intersection point

this question is more related to maths rather than autocad. Any how I am not able to find a solution so I am sending this post. any help will be deeply appreciated.

we have two non parallel lines intersecting each other. Now we offset first line by x distance and the second one by y distance and their point of intersection changes. I want to know how can we find the coordinates of their new point of intersection.

Thanks.

I would fillet the lines with 0 radius

here's a quicky... returns a list of the intersection point(s)

(defun c:test ()
(vl-load-com)
(setq obj1 (vlax-ename->vla-object (car (entsel "\nPick first object: ")))
     obj2 (vlax-ename->vla-object (car (entsel "\nPick object to intersect: ")))
     )
(setq var (vla-intersectwith obj1 obj2 acExtendBoth)
     sa (vlax-variant-value var)
     ip (vlax-safearray->list sa)
     )
)

Or in plain AutoLisp, even if the lines no longer intersect:

[b][color=BLACK]([/color][/b]defun c:lint [b][color=FUCHSIA]([/color][/b]/ s1 s2 l1 l2[b][color=FUCHSIA])[/color][/b]
 [b][color=FUCHSIA]([/color][/b]while [b][color=NAVY]([/color][/b]or [b][color=MAROON]([/color][/b]not s1[b][color=MAROON])[/color][/b]
            [b][color=MAROON]([/color][/b]> [b][color=GREEN]([/color][/b]sslength s1[b][color=GREEN])[/color][/b] 1[b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b]
        [b][color=NAVY]([/color][/b]princ [color=#2f4f4f]"\nSelect 1st Line:   "[/color][b][color=NAVY])[/color][/b]
        [b][color=NAVY]([/color][/b]setq s1 [b][color=MAROON]([/color][/b]ssget '[b][color=GREEN]([/color][/b][b][color=BLUE]([/color][/b]0 . [color=#2f4f4f]"LINE"[/color][b][color=BLUE])[/color][/b][b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b][b][color=FUCHSIA])[/color][/b]

 [b][color=FUCHSIA]([/color][/b]while [b][color=NAVY]([/color][/b]or [b][color=MAROON]([/color][/b]not s2[b][color=MAROON])[/color][/b]
            [b][color=MAROON]([/color][/b]> [b][color=GREEN]([/color][/b]sslength s2[b][color=GREEN])[/color][/b] 1[b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b]
        [b][color=NAVY]([/color][/b]princ [color=#2f4f4f]"\nSelect 2nd Line:   "[/color][b][color=NAVY])[/color][/b]
        [b][color=NAVY]([/color][/b]setq s2 [b][color=MAROON]([/color][/b]ssget '[b][color=GREEN]([/color][/b][b][color=BLUE]([/color][/b]0 . [color=#2f4f4f]"LINE"[/color][b][color=BLUE])[/color][/b][b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b][b][color=FUCHSIA])[/color][/b]

 [b][color=FUCHSIA]([/color][/b]setq l1 [b][color=NAVY]([/color][/b]ssname s1 0[b][color=NAVY])[/color][/b]
       l2 [b][color=NAVY]([/color][/b]ssname s2 0[b][color=NAVY])[/color][/b][b][color=FUCHSIA])[/color][/b]

 [b][color=FUCHSIA]([/color][/b]inters [b][color=NAVY]([/color][/b]cdr [b][color=MAROON]([/color][/b]assoc 10 [b][color=GREEN]([/color][/b]entget l1[b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b]
         [b][color=NAVY]([/color][/b]cdr [b][color=MAROON]([/color][/b]assoc 11 [b][color=GREEN]([/color][/b]entget l1[b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b]
         [b][color=NAVY]([/color][/b]cdr [b][color=MAROON]([/color][/b]assoc 10 [b][color=GREEN]([/color][/b]entget l2[b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b]
         [b][color=NAVY]([/color][/b]cdr [b][color=MAROON]([/color][/b]assoc 11 [b][color=GREEN]([/color][/b]entget l2[b][color=GREEN])[/color][/b][b][color=MAROON])[/color][/b][b][color=NAVY])[/color][/b] nil[b][color=FUCHSIA])[/color][/b]
 [b][color=BLACK])[/color][/b]

Hopefully the lines are 2D and in the same plane. -David

I must have been bored...

(defun c:test ()
 (vl-load-com)
 (setq oldsnap(getvar "osmode")
   oldecho (getvar "cmdecho"))
 (setvar "osmode" 0)
 (setvar "cmdecho" 0)

 (setq ent1 (entsel "\nSelect first object to offset: ")
   od1 (getdist "\nSpecify offset distance: ")
   pt1 (getpoint "\nSpecify point on side to offset: "))
 (vl-cmdf "offset" od1 ent1 pt1 "")
 (setq obj1 (vlax-ename->vla-object (entlast)))
 

 (setq ent2 (entsel "\nSelect second object to offset: ")
   od2 (getdist "\nSpecify offset distance: ")
   pt2 (getpoint "\nSpecify point on side to offset: "))
 (vl-cmdf "offset" od2 ent2 pt2 "")
 (setq obj2 (vlax-ename->vla-object (entlast)))
 
   
(setq var (vla-intersectwith obj1 obj2 acExtendBoth)
     sa (vlax-variant-value var)
     ip (vlax-safearray->list sa)
     )
 (print (strcat "The intersection point is " (rtos (car ip) 2 2)","(rtos (cadr ip)2 2)","(rtos (caddr ip)2 2)))
 (entdel (entlast))
 (entdel (entlast))
 (setvar "osmode" oldsnap)
 (setvar "cmdecho" oldecho)
 (princ)
)

You can use the quick calculator to find-out intersection points.

From the AutoCAD help file:

ill(p1,p2,p3,p4)

Determines the intersection point between two lines (p1,p2) and (p3,p4). All points are considered three-dimensional.