Line Int with Circle

[jbryant4]

Looking for a built-in reoutine (maybe vl vlx) that calcualtes an intersection between a line and a circle. The line is designated by 2 points and the circle is designated by centerpoint and rad. The line and circle are not entities in the drawing.....Something like this...(cint p1 p2 (list 2.0 3.0) 3.5)).....p1 is first point of line p2 is secong point of line (list 2.0 3.0) is center or circle and 3.5 is circle rad......Seems like I remember seeing something like this?

 

[David Bethel]

not built in but a very simple (inters) call. -David

(inters p10 p11 cen (polar cen (+ (angle p10 p11) (* pi 0.5)) rad))

 

[Kent Cooper, AIA]

I don't think this will work, except maybe under extraordinary-coincidence
circumstances. I am assuming "cen" means the center point of the circle and
"rad" is its radius. I am also assuming that jbrant4 wants to find where
the hypothetical line would intersect the CURVE of the hypothetical circle
(like INT osnap).

(inters) takes four points and finds where the "first" hypothetical line
(between the 1st & 2nd points) would intersect the "second" line (between
the 3rd and 4th). [Of course no actual lines need to be involved, just as
jbryant4's line and circle are not entities in the drawing.] David's
routine makes that "second" line a radius of the circle, whose direction is
perpendicular to the "first" line. But that radius line won't intersect the
"first" line where the "first" line intersects the circle itself, unless it
happens to hit at exactly the right spot at the outside end of that radius.

Simple example: p1 is at 0,0, p2 is at 4,0, the center of the circle is at
1,0, and its radius is 2. The line is horizontal, and happens to pass
through the center of the circle for simplicity of visualization. The line
and circle intersect at 3,0. This routine will look for the intersection
point between four points: 0,0 4,0 1,0 1,2 (the end of the radius at 90
degrees from the direction of the line). That will return 1,0, which
happens to be the center of the circle, and one end of that "second" line,
but not where the line and circle intersect.

If the line happened to be horizontal along the 2 level in the y direction,
it would happen to give the right answer.

I don't see a way to do what I think jbryant4 wants, except maybe to convert
the line and circle into equations representing them, and solve the
simultaneous equations for an intersection. I don't know if you can do that
in any of the languages available for AutoCAD customization, but I assume
something like that is what (inters) does, so maybe someone out there has an
idea. It's just a lot more complicated with the circle involved, but I
guess INT and APPINT osnap must do it somehow.

 

[David Bethel]

;;;Intersection Point Of LINE & CIRCLE
;;;ARG -> LINE ename CIRCLE ename
;;;RETURNS 2D point list or nil
(defun inters_line_circle (le ce / p10 p11 cen rad ppt pds osd ipt p2d)
(setq p2d (lambda (p) (list (car p) (cadr p))))
(and (= (type le) 'ENAME)
(= (type ce) 'ENAME)
(= "LINE" (cdr (assoc 0 (entget le))))
(= "CIRCLE" (cdr (assoc 0 (entget ce))))
(setq p10 (p2d (cdr (assoc 10 (entget le))))
p11 (p2d (cdr (assoc 11 (entget le))))
cen (p2d (cdr (assoc 10 (entget ce))))
rad (cdr (assoc 40 (entget ce))))
(cond ((equal p10 p11 1e-14))
((equal cen p10 1e-11)
(setq ipt (polar cen (angle cen p11) rad)))
((equal cen p11 1e-11)
(setq ipt (polar cen (angle cen p10) rad)))
((setq ppt (inters p10 p11 cen
(polar cen (+ (angle p10 p11) (* pi
0.5)) rad) nil))
(and (setq pds (distance cen ppt))
(<= pds rad)
(setq osd (sqrt (- (* rad rad) (* pds pds)))
ipt (polar ppt (angle ppt p10) osd))))))
ipt)


then something like could work. It would have to be modified to accept
the point directly. -David

 

[Kent Cooper, AIA]

I think I get where you and Pythagoras are going, and yes, it would have to
be modified for hypothetical-point input (this appears to require line and
circle entities to exist already, and it looks like they would have to be
pre-selected). One thing I don't understand -- could you explain the
"le-14" and "le-11" fuzz factors in the (equal) functions?

 

[David Bethel]

As to why they are, I really don't remember. This snippet is probably 8
years old or so. (inters) might have been a little more tolerant than
short line lengths. -David

 

[jbryant4]

This is actually what I have been using(watch word wrap). I had a college coop here at work figure out the formulas, and I converted it to lisp. I have been using this for 7-8 years, however there seems to be times (rarely) where it doesn't quite work right....I thought a while back I saw a VLISP funtion that did the same...Maybe I was wrong.

(defun cint (cen r sp ep / h k x1 x2 y1 y2 rot_flag ang_sp ang_ep
dist_sp dist_ep m yint a b c x11 x22 x y int_pt int_pt_ang
int_pt_dist new_pt
)
(setq
h (nth 0 cen)
k (nth 1 cen)
x1 (nth 0 sp)
x2 (nth 0 ep)
y1 (nth 1 sp)
y2 (nth 1 ep)
)
(if (= x2 x1)
(progn
(setq
rot_flag 1
ang_sp (angle cen sp)
ang_ep (angle cen ep)
dist_sp (distance cen sp)
dist_ep (distance cen ep)
sp (polar cen (+ (dtr 90) ang_sp) dist_sp)
ep (polar cen (+ (dtr 90) ang_ep) dist_ep)
x1 (nth 0 sp)
x2 (nth 0 ep)
y1 (nth 1 sp)
y2 (nth 1 ep)
)
)
(setq rot_flag 0)
)
(setq
m (/ (- y2 y1) (- x2 x1))
yint (- y1 (* m x1))
a (+ (* m m) 1.0)
b (- (* 2.0 m yint) (* 2.0 h) (* 2.0 k m))
c
(+
(* h h)
(* k k)
(* yint yint)
(- (* 2.0 k yint))
(- (* r r))
)
)
(if (> (- (* b b) (* 4.0 a c)) 0.0)
(progn
(setq
x11 (/
(+
(- b)
(sqrt
(- (* b b) (* 4.0 a c))
)
)
(* 2.0 a)
)
x22 (/
(-
(- b)
(sqrt
(- (* b b) (* 4.0 a c))
)
)
(* 2.0 a)
)
)
(if (<= (abs (- x1 x11)) (abs (- x1 x22)))
(setq x x11)
(setq x x22)
)
(setq y (+ (* m x) yint))
)
)
(setq int_pt (list x y))
(if (= rot_flag 1)
(progn
(setq
int_pt_ang (angle cen int_pt)
int_pt_dist (distance cen int_pt)
new_pt (polar cen (- int_pt_ang (dtr 90.0)) int_pt_dist)
)
)
(list x y)
)
)