Find the intersection of two lines: Difference between revisions
Find the intersection of two lines (view source)
Revision as of 16:03, 11 January 2024
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Line 15:
{{trans|Python}}
<
V d = (By2 - By1) * (Ax2 - Ax1) - (Bx2 - Bx1) * (Ay2 - Ay1)
I d == 0
Line 33:
V (e, f, g, h) = (0.0, 3.0, 10.0, 7.0)
V pt = line_intersect(a, b, c, d, e, f, g, h)
print(pt)</
{{out}}
Line 42:
=={{header|360 Assembly}}==
{{trans|Rexx}}
<
INTERSEC CSECT
USING INTERSEC,R13 base register
Line 176:
PG DC CL80' '
REGEQU
END INTERSEC</
{{out}}
<pre>
Line 184:
=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
<
DEFINE REALPTR="CARD"
Line 282:
IntToReal(4,x4) IntToReal(5,y4)
Test(p1,p2,p3,p4)
RETURN</
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Find_the_intersection_of_two_lines.png Screenshot from Atari 8-bit computer]
Line 298:
{{works with|Ada|Ada|2005}}
<
procedure Intersection_Of_Two_Lines
Line 342:
Ada.Text_IO.Put_Line(p.y'Img);
end Intersection_Of_Two_Lines;
</syntaxhighlight>
{{out}}
<pre> 5.00000E+00 5.00000E+00
Line 349:
=={{header|ALGOL 68}}==
Using "school maths".
<
# mode to hold a point #
MODE POINT = STRUCT( REAL x, y );
Line 378:
print( ( fixed( x OF i, -8, 4 ), fixed( y OF i, -8, 4 ), newline ) )
END</
{{out}}
<pre>
Line 384:
</pre>
=={{header|APL}}==
<
⍝ APL has a powerful operator the « dyadic domino » to solve a system of N linear equations with N unknowns
⍝ We use it first to solve the a and b, defining the 2 lines as y = ax + b, with the x and y of the given points
Line 410:
solver ← {(,2 ¯1↑⍵)⌹(2 1↑⍵),1}
I ← solver 2 2⍴((¯1 1)×solver 2 2⍴A,B),(¯1 1)×solver 2 2⍴C,D
</syntaxhighlight>
{{out}}
<pre>
Line 419:
=={{header|Arturo}}==
{{trans|Go}}
<
define :line [a, b][
init: [
Line 441:
l2: to :line @[to :point [0.0 3.0] to :point [10.0 7.0]]
print intersect l1 l2</
{{out}}
Line 448:
=={{header|AutoHotkey}}==
<
x1 := L1[1,1], y1 := L1[1,2]
x2 := L1[2,1], y2 := L1[2,2]
Line 455:
return ((x1*y2-y1*x2)*(x3-x4) - (x1-x2)*(x3*y4-y3*x4)) / ((x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)) ", "
. ((x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)) / ((x1-x2)*(y3-y4) - (y1-y2)*(x3-x4))
}</
Examples:<
L2 := [[0,3], [10,7]]
MsgBox % LineIntersectionByPoints(L1, L2)</
Outputs:<pre>5.000000, 5.000000</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f FIND_THE_INTERSECTION_OF_TWO_LINES.AWK
# converted from Ring
Line 489:
return(1)
}
</syntaxhighlight>
{{out}}
<pre>
Line 504:
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
<syntaxhighlight lang="gwbasic"> 0 A = 1:B = 2: HOME : VTAB 21: HGR : HCOLOR= 3: FOR L = A TO B: READ X1(L),Y1(L),X2(L),Y2(L): HPLOT X1(L),Y1(L) TO X2(L),Y2(L): NEXT : DATA4,0,6,10,0,3,10,7
1 GOSUB 5: IF NAN THEN PRINT "THE LINES DO NOT INTERSECT, THEY ARE EITHER PARALLEL OR CO-INCIDENT."
2 IF NOT NAN THEN PRINT "POINT OF INTERSECTION : "X" "Y
3 PRINT CHR$ (13)"HIT ANY KEY TO END PROGRAM": IF NOT NAN THEN FOR K = 0 TO 1 STEP 0:C = C = 0: HCOLOR= 3 * C: HPLOT X,Y: FOR I = 1 TO 30:K = PEEK (49152) > 127: NEXT I,K
4 GET K$: TEXT : END
5 FOR L = A TO B:S$(L) = "NAN": IF X1(L) < > X2(L) THEN S(L) = (Y1(L) - Y2(L)) / (X1(L) - X2(L)):S$(L) = STR$ (S(L))
6 NEXT L:NAN = S$(A) = S$(B): IF NAN THEN RETURN
7 IF S$(A) = "NAN" AND S$(B) < > "NAN" THEN X = X1(A):Y = (X1(A) - X1(B)) * S(B) + Y1(B): RETURN
8 IF S$(B) = "NAN" AND S$(A) < > "NAN" THEN X = X1(B):Y = (X1(B) - X1(A)) * S(A) + Y1(A): RETURN
9 X = (S(A) * X1(A) - S(B) * X1(B) + Y1(B) - Y1(A)) / (S(A) - S(B)):Y = S(B) * (X - X1(B)) + Y1(B): RETURN</syntaxhighlight>
==={{header|QBasic}}===
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{works with|BASIC256}}
{{works with|Just BASIC}}
{{works with|Run BASIC}}
<syntaxhighlight lang="qbasic">xa = 4: xb = 6: xc = 0: xd = 10
ya = 0: yb = 10: yc = 3: yd = 7
PRINT "The two lines are:"
PRINT "yab ="; (ya - xa * ((yb - ya) / (xb - xa))); "+ x*"; ((yb - ya) / (xb - xa))
PRINT "ycd ="; (yc - xc * ((yd - yc) / (xd - xc))); "+ x*"; ((yd - yc) / (xd - xc))
x = ((yc - xc * ((yd - yc) / (xd - xc))) - (ya - xa * ((yb - ya) / (xb - xa)))) / (((yb - ya) / (xb - xa)) - ((yd - yc) / (xd - xc)))
PRINT "x ="; x
y = ya - xa * ((yb - ya) / (xb - xa)) + x * ((yb - ya) / (xb - xa))
PRINT "yab ="; y
PRINT "ycd ="; (yc - xc * ((yd - yc) / (xd - xc)) + x * ((yd - yc) / (xd - xc)))
PRINT "intersection: ("; x; ","; y; ")"</syntaxhighlight>
{{out}}
<pre>The two lines are:
yab =-20 + x* 5
ycd = 3 + x* 0.4
x = 5
yab = 5
ycd = 5
intersection: ( 5, 5 )</pre>
==={{header|BASIC256}}===
{{works with|QBasic}}
{{works with|Just BASIC}}
{{works with|Run BASIC}}
<syntaxhighlight lang="freebasic">xa = 4 : xb = 6 : xc = 0 : xd = 10
ya = 0 : yb = 10 : yc = 3 : yd = 7
print "The two lines are:"
print "yab = "; (ya-xa*((yb-ya)/(xb-xa))); " + x*"; ((yb-ya)/(xb-xa))
print "ycd = "; (yc-xc*((yd-yc)/(xd-xc))); " + x*"; ((yd-yc)/(xd-xc))
x = ((yc-xc*((yd-yc)/(xd-xc)))-(ya-xa*((yb-ya)/(xb-xa))))/(((yb-ya)/(xb-xa))-((yd-yc)/(xd-xc)))
print "x = "; x
y = ya-xa*((yb-ya)/(xb-xa))+x*((yb-ya)/(xb-xa))
print "yab = "; y
print "ycd = "; (yc-xc*((yd-yc)/(xd-xc))+x*((yd-yc)/(xd-xc)))
print "intersection: ("; x; ", "; y ; ")"</syntaxhighlight>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">define xa = 4, xb = 6, xc = 0, xd = 10
define ya = 0, yb = 10, yc = 3, yd = 7
print "The two lines are:"
print "yab = ", (ya - xa * ((yb - ya) / (xb - xa))), " + x * ", ((yb - ya) / (xb - xa))
print "ycd = ", (yc - xc * ((yd - yc) / (xd - xc))), " + x * ", ((yd - yc) / (xd - xc))
let x = ((yc - xc * ((yd - yc) / (xd - xc))) - (ya - xa * ((yb - ya) / (xb - xa)))) / (((yb - ya) / (xb - xa)) - ((yd - yc) / (xd - xc)))
print "x = ", x
let y = ya - xa * ((yb - ya) / (xb - xa)) + x * ((yb - ya) / (xb - xa))
print "yab = ", y
print "ycd = ", (yc - xc * ((yd - yc) / (xd - xc)) + x * ((yd - yc) / (xd - xc)))
print "intersection: (", x, comma, " ", y, ")"</syntaxhighlight>
{{out| Output}}<pre>The two lines are:
yab = -20 + x * 5
ycd = 3 + x * 0.4000
x = 5
yab = 5
ycd = 5
intersection: (5, 5)</pre>
==={{header|Run BASIC}}===
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
{{works with|QBasic}}
<syntaxhighlight lang="lb">xa = 4: xb = 6: xc = 0: xd = 10
ya = 0: yb = 10: yc = 3: yd = 7
print "The two lines are:"
print "yab = "; (ya - xa * ((yb - ya) / (xb - xa))); "+ x*"; ((yb - ya) / (xb - xa))
print "ycd = "; (yc - xc * ((yd - yc) / (xd - xc))); "+ x*"; ((yd - yc) / (xd - xc))
x = ((yc - xc * ((yd - yc) / (xd - xc))) - (ya - xa * ((yb - ya) / (xb - xa)))) / (((yb - ya) / (xb - xa)) - ((yd - yc) / (xd - xc)))
print "x = "; x
y = ya - xa * ((yb - ya) / (xb - xa)) + x * ((yb - ya) / (xb - xa))
print "yab = "; y
print "ycd = "; (yc - xc * ((yd - yc) / (xd - xc)) + x * ((yd - yc) / (xd - xc)))
print "intersection: ("; x; ","; y; " )"</syntaxhighlight>
==={{header|Sinclair ZX81 BASIC}}===
{{trans|REXX}} (version 1)
Works with 1k of RAM.
<
20 LET YA=0
30 LET XB=6
Line 523 ⟶ 613:
150 PRINT "YAB=";Y
160 PRINT "YCD=";YC-XC*((YD-YC)/(XD-XC))+X*((YD-YC)/(XD-XC))
170 PRINT "INTERSECTION: ";X;",";Y</
{{out}}
<pre>THE TWO LINES ARE:
Line 532 ⟶ 622:
YCD=5
INTERSECTION: 5,5</pre>
==={{header|True BASIC}}===
{{works with|QBasic}}
{{works with|BASIC256}}
{{works with|Just BASIC}}
{{works with|Run BASIC}}
<syntaxhighlight lang="qbasic">LET xa = 4
LET ya = 0
LET xb = 6
LET yb = 10
LET xc = 0
LET yc = 3
LET xd = 10
LET yd = 7
PRINT "The two lines are:"
PRINT "yab ="; (ya-xa*((yb-ya)/(xb-xa))); " + x*"; ((yb-ya)/(xb-xa))
PRINT "ycd ="; (yc-xc*((yd-yc)/(xd-xc))); " + x*"; ((yd-yc)/(xd-xc))
LET x = ((yc-xc*((yd-yc)/(xd-xc)))-(ya-xa*((yb-ya)/(xb-xa))))/(((yb-ya)/(xb-xa))-((yd-yc)/(xd-xc)))
PRINT "x ="; x
LET y = ya-xa*((yb-ya)/(xb-xa))+x*((yb-ya)/(xb-xa))
PRINT "yab ="; y
PRINT "ycd ="; (yc-xc*((yd-yc)/(xd-xc))+x*((yd-yc)/(xd-xc)))
PRINT "intersection: ("; x; ","; y ; " )"
END</syntaxhighlight>
==={{header|Yabasic}}===
<syntaxhighlight lang="freebasic">xa = 4: xb = 6: xc = 0: xd = 10
ya = 0: yb = 10: yc = 3: yd = 7
print "The two lines are:"
print "yab = ", (ya - xa * ((yb - ya) / (xb - xa))), " + x*", ((yb - ya) / (xb - xa))
print "ycd = ", (yc - xc * ((yd - yc) / (xd - xc))), " + x*", ((yd - yc) / (xd - xc))
x = ((yc - xc * ((yd - yc) / (xd - xc))) - (ya - xa * ((yb - ya) / (xb - xa)))) / (((yb - ya) / (xb - xa)) - ((yd - yc) / (xd - xc)))
print "x = ", x
y = ya - xa * ((yb - ya) / (xb - xa)) + x * ((yb - ya) / (xb - xa))
print "yab = ", y
print "ycd = ", (yc - xc * ((yd - yc) / (xd - xc)) + x * ((yd - yc) / (xd - xc)))
print "intersection: (", x, ", ", y, ")"</syntaxhighlight>
=={{header|C}}==
This implementation is generic and considers any two lines in the XY plane and not just the specified example. Usage is printed on incorrect invocation.
<syntaxhighlight lang="c">
#include<stdlib.h>
#include<stdio.h>
Line 626 ⟶ 753:
return 0;
}
</syntaxhighlight>
Invocation and output:
<pre>
Line 634 ⟶ 761:
=={{header|C sharp|C#}}==
<
using System.Drawing;
public class Program
Line 658 ⟶ 785:
Console.WriteLine(FindIntersection(p(0f, 0f), p(1f, 1f), p(1f, 2f), p(4f, 5f)));
}
}</
{{out}}
<pre>
Line 667 ⟶ 794:
=={{header|C++}}==
<
#include <cmath>
#include <cassert>
Line 735 ⟶ 862:
assert(fabs(iy - 5.0) < eps);
return 0;
}</
{{out}}
Line 741 ⟶ 868:
=={{header|Clojure}}==
<
(defn compute-line [pt1 pt2]
(let [[x1 y1] pt1
Line 754 ⟶ 881:
{:x x
:y (+ (* (:slope line1) x)
(:offset line1))}))</
{{out}}
Line 767 ⟶ 894:
=={{header|Common Lisp}}==
<syntaxhighlight lang="lisp">
;; Point is [x y] tuple
(defun point-of-intersection (x1 y1 x2 y2 x3 y3 x4 y4)
Line 779 ⟶ 906:
(list (/ (+ (* (- y3 y1) dx1 dx2) (* x1 dy1 dx2) (* -1 x3 dy2 dx1)) den)
(/ (+ (* (+ x3 x1) dy1 dy2) (* -1 y1 dx1 dy2) (* y3 dx2 dy1)) den) ))))
</syntaxhighlight>
{{out}}
<pre>
Line 788 ⟶ 915:
=={{header|D}}==
{{trans|Kotlin}}
<
struct Point {
Line 828 ⟶ 955:
l2 = Line(Point(1.0, 2.0), Point(4.0, 5.0));
writeln(findIntersection(l1, l2));
}</
{{out}}
<pre>{5.000000, 5.000000}
{-inf, -inf}</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
This subroutine not only finds the intersection, it test for various degenerate condition where the intersection can fail.
<syntaxhighlight lang="Delphi">
{Vector structs and operations - these would normally be in}
{a library, but are produced here so everything is explicit}
type T2DVector=packed record
X,Y: double;
end;
type T2DLine = packed record
P1,P2: T2DVector;
end;
function MakeVector2D(const X,Y: double): T2DVector;
begin
Result.X:=X;
Result.Y:=Y;
end;
function MakeLine2D(X1,Y1,X2,Y2: double): T2DLine;
begin
Result.P1:=MakeVector2D(X1,Y1);
Result.P2:=MakeVector2D(X2,Y2);
end;
function DoLinesIntersect2D(L1,L2: T2DLine; var Point: T2DVector): boolean;
{Finds intersect point only if the lines actually intersect}
var distAB, theCos, theSin, newX, ABpos: double;
begin
Result:=False;
{ Fail if either line segment is zero-length.}
if (L1.P1.X=L1.P2.X) and (L1.P1.Y=L1.P2.Y) or
(L2.P1.X=L2.P2.X) and (L2.P1.Y=L2.P2.Y) then exit;
{ Fail if the segments share an end-point.}
if (L1.P1.X=L2.P1.X) and (L1.P1.Y=L2.P1.Y) or
(L1.P2.X=L2.P1.X) and (L1.P2.Y=L2.P1.Y) or
(L1.P1.X=L2.P2.X) and (L1.P1.Y=L2.P2.Y) or
(L1.P2.X=L2.P2.X) and (L1.P2.Y=L2.P2.Y) then exit;
{ (1) Translate the system so that point A is on the origin.}
L1.P2.X:=L1.P2.X-L1.P1.X; L1.P2.Y:=L1.P2.Y-L1.P1.Y;
L2.P1.X:=L2.P1.X-L1.P1.X; L2.P1.Y:=L2.P1.Y-L1.P1.Y;
L2.P2.X:=L2.P2.X-L1.P1.X; L2.P2.Y:=L2.P2.Y-L1.P1.Y;
{ Discover the length of segment A-B.}
distAB:=sqrt(L1.P2.X*L1.P2.X+L1.P2.Y*L1.P2.Y);
{ (2) Rotate the system so that point B is on the positive X L1.P1.Xis.}
theCos:=L1.P2.X/distAB;
theSin:=L1.P2.Y/distAB;
newX:=L2.P1.X*theCos+L2.P1.Y*theSin;
L2.P1.Y :=L2.P1.Y*theCos-L2.P1.X*theSin; L2.P1.X:=newX;
newX:=L2.P2.X*theCos+L2.P2.Y*theSin;
L2.P2.Y :=L2.P2.Y*theCos-L2.P2.X*theSin; L2.P2.X:=newX;
{ Fail if segment C-D doesn't cross line A-B.}
if (L2.P1.Y<0) and (L2.P2.Y<0) or (L2.P1.Y>=0) and (L2.P2.Y>=0) then exit;
{ (3) Discover the position of the intersection point along line A-B.}
ABpos:=L2.P2.X+(L2.P1.X-L2.P2.X)*L2.P2.Y/(L2.P2.Y-L2.P1.Y);
{ Fail if segment C-D crosses line A-B outside of segment A-B.}
if (ABpos<0) or (ABpos>distAB) then exit;
{ (4) Apply the discovered position to line A-B in the original coordinate system.}
Point.X:=L1.P1.X+ABpos*theCos;
Point.Y:=L1.P1.Y+ABpos*theSin;
Result:=True;
end;
procedure TestIntersect(Memo: TMemo; L1,L2: T2DLine);
var Int: T2DVector;
var S: string;
begin
Memo.Lines.Add('Line-1: '+Format('(%1.0f,%1.0f)->(%1.0f,%1.0f)',[L1.P1.X,L1.P1.Y,L1.P2.X,L1.P2.Y]));
Memo.Lines.Add('Line-2: '+Format('(%1.0f,%1.0f)->(%1.0f,%1.0f)',[L2.P1.X,L2.P1.Y,L2.P2.X,L2.P2.Y]));
if DoLinesIntersect2D(L1,L2,Int) then Memo.Lines.Add(Format('Intersect = %2.1f %2.1f',[Int.X,Int.Y]))
else Memo.Lines.Add('No Intersect.');
end;
procedure TestLineIntersect(Memo: TMemo);
var L1,L2: T2DLine;
var S: string;
begin
L1:=MakeLine2D(4,0,6,10);
L2:=MakeLine2D(0,3,10,7);
TestIntersect(Memo,L1,L2);
Memo.Lines.Add('');
L1:=MakeLine2D(0,0,1,1);
L2:=MakeLine2D(1,2,4,5);
TestIntersect(Memo,L1,L2);
end;
</syntaxhighlight>
{{out}}
<pre>
Line-1: (4,0)->(6,10)
Line-2: (0,3)->(10,7)
Intersect = 5.0 5.0
Line-1: (0,0)->(1,1)
Line-2: (1,2)->(4,5)
No Intersect.
</pre>
=={{header|EasyLang}}==
{{trans|Python}}
<syntaxhighlight>
proc intersect ax1 ay1 ax2 ay2 bx1 by1 bx2 by2 . rx ry .
rx = 1 / 0
ry = 1 / 0
d = (by2 - by1) * (ax2 - ax1) - (bx2 - bx1) * (ay2 - ay1)
if d = 0
return
.
ua = ((bx2 - bx1) * (ay1 - by1) - (by2 - by1) * (ax1 - bx1)) / d
ub = ((ax2 - ax1) * (ay1 - by1) - (by2 - by1) * (ax1 - bx1)) / d
if abs ua > 1 or abs ub > 1
return
.
rx = ax1 + ua * (ax2 - ax1)
ry = ay1 + ua * (ay2 - ay1)
.
intersect 4 0 6 10 0 3 10 7 rx ry
print rx & " " & ry
intersect 4 0 6 10 0 3 10 7.1 rx ry
print rx & " " & ry
intersect 0 0 1 1 1 2 4 5 rx ry
print rx & " " & ry
</syntaxhighlight>
=={{header|Emacs Lisp}}==
<syntaxhighlight lang="lisp">
;; y = a*x + b
(let ()
(defun line-prop (p1 p2)
(let* ((prop-a (/ (- (plist-get p2 'y) (plist-get p1 'y))
(- (plist-get p2 'x) (plist-get p1 'x))))
(prop-b (- (plist-get p1 'y) (* prop-a (plist-get p1 'x)))))
(list 'a prop-a 'b prop-b) ) )
(defun calculate-intersection (line1 line2)
(if (= (plist-get line1 'a) (plist-get line2 'a))
(progn (error "The two lines don't have any intersection.") nil)
(progn
(let (int-x int-y)
(setq int-x (/ (- (plist-get line2 'b) (plist-get line1 'b))
(- (plist-get line1 'a) (plist-get line2 'a))))
(setq int-y (+ (* (plist-get line1 'a) int-x) (plist-get line1 'b)))
(list 'x int-x 'y int-y) ) ) ) )
(let ((p1 '(x 4.0 y 0.0)) (p2 '(x 6.0 y 10.0))
(p3 '(x 0.0 y 3.0)) (p4 '(x 10.0 y 7.0)))
(let ((line1 (line-prop p1 p2))
(line2 (line-prop p3 p4)))
(message "%s" (calculate-intersection line1 line2)) ) )
)
</syntaxhighlight>
{{out}}
<pre>
(x 5.0 y 5.0)
</pre>
=={{header|EMal}}==
<syntaxhighlight lang="emal">
type Intersection
model
Point point
fun asText = <|when(me.point == null, "No intersection", me.point.asText())
end
type Point
model
real x, y
fun asText = <|"(" + me.x + "," + me.y + ")"
end
type Line
model
Point s,e
end
type Main
fun getIntersectionByLines = Intersection by Line n1, Line n2
real a1 = n1.e.y - n1.s.y
real b1 = n1.s.x - n1.e.x
real c1 = a1 * n1.s.x + b1 * n1.s.y
real a2 = n2.e.y - n2.s.y
real b2 = n2.s.x - n2.e.x
real c2 = a2 * n2.s.x + b2 * n2.s.y
real delta = a1 * b2 - a2 * b1
if delta == 0 do return Intersection() end
return Intersection(Point((b2 * c1 - b1 * c2) / delta, (a1 * c2 - a2 * c1) / delta))
end
Line n1 = Line(Point(4, 0), Point(6, 10))
Line n2 = Line(Point(0, 3), Point(10, 7))
writeLine(getIntersectionByLines(n1, n2))
n1 = Line(Point(0, 0), Point(1, 1))
n2 = Line(Point(1, 2), Point(4, 5))
writeLine(getIntersectionByLines(n1, n2))
</syntaxhighlight>
{{out}}
<pre>
(5.0,5.0)
No intersection
</pre>
=={{header|F_Sharp|F#}}==
<
(*
Find the point of intersection of 2 lines.
Line 847 ⟶ 1,190:
intersect (fn (4.0,0.0) (6.0,10.0)) (fn (0.0,3.0) (10.0,7.0))
intersect {a=3.18;b=4.23;c=7.13} {a=6.36;b=8.46;c=9.75}
</syntaxhighlight>
{{out}}
<pre>
Line 856 ⟶ 1,199:
=={{header|Factor}}==
{{works with|Factor|0.99 2020-01-23}}
<
math.matrices.laplace math.vectors prettyprint sequences ;
Line 875 ⟶ 1,218:
{ 4 0 } { 6 10 } { 0 3 } { 10 7 } intersection .
{ 4 0 } { 6 10 } { 0 3 } { 10 7+1/10 } intersection .
{ 0 0 } { 1 1 } { 1 2 } { 4 5 } intersection .</
{{out}}
<pre>
Line 885 ⟶ 1,228:
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<
implicit none
Line 931 ⟶ 1,274:
write(*,*)x,y
end subroutine intersect
end program intersect_two_lines</
{{out}}
<pre> 5.00000000 5.00000000 </pre>
=={{header|FreeBASIC}}==
<
' compile with: fbc -s console
#Define NaN 0 / 0 ' FreeBASIC returns -1.#IND
Line 980 ⟶ 1,323:
Print : Print "hit any key to end program"
Sleep
End</
{{out}}
<pre> 5 5
Line 986 ⟶ 1,329:
=={{header|Frink}}==
<
{
det = (x1 - x2)(y3 - y4) - (y1 - y2)(x3 - x4)
Line 999 ⟶ 1,342:
}
println[lineIntersection[4, 0, 6, 10, 0, 3, 10, 7]]</
{{out}}
<pre>
Line 1,007 ⟶ 1,350:
=={{header|Go}}==
<syntaxhighlight lang="go">
package main
Line 1,053 ⟶ 1,396:
}
}
</syntaxhighlight>
{{Out}}
<pre>{5 5}</pre>
Line 1,059 ⟶ 1,402:
=={{header|Groovy}}==
{{trans|Java}}
<
private static class Point {
double x, y
Line 1,105 ⟶ 1,448:
println(findIntersection(l1, l2))
}
}</
{{out}}
<pre>(5.0, 5.0)
Line 1,111 ⟶ 1,454:
=={{header|Haskell}}==
<
type Point = (Float, Float)
Line 1,146 ⟶ 1,489:
case interSection of
Left x -> x
Right x -> show x</
{{Out}}
<pre>(5.0,5.0)</pre>
Line 1,153 ⟶ 1,496:
{{trans|C++}}
'''Solution:'''
<
findIntersection=: (det ,."1 [: |: -/"2) %&det -/"2</
'''Examples:'''
<
line2=: 0 3 ,: 10 7
line3=: 0 3 ,: 10 7.1
Line 1,172 ⟶ 1,515:
__ __
findIntersection line6 ,: line7
2.5 1.5</
=={{header|Java}}==
{{trans|Kotlin}}
<
private static class Point {
double x, y;
Line 1,222 ⟶ 1,565:
System.out.println(findIntersection(l1, l2));
}
}</
{{out}}
<pre>{5.000000, 5.000000}
Line 1,230 ⟶ 1,573:
{{Trans|Haskell}}
===ES6===
<
'use strict';
// INTERSECTION OF TWO LINES ----------------------------------------------
Line 1,303 ⟶ 1,646:
]);
return show(lrIntersection.Left || lrIntersection.Right);
})();</
{{Out}}
<pre>[5,5]</pre>
Line 1,312 ⟶ 1,655:
points P1 and P2. Array destructuring is used for simplicity.
<
def det(a;b;c;d): a*d - b*c ;
Line 1,333 ⟶ 1,676:
then error("lineIntersect: parallel lines")
else [.xnom/.denom, .ynom/.denom]
end ;</
Example:
<
{{out}}
<syntaxhighlight lang
=={{header|Julia}}==
Line 1,343 ⟶ 1,686:
{{trans|Kotlin}}
<
x::T
y::T
Line 1,373 ⟶ 1,716:
l1 = Line(Point{Float64}(0, 0), Point{Float64}(1, 1))
l2 = Line(Point{Float64}(1, 2), Point{Float64}(4, 5))
println(intersection(l1, l2))</
{{out}}
Line 1,380 ⟶ 1,723:
==== GeometryTypes library version ====
<
a = LineSegment(Point2f0(4, 0), Point2f0(6, 10))
b = LineSegment(Point2f0(0, 3), Point2f0(10, 7))
@show intersects(a, b) # --> intersects(a, b) = (true, Float32[5.0, 5.0])
</syntaxhighlight>
=={{header|Kotlin}}==
{{trans|C#}}
<
class PointF(val x: Float, val y: Float) {
Line 1,418 ⟶ 1,761:
l2 = LineF(PointF(1f, 2f), PointF(4f, 5f))
println(findIntersection(l1, l2))
}</
{{out}}
Line 1,425 ⟶ 1,768:
{-Infinity, -Infinity}
</pre>
=={{header|Lambdatalk}}==
{{trans|Python}}
<syntaxhighlight lang="scheme">
{def line_intersect
{def line_intersect.sub
{lambda {:111 :121 :112 :122 :211 :221 :212 :222}
{let { {:x :111} {:y :121}
{:z {- {* {- :222 :221} {- :112 :111}}
{* {- :212 :211} {- :122 :121}} } }
{:a {- :112 :111}} {:b {- :122 :121}}
{:c {- :212 :211}} {:d {- :222 :221}}
{:e {- :121 :221}} {:f {- :111 :211}}
{:g {- :121 :211}} {:h {- :122 :121}}
} {if {> :z 0}
then {A.new ∞ ∞}
else {let { {:x :x} {:y :y} {:a :a} {:b :b}
{:t1 {/ {- {* :c :e} {* :d :f}} :z} }
{:t2 {/ {- {* :a :g} {* :h :f}} :z} }
} {if {and {>= :t1 0} {<= :t1 1} {>= :t2 0} {<= :t2 1}}
then {A.new {+ :x {* :t1 :a}} {+ :y {* :t1 :b}} }
else {A.new ∞ ∞}} }}}}}
{lambda {:1 :2}
{line_intersect.sub
{A.first {A.first :1}} {A.last {A.first :1}}
{A.first {A.last :1}} {A.last {A.last :1}}
{A.first {A.first :2}} {A.last {A.first :2}}
{A.first {A.last :2}} {A.last {A.last :2}} }}}
-> line_intersect
{line_intersect {A.new {A.new 4 0} {A.new 6 10}}
{A.new {A.new 0 3} {A.new 10 7}}}
-> [5,5]
{line_intersect {A.new {A.new 4 0} {A.new 6 10}}
{A.new {A.new 0 3} {A.new 10 7.1}}}
-> [5.010893246187364,5.05446623093682]
{line_intersect {A.new {A.new 1 -1} {A.new 4 4}}
{A.new {A.new 2 5} {A.new 3 -2}}}
-> [2.5,1.5]
{line_intersect {A.new {A.new 0 0} {A.new 0 0}}
{A.new {A.new 0 3} {A.new 10 7}}}
-> [∞,∞]
{line_intersect {A.new {A.new 0 0} {A.new 1 1}}
{A.new {A.new 1 2} {A.new 4 5}}}
-> [∞,∞]
</syntaxhighlight>
=={{header|Lua}}==
{{trans|C#}}
<
local d = (s1.x - e1.x) * (s2.y - e2.y) - (s1.y - e1.y) * (s2.x - e2.x)
local a = s1.x * e1.y - s1.y * e1.x
Line 1,439 ⟶ 1,828:
local line1start, line1end = {x = 4, y = 0}, {x = 6, y = 10}
local line2start, line2end = {x = 0, y = 3}, {x = 10, y = 7}
print(intersection(line1start, line1end, line2start, line2end))</
{{out}}
<pre>5 5</pre>
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
Module Lineintersection (lineAtuple, lineBtuple) {
class line {
Line 1,474 ⟶ 1,863:
}
Lineintersection (4,0,6,10), (0,3,10,7) ' print 5 5
</syntaxhighlight>
{{out}}
<pre>
Line 1,481 ⟶ 1,870:
=={{header|Maple}}==
<
line(L1, [point(A,[4,0]), point(B,[6,10])]):
line(L2, [point(C,[0,3]), point(E,[10,7])]):
coordinates(intersection(x,L1,L2));</
{{Output|Out}}
<pre>[5, 5]</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
InfiniteLine[{{4, 0}, {6, 10}}],
InfiniteLine[{{0, 3}, {10, 7}}]
]</
{{out}}
<pre>Point[{5, 5}]</pre>
=={{header|MATLAB}}==
<syntaxhighlight lang="matlab">
function cross=intersection(line1,line2)
a=polyfit(line1(:,1),line1(:,2),1);
Line 1,503 ⟶ 1,892:
cross=[a(1) -1; b(1) -1]\[-a(2);-b(2)];
end
</syntaxhighlight>
{{out}}
<pre>line1=[4 0; 6 10]; line2=[0 3; 10 7]; cross=intersection(line1,line2)
Line 1,513 ⟶ 1,902:
=={{header|Modula-2}}==
<
FROM RealStr IMPORT RealToStr;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
Line 1,569 ⟶ 1,958:
ReadChar;
END LineIntersection.</
=={{header|Nim}}==
{{trans|Go}}
<
Line = tuple
slope: float
Line 1,598 ⟶ 1,987:
line1 = createLine((0.0, 0.0), (1.0, 1.0))
line2 = createLine((1.0, 2.0), (4.0, 5.0))
echo intersection(line1, line2)</
{{out}}
<pre>
Line 1,609 ⟶ 1,998:
If warning are enabled the second print will issue a warning since we are trying to print out an undef
<
sub intersect {
my ($x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4) = @_;
Line 1,630 ⟶ 2,019:
($ix, $iy) = intersect(0, 0, 1, 1, 1, 2, 4, 5);
print "$ix $iy\n";
</syntaxhighlight>
=={{header|Phix}}==
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/intersect.htm here].
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">X</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Y</span>
Line 1,660 ⟶ 2,049:
<span style="color: #000000;">intersect</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- "parallel lines/do not intersect"</span>
<span style="color: #000000;">intersect</span><span style="color: #0000FF;">({</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- {2.5,1.5}</span>
<!--</
=={{header|Processing}}==
<
// test lineIntersect() with visual and textual output
float lineA[] = {4, 0, 6, 10}; // try 4, 0, 6, 4
Line 1,699 ⟶ 2,088:
float y = Ay1 + uA * (Ay2 - Ay1);
return new PVector(x, y);
}</
==={{header|Processing Python mode}}===
<
def setup():
Line 1,731 ⟶ 2,120:
x = Ax1 + uA * (Ax2 - Ax1)
y = Ay1 + uA * (Ay2 - Ay1)
return x, y</
=={{header|Python}}==
Find the intersection without importing third-party libraries.
<
""" returns a (x, y) tuple or None if there is no intersection """
d = (By2 - By1) * (Ax2 - Ax1) - (Bx2 - Bx1) * (Ay2 - Ay1)
Line 1,754 ⟶ 2,143:
(e, f), (g, h) = (0, 3), (10, 7) # for non intersecting test
pt = line_intersect(a, b, c, d, e, f, g, h)
print(pt)</
{{Out}}
Line 1,763 ⟶ 2,152:
{{Works with|Python|3.7}}
<
from itertools import product
Line 1,878 ⟶ 2,267:
# MAIN ---
if __name__ == '__main__':
main()</
{{out}}
<pre>(5.0, 5.0)</pre>
{{libheader|Shapely}}
Find the intersection by importing the external [https://shapely.readthedocs.io/en/latest/manual.html Shapely] library.
<
if __name__ == "__main__":
line1 = LineString([(4, 0), (6, 10)])
line2 = LineString([(0, 3), (10, 7)])
print(line1.intersection(line2))</
{{out}}
<pre>POINT (5 5)</pre>
Line 1,894 ⟶ 2,283:
=={{header|Racket}}==
{{trans|C++}}
<
(define (det a b c d) (- (* a d) (* b c))) ; determinant
Line 1,912 ⟶ 2,301:
(module+ test (line-intersect 4 0 6 10
0 3 10 7))</
{{out}}
Line 1,923 ⟶ 2,312:
{{trans|zkl}}
<syntaxhighlight lang="raku"
Real $cx, Real $cy, Real $dx, Real $dy ) {
Line 1,948 ⟶ 2,337:
say 'Intersection point: ', intersection( 4,0, 6,10, 0,3, 10,7 );
say 'Intersection point: ', intersection( 4,0, 6,10, 0,3, 10,7.1 );
say 'Intersection point: ', intersection( 0,0, 1,1, 1,2, 4,5 );</
{{out}}
<pre>Intersection point: (5 5)
Line 1,954 ⟶ 2,343:
Intersection point: Lines are parallel
</pre>
===Using a geometric algebra library===
See task [[geometric algebra]].
<syntaxhighlight lang=raku>use Clifford;
# We pick a projective basis,
# and we compute its pseudo-scalar and its square.
my ($i, $j, $k) = @e;
my $I = $i∧$j∧$k;
my $I2 = ($I**2).narrow;
# Homogeneous coordinates of point (X,Y) are (X,Y,1)
my $A = 4*$i + 0*$j + $k;
my $B = 6*$i + 10*$j + $k;
my $C = 0*$i + 3*$j + $k;
my $D = 10*$i + 7*$j + $k;
# We form lines by joining points
my $AB = $A∧$B;
my $CD = $C∧$D;
# The intersection is their meet, which we
# compute by using the De Morgan law
my $ab = $AB*$I/$I2;
my $cd = $CD*$I/$I2;
my $M = ($ab ∧ $cd)*$I/$I2;
# Affine coordinates are (X/Z, Y/Z)
say $M/($M·$k) X· $i, $j;</syntaxhighlight>
{{out}}
<pre>(5 5)</pre>
=={{header|REXX}}==
Line 1,959 ⟶ 2,383:
Naive implementation.
To be improved for parallel lines and degenerate lines such as y=5 or x=8.
<
Parse Value '(4.0,0.0)' With '(' xa ',' ya ')'
Parse Value '(6.0,10.0)' With '(' xb ',' yb ')'
Line 1,975 ⟶ 2,399:
Say 'yab='y
Say 'ycd='yc-xc*((yd-yc)/(xd-xc))+x*((yd-yc)/(xd-xc))
Say 'Intersection: ('||x','y')'</
{{out}}
<pre>The two lines are:
Line 1,989 ⟶ 2,413:
<br>
Variables are named after the Austrian notation for a straight line: y=k*x+d
<
say ggx1('0.0 0.0 0.0 10.0 0.0 3.0 10.0 7.0')
say ggx1('0.0 0.0 0.0 10.0 0.0 3.0 10.0 7.0')
Line 2,060 ⟶ 2,484:
If res='' Then /* not any special case */
res='Intersection is ('||x'/'y')' /* that's the result */
Return ' -->' res</
{{out}}
<pre>A=(4.0/0.0) B=(6.0/10.0) C=(0.0/3.0) D=(10.0/7.0)
Line 2,078 ⟶ 2,502:
=={{header|Ring}}==
<
# Project : Find the intersection of two lines
Line 2,098 ⟶ 2,522:
see "ycd=" + (yc-xc*((yd-yc)/(xd-xc))+x*((yd-yc)/(xd-xc))) + nl
see "intersection: " + x + "," + y + nl
</syntaxhighlight>
Output:
<pre>
Line 2,108 ⟶ 2,532:
ycd=5
intersection: 5,5
</pre>
=={{header|RPL}}==
{{works with|HP|48}}
« C→R ROT C→R ROT →V2
SWAP 1 4 ROLL 1 { 2 2 } →ARRY /
» '<span style="color:blue">→LINECOEFF</span>' STO
« <span style="color:blue">→LINECOEFF</span> ROT ROT <span style="color:blue">→LINECOEFF</span> OVER -
ARRY→ DROP NEG SWAP /
DUP2 * 1 GET ROT 2 GET + R→C
» '<span style="color:blue">INTERSECT</span>' STO
Latest versions of RPL have powerful equation handling and solving functions:
{{works with|HP|49}}
« DROITE UNROT DROITE OVER -
'X' SOLVE DUP EQ→ NIP
UNROT SUBST EQ→ NIP COLLECT R→C
» '<span style="color:blue">INTERSECT</span>' STO
(4,0) (6,10) (0,3) (10,7) <span style="color:blue">INTERSECT</span>
{{out}}
<pre>
1: (5,5)
</pre>
=={{header|Ruby}}==
<
class Line
Line 2,129 ⟶ 2,576:
def to_s
"y = #{@a}x #{@b.positive? ? '+' : '-'} #{@b.abs}"
end
Line 2,138 ⟶ 2,585:
puts "Line #{l1} intersects line #{l2} at #{l1.intersect(l2)}."
</syntaxhighlight>
{{out}}
<pre>Line y = 5.0x
=={{header|Rust}}==
<
struct Point {
x: f64,
Line 2,189 ⟶ 2,636:
let l2 = Line(Point::new(1.0, 2.0), Point::new(4.0, 5.0));
println!("{:?}", l1.intersect(l2));
}</
{{Out}}
<pre>
Line 2,197 ⟶ 2,644:
=={{header|Scala}}==
<
val (l1, l2) = (LineF(PointF(4, 0), PointF(6, 10)), LineF(PointF(0, 3), PointF(10, 7)))
Line 2,226 ⟶ 2,673:
println(findIntersection(l01, l02))
}</
{{Out}}See it in running in your browser by [https://scalafiddle.io/sf/DAqMtEx/0 (JavaScript)]
or by [https://scastie.scala-lang.org/WQOqakOlQnaBRFBa1PuRYw Scastie (JVM)].
Line 2,233 ⟶ 2,680:
{{trans|Raku}}
<
func intersection(ax, ay, bx, by,
Line 2,256 ⟶ 2,703:
say ('Intersection point: ', intersection(4,0, 6,10, 0,3, 10,7))
say ('Intersection point: ', intersection(4,0, 6,10, 0,3, 10,7.1))
say ('Intersection point: ', intersection(0,0, 1,1, 1,2, 4,5))</
{{out}}
<pre>
Line 2,265 ⟶ 2,712:
=={{header|Swift}}==
<
var x: Double
var y: Double
Line 2,300 ⟶ 2,747:
let l2 = Line(p1: Point(x: 0.0, y: 3.0), p2: Point(x: 10.0, y: 7.0))
print("Intersection at : \(l1.intersection(of: l2)!)")</
{{out}}
<pre>Intersection at : Point(x: 5.0, y: 5.0)</pre>
Line 2,308 ⟶ 2,755:
{{trans|Rexx}}
Simple version:
<
([A](2,2)-[A](1,2))/([A](2,1)-[A](1,1))→B
[A](1,2)-[A](1,1)*B→A
Line 2,316 ⟶ 2,763:
A+X*B→Y
C+X*D→Z
Disp {X,Y}</
{{out}}
<pre>
Line 2,322 ⟶ 2,769:
</pre>
Full version:
<
{4,2}→Dim([B])
0→M
Line 2,375 ⟶ 2,822:
End
End
Disp {X,Y,M}</
{{out}}
<pre>
Line 2,386 ⟶ 2,833:
{{works with|VBA|6.5}}
{{works with|VBA|7.1}}
<
Public Type Point
Line 2,451 ⟶ 2,898:
Debug.Assert ip.invalid
End Sub</
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<
Module Module1
Line 2,480 ⟶ 2,927:
End Sub
End Module</
{{out}}
<pre>{X=5, Y=5}
Line 2,487 ⟶ 2,934:
=={{header|Wren}}==
{{trans|Kotlin}}
<
construct new(x, y) {
_x = x
Line 2,528 ⟶ 2,975:
l1 = Line.new(Point.new(0, 0), Point.new(1, 1))
l2 = Line.new(Point.new(1, 2), Point.new(4, 5))
System.print(findIntersection.call(l1, l2))</
{{out}}
Line 2,537 ⟶ 2,984:
=={{header|XPL0}}==
<
return A0*B1 - A1*B0;
Line 2,553 ⟶ 3,000:
M1:= (L1(1,1) - L1(0,1)) / (L1(1,0) - L1(0,0));
Cramer(M0, -1., M0*L0(0,0)-L0(0,1), M1, -1., M1*L1(0,0)-L1(0,1));
]</
{{out}}
Line 2,562 ⟶ 3,009:
=={{header|zkl}}==
{{trans|C++}}
<
detAB,detCD := det(ax,ay, bx,by), det(cx,cy, dx,dy);
abDx,cdDx := ax - bx, cx - dx; // delta x
Line 2,574 ⟶ 3,021:
return(xnom/denom, ynom/denom);
}
fcn det(a,b,c,d){ a*d - b*c } // determinant</
<
{{out}}
<pre>
| |||