掉生成的临时实体。

ysq101 · 发表于 2014-8-30 17:09:37

newer 发表于 2014-8-30 13:49
你可以根据参数生成两个临时的实体，求交后，再删除掉生成的临时实体。

我的意思就是这样。。。可惜我只想到。。。我做不到啊

lgx9612 · 发表于 2014-8-31 22:02:10

我的程序(只是我的程序的一部分，拿出分享一下，当然我也从大家身上学到很多)臃肿，长而不好理解，但并对机算机来说，运行并不在乎你的程序是否简短，下面的对比会让你吃惊。
当然要看程序用在哪一方面，单解决一个问题的话运行时间自然不会加以考虑。
如果你懂汇编的话,就像需要敲几万行汇编代码你甚至可以用一两个win函数搞定。
(progn
(setq time_start (* 1000000 (getvar "cdate")))
(repeat 100000
(arc&arc a1c a1r a1san a1ean a2c  a2r a2san a2ean)
)
(setq time_end (* 1000000 (getvar "cdate")))
(princ (rtos (- time_end time_start)))
(princ)
);;;用时167.0664

(progn
(setq time_start (* 1000000 (getvar "cdate")))
(repeat 100000
(inters_arc&arc a1c a1r a1san a1ean a2c  a2r a2san a2ean)
)
(setq time_end (* 1000000 (getvar "cdate")))
(princ (rtos (- time_end time_start)))
(princ)
);;;用时76.0469

st788796 · 发表于 2014-8-31 22:27:19

本帖最后由 st788796 于 2014-8-31 22:30 编辑

lgx9612 发表于 2014-8-31 22:02
我的程序(只是我的程序的一部分，拿出分享一下，当然我也从大家身上学到很多)臃肿，长而不好理解，但并对机 ...

这样的应用会到那么多级别吗？ 10W次才差一倍，可以忽略

如果你做专业开发也不会用选择 alisp，ARX 有更高效方法，平时应用快捷才是主要的

吴外安放 · 发表于 2020-7-26 14:55:14

谢谢版主分享

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