[討論]三度空間的任意兩條直線的公垂線的做圖方法？

三度空間的兩條直線，如果不平行，也不相交，
叫做 歪斜線。

歪斜線的最短距離，就是 公垂線的長度。
所謂的公垂線，就是一組歪斜線，
只有一條公垂線，同時垂直這一組歪斜線的兩條直線。

請問，如何使用 AUTOCAD 做出歪斜線的 公垂線？
舉例：
LINE (0,0,0) - (5,4,3)
LINE (5,0,3) - (0,4,3)

求上面這兩條歪斜線的最短距離，
還有，公垂線的 中間點 MID-POINT 座標值，

小數點要 四位數。

單純以AutoCAD內建功能繪製，請參考 這裡 的作法。

使用 Lisp 請參考 原發文處

代碼:


; LSQ.LSP - "LINE SKEW" Connects SKEW lines with the shortest connector
; From original code (c)1992, Mitchell A. Wawzonek
; Mitchell A. Wawzonek, P.Eng., Professor
; School of Engineering Technology
; Conestoga College
; 299 Doon Valley Drive
; Kitchener, ON N2G 4M4
; Canada
;
; FINDS THE COMMON PERPENDICULAR
; BETWEEN 2 SKEW LINES
;
; 5-26-06 Added error handling and useability in any UCS.
; Also declared local variables.
;
(defun lsq_error (msg)
(setq *error* sys_error)
(command "UCS" "R" "SYSUCS")
(command "UCS" "D" "SYSUCS")
(setvar "OSMODE" OLDSNAP)
(setvar "CMDECHO" 1)
(redraw)
(princ)
)
(defun C:LSQ (/ E1 E2 P1 P2 P3 P4 X1 X2 X3 X4 Y1 Y2 Y3 Y4
Z1 Z2 Z3 Z4 A D B C F CA SA ANG R1 R P5 P6 DS )

(setq sys_error *error*)
(setq *error* lsq_error)
(setvar "CMDECHO" 0)
(setq OLDSNAP (getvar "OSMODE"))
(setvar "OSMODE" 0)
(command "UCS" "S" "SYSUCS")
(command "UCS" "")
(setq E1 nil E2 nil)
(while (null E1)
(setq E1 (entsel "\nLine 1:"))
(if E1
(progn
(setq E1 (car E1))
(redraw E1 3)
(if (/= (cdr (assoc 0 (entget E1))) "LINE")
(progn
(prompt "\nEntity is a ")
(princ (cdr (assoc 0 (entget E1))))
(princ ". Select a LINE")
(setq E1 nil)
)
)
)
)
) ;endwhile
(while (null E2)
(setq E2 (entsel "\nLine 2:"))
(if E2
(progn
(setq E2 (car E2))
(if (/= (cdr (assoc 0 (entget E2))) "LINE")
(progn
(prompt "\nEntity is a ")
(princ (cdr (assoc 0 (entget E2))))
(princ ". Select a LINE")
(setq E2 nil)
)
)
)
)
) ;endwhile
(setq P1 (cdr (assoc 10 (entget E1)))) ; start point line 1
(setq P2 (cdr (assoc 11 (entget E1)))) ; end point line 1
(setq P3 (cdr (assoc 10 (entget E2)))) ; start point line 2
(setq P4 (cdr (assoc 11 (entget E2)))) ; end point line 2
(setq X1 (car P1) Y1 (cadr P1) Z1 (caddr P1)) ; components of P1
(setq X2 (car P2) Y2 (cadr P2) Z2 (caddr P2)) ; " " " P2
(setq X3 (car P3) Y3 (cadr P3) Z3 (caddr P3)) ; " " " P3
(setq X4 (car P4) Y4 (cadr P4) Z4 (caddr P4)) ; " " " P4
(setq A (+ (* (- X2 X1)(- X1 X3)) (* (- Y2 Y1)(- Y1 Y3)) (* (- Z2 Z1)(- Z1 Z3))))
(setq D (+ (* (- X4 X3)(- X1 X3)) (* (- Y4 Y3)(- Y1 Y3)) (* (- Z4 Z3)(- Z1 Z3))))
(setq B (+ (* (- X2 X1)(- X2 X1)) (* (- Y2 Y1)(- Y2 Y1)) (* (- Z2 Z1)(- Z2 Z1))))
(setq C (+ (* (- X2 X1)(- X4 X3)) (* (- Y2 Y1)(- Y4 Y3)) (* (- Z2 Z1)(- Z4 Z3))))
(setq F (+ (* (- X4 X3)(- X4 X3)) (* (- Y4 Y3)(- Y4 Y3)) (* (- Z4 Z3)(- Z4 Z3))))
(setq CA (ABS (/ C (* (SQRT B)(SQRT F))))) ;Cosine CA=1
(setq SA (SQRT (ABS (- 1 (* CA CA))))) ;Sine SA=0
(setq ANG (ATAN SA CA))
(princ (strcat "\nAngle = " (angtos ANG 0 4)))
(IF (< ANG 0.000005)
(princ "\nLines are parallel - No connector\n")
(progn
(setq R1 (/ (- (* A C) (* B D)) (- (* C C) (* B F))))
(setq R (/ (- (* C R1) A) B))
; connector end pnts
(setq P5 (LIST (+ X1 (* (- X2 X1) R))(+ Y1 (* (- Y2 Y1) R))(+ Z1 (* (- Z2 Z1) R))))
(setq P6 (LIST (+ X3 (* (- X4 X3) R1))(+ Y3 (* (- Y4 Y3) R1))(+ Z3 (* (- Z4 Z3) R1))))
(setq DS (distance P5 P6)) ; connector length
(if (or (< 1 R) (< 1 R1))
(princ " * * * CAUTION: Connector past end of Line 1 or 2"))
(if (or (< R 0) (< R1 0))
(princ " * * * CAUTION: Connector past end of Line 1 or 2"))
(princ (strcat "\nConnector length = " (rtos DS)))
(if (> DS 0.00000000001)
(command ".LINE" P5 P6 "")
(princ "\nLines intersect - no connection")
)
);endprogn
);endif
(setq *error* sys_error)
(command "UCS" "R" "SYSUCS")
(command "UCS" "D" "SYSUCS")
(setvar "OSMODE" OLDSNAP)
(setvar "CMDECHO" 1)
(princ "\r")
(redraw)
(princ)
)


謝謝您的回覆！
我贈送一個 感恩給您。

我研究 研究之後，再發表一下 研究心得。