Find if a point is within a triangle: Difference between revisions

Content added Content deleted
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m (syntax highlighting fixup automation)
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{{trans|Kotlin}}
{{trans|Kotlin}}


<lang 11l>V EPS = 0.001
<syntaxhighlight lang="11l">V EPS = 0.001
V EPS_SQUARE = EPS * EPS
V EPS_SQUARE = EPS * EPS


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p3 = (-100.0 / 8, 100.0 / 6)
p3 = (-100.0 / 8, 100.0 / 6)
tri = Triangle(p1, p2, p3)
tri = Triangle(p1, p2, p3)
test(tri, pt)</lang>
test(tri, pt)</syntaxhighlight>


{{out}}
{{out}}
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It uses a generic two-dimensional geometry, that could be affine, euclidean, or a lot stranger than that. You only need to specify the type of one dimension, and the library ''should'' handle the rest. Edge cases probably exist where they shouldn't, as the area formula might add some imprecision.
It uses a generic two-dimensional geometry, that could be affine, euclidean, or a lot stranger than that. You only need to specify the type of one dimension, and the library ''should'' handle the rest. Edge cases probably exist where they shouldn't, as the area formula might add some imprecision.


<lang Ada>-- triangle.ads
<syntaxhighlight lang="ada">-- triangle.ads
generic
generic
type Dimension is private;
type Dimension is private;
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with Inline;
with Inline;
end;
end;
</syntaxhighlight>
</lang>
<lang Ada>-- triangle.adb
<syntaxhighlight lang="ada">-- triangle.adb


package body Triangle is
package body Triangle is
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end IsPointInTriangle;
end IsPointInTriangle;
end;
end;
</syntaxhighlight>
</lang>
<lang Ada>-- test_triangle.adb
<syntaxhighlight lang="ada">-- test_triangle.adb
with Ada.Text_IO;
with Ada.Text_IO;
use Ada.Text_IO;
use Ada.Text_IO;
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Put_Line("IsPointInTriangle("&Image(origin)&", "&Image(tri2)&") yields "&IsPointInTriangle(origin,tri2)'Image);
Put_Line("IsPointInTriangle("&Image(origin)&", "&Image(tri2)&") yields "&IsPointInTriangle(origin,tri2)'Image);
end test_triangle;
end test_triangle;
</syntaxhighlight>
</lang>


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With additional material
With additional material
{{Trans|Wren}}
{{Trans|Wren}}
<lang algol68>BEGIN # determine whether a point is within a triangle or not #
<syntaxhighlight lang="algol68">BEGIN # determine whether a point is within a triangle or not #
# tolerance for the accurate test #
# tolerance for the accurate test #
REAL eps = 0.001;
REAL eps = 0.001;
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, ( 0.1, 0.11111111111111 ), ( 12.5, 33.333333333333 ), ( -12.5, 16.666666666667 )
, ( 0.1, 0.11111111111111 ), ( 12.5, 33.333333333333 ), ( -12.5, 16.666666666667 )
)
)
END</lang>
END</syntaxhighlight>
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{{out}}
<pre>
<pre>
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=={{header|AutoHotkey}}==
=={{header|AutoHotkey}}==
<lang AutoHotkey>T := [[1.5, 2.4], [5.1, -3.1], [-3.8, 1.2]]
<syntaxhighlight lang="autohotkey">T := [[1.5, 2.4], [5.1, -3.1], [-3.8, 1.2]]
for i, p in [[0, 0], [0, 1], [3, 1], [5.4142857, 14.349206]]
for i, p in [[0, 0], [0, 1], [3, 1], [5.4142857, 14.349206]]
result .= "[" p.1 ", " p.2 "] is within triangle?`t" (TriHasP(T, p) ? "ture" : "false") "`n"
result .= "[" p.1 ", " p.2 "] is within triangle?`t" (TriHasP(T, p) ? "ture" : "false") "`n"
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TriArea(x1, y1, x2, y2, x3, y3){
TriArea(x1, y1, x2, y2, x3, y3){
return Abs((x1 * (y2-y3) + x2 * (y3-y1) + x3 * (y1-y2)) / 2)
return Abs((x1 * (y2-y3) + x2 * (y3-y1) + x3 * (y1-y2)) / 2)
}</lang>
}</syntaxhighlight>
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{{out}}
<pre>[0, 0] is within triangle? ture
<pre>[0, 0] is within triangle? ture
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=={{header|C}}==
=={{header|C}}==
{{trans|Go}}
{{trans|Go}}
<lang c>#include <stdbool.h>
<syntaxhighlight lang="c">#include <stdbool.h>
#include <stdio.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdlib.h>
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return 0;
return 0;
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle is [(1.500000, 2.400000), (5.100000, -3.100000), (-3.800000, 1.200000)]
<pre>Triangle is [(1.500000, 2.400000), (5.100000, -3.100000), (-3.800000, 1.200000)]
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=={{header|C++}}==
=={{header|C++}}==
{{trans|C}}
{{trans|C}}
<lang cpp>#include <iostream>
<syntaxhighlight lang="cpp">#include <iostream>


const double EPS = 0.001;
const double EPS = 0.001;
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return 0;
return 0;
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
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=={{header|Common Lisp}}==
=={{header|Common Lisp}}==
<syntaxhighlight lang="lisp">
<lang Lisp>
; There are different algorithms to solve this problem, such as adding areas, adding angles, etc... but these
; There are different algorithms to solve this problem, such as adding areas, adding angles, etc... but these
; solutions are sensitive to rounding errors intrinsic to float operations. We want to avoid these issues, therefore we
; solutions are sensitive to rounding errors intrinsic to float operations. We want to avoid these issues, therefore we
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(- (car P) (car A)) ))))
(- (car P) (car A)) ))))


</syntaxhighlight>
</lang>
{{out}}
{{out}}
<pre>
<pre>
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=={{header|D}}==
=={{header|D}}==
{{trans|C++}}
{{trans|C++}}
<lang d>import std.algorithm; //.comparison for min and max
<syntaxhighlight lang="d">import std.algorithm; //.comparison for min and max
import std.stdio;
import std.stdio;


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test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, -12.5, 16.666666666666668, 5.414285714285714, 14.349206349206348);
test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, -12.5, 16.666666666666668, 5.414285714285714, 14.349206349206348);
writeln;
writeln;
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
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=={{header|Factor}}==
=={{header|Factor}}==
Uses the parametric equations method from [https://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html].
Uses the parametric equations method from [https://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html].
<lang factor>USING: accessors fry io kernel locals math math.order sequences ;
<syntaxhighlight lang="factor">USING: accessors fry io kernel locals math math.order sequences ;


TUPLE: point x y ;
TUPLE: point x y ;
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3 3 <point> 16 10 <point> 10 16 <point> <triangle> ! Make a triangle
3 3 <point> 16 10 <point> 10 16 <point> <triangle> ! Make a triangle
'[ [ _ point-in-triangle? "#" "." ? write ] each nl ] each nl ! Show points inside the triangle with '#'
'[ [ _ point-in-triangle? "#" "." ? write ] each nl ] each nl ! Show points inside the triangle with '#'
</syntaxhighlight>
</lang>
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<pre>
<pre>
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=={{header|Fortran}}==
=={{header|Fortran}}==
<syntaxhighlight lang="fortran">
<lang Fortran>
PROGRAM POINT_WITHIN_TRIANGLE
PROGRAM POINT_WITHIN_TRIANGLE


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END PROGRAM POINT_WITHIN_TRIANGLE
END PROGRAM POINT_WITHIN_TRIANGLE
</syntaxhighlight>
</lang>
{{out}}<pre>
{{out}}<pre>
Point ( 0.0000000000000000 , 0.0000000000000000 ) is within triangle [( 1.5000000000000000 , 2.4000000953674316 ), ( 5.0999999046325684 , -3.0999999046325684 ), ( -3.7999999523162842 , 1.2000000476837158 )].
Point ( 0.0000000000000000 , 0.0000000000000000 ) is within triangle [( 1.5000000000000000 , 2.4000000953674316 ), ( 5.0999999046325684 , -3.0999999046325684 ), ( -3.7999999523162842 , 1.2000000476837158 )].
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=={{header|FreeBASIC}}==
=={{header|FreeBASIC}}==
<lang freebasic>
<syntaxhighlight lang="freebasic">
type p2d
type p2d
x as double 'define a two-dimensional point
x as double 'define a two-dimensional point
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print
print
next y
next y
</syntaxhighlight>
</lang>
{{out}}<pre>........................................
{{out}}<pre>........................................
........................................
........................................
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=={{header|Go}}==
=={{header|Go}}==
{{trans|Wren}}
{{trans|Wren}}
<lang go>package main
<syntaxhighlight lang="go">package main


import (
import (
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within = accuratePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)
within = accuratePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)
fmt.Println("Point", pt, "is within triangle ?", within)
fmt.Println("Point", pt, "is within triangle ?", within)
}</lang>
}</syntaxhighlight>


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{{out}}
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=={{header|GW-BASIC}}==
=={{header|GW-BASIC}}==
<lang gwbasic>10 PIT1X! = 3 : PIT1Y! = 1.3 : REM arbitrary triangle for demonstration
<syntaxhighlight lang="gwbasic">10 PIT1X! = 3 : PIT1Y! = 1.3 : REM arbitrary triangle for demonstration
20 PIT2X! = 17.222 : PIT2Y! = 10
20 PIT2X! = 17.222 : PIT2Y! = 10
30 PIT3X! = 5.5 : PIT3Y! = 18.212
30 PIT3X! = 5.5 : PIT3Y! = 18.212
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1110 IF PITXXS!+PITXXT!>=1 THEN RETURN
1110 IF PITXXS!+PITXXT!>=1 THEN RETURN
1120 PITRES% = 1
1120 PITRES% = 1
1130 RETURN</lang>
1130 RETURN</syntaxhighlight>
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{{out}}<pre>.........................................
.........................................
.........................................
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The point to be tested is transformed by affine transformation which turns given triangle to the simplex: Triangle (0,0) (0,s) (s,0), where s is half of the triangles' area. After that criteria of overlapping become trivial. Affinity allows to avoid division, so all functions work for points on the integer, or rational, or even modular meshes as well.
The point to be tested is transformed by affine transformation which turns given triangle to the simplex: Triangle (0,0) (0,s) (s,0), where s is half of the triangles' area. After that criteria of overlapping become trivial. Affinity allows to avoid division, so all functions work for points on the integer, or rational, or even modular meshes as well.


<lang haskell>type Pt a = (a, a)
<syntaxhighlight lang="haskell">type Pt a = (a, a)


data Overlapping = Inside | Outside | Boundary
data Overlapping = Inside | Outside | Boundary
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(y <= s && y >= 0) &&
(y <= s && y >= 0) &&
(x == 0 || y == 0 || y == s - x) -> Boundary
(x == 0 || y == 0 || y == s - x) -> Boundary
| otherwise -> Outside</lang>
| otherwise -> Outside</syntaxhighlight>


Testing
Testing
<lang haskell>tests = let
<syntaxhighlight lang="haskell">tests = let
t1 = Triangle (2,0) (-1,2) (-2,-2)
t1 = Triangle (2,0) (-1,2) (-2,-2)
bs = [(2,0), (-1,2), (-2,-2), (0,-1), (1/2,1), (-3/2,0)]
bs = [(2,0), (-1,2), (-2,-2), (0,-1), (1/2,1), (-3/2,0)]
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| i <- [-10..10] :: [Int] ]
| i <- [-10..10] :: [Int] ]
| j <- [-5..5] :: [Int] ]
| j <- [-5..5] :: [Int] ]
where t = Triangle (-8,-3) (8,1) (-1,4)</lang>
where t = Triangle (-8,-3) (8,1) (-1,4)</syntaxhighlight>


<pre>λ> tests
<pre>λ> tests
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=={{header|J}}==
=={{header|J}}==
Implementation, using complex numbers to represent x,y coordinates:
Implementation, using complex numbers to represent x,y coordinates:
<lang J>area=: [:| 0.5-/ .*@,.+. NB. signed area of triangle
<syntaxhighlight lang="j">area=: [:| 0.5-/ .*@,.+. NB. signed area of triangle
I3=: =i.3 NB. identity matrix
I3=: =i.3 NB. identity matrix
inside=: {{ (area y)=+/area"1|:(I3*x)+(1-I3)*y }}</lang>
inside=: {{ (area y)=+/area"1|:(I3*x)+(1-I3)*y }}</syntaxhighlight>


This is based on the algorithm documented for the ada implementation: compute the area of triangles using the determinant method (we want the absolute area here), and check whether the triangles formed with the test point and the sides of the test triangle matches the area of the test triangle.
This is based on the algorithm documented for the ada implementation: compute the area of triangles using the determinant method (we want the absolute area here), and check whether the triangles formed with the test point and the sides of the test triangle matches the area of the test triangle.


Examples:<lang J> 0j0 inside 1.5j2.4 5.1j_3.1 _3.8j1.2
Examples:<syntaxhighlight lang="j"> 0j0 inside 1.5j2.4 5.1j_3.1 _3.8j1.2
1
1
0j1 inside 1.5j2.4 5.1j_3.1 _3.8j1.2
0j1 inside 1.5j2.4 5.1j_3.1 _3.8j1.2
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1
1
5.414285714285714j14.349206349206348 inside 0.1j1r9 12.5j100r3 _12.5j100r6
5.414285714285714j14.349206349206348 inside 0.1j1r9 12.5j100r3 _12.5j100r6
1</lang>
1</syntaxhighlight>


=={{header|Java}}==
=={{header|Java}}==
{{trans|Go}}
{{trans|Go}}
<lang java>import java.util.Objects;
<syntaxhighlight lang="java">import java.util.Objects;


public class FindTriangle {
public class FindTriangle {
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test(tri, pt);
test(tri, pt);
}
}
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle[(1.500000, 2.400000), (5.100000, -3.100000), (-3.800000, 1.200000)]
<pre>Triangle[(1.500000, 2.400000), (5.100000, -3.100000), (-3.800000, 1.200000)]
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'''Preliminaries'''
'''Preliminaries'''
<lang jq>def sum_of_squares(stream): reduce stream as $x (0; . + $x * $x);
<syntaxhighlight lang="jq">def sum_of_squares(stream): reduce stream as $x (0; . + $x * $x);


def distanceSquared(P1; P2): sum_of_squares(P1[0]-P2[0], P1[1]-P2[1]);
def distanceSquared(P1; P2): sum_of_squares(P1[0]-P2[0], P1[1]-P2[1]);
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def EPS: 0.001;
def EPS: 0.001;
def EPS_SQUARE: EPS * EPS; </lang>
def EPS_SQUARE: EPS * EPS; </syntaxhighlight>
<lang jq>def side(P1; P2; Q):
<syntaxhighlight lang="jq">def side(P1; P2; Q):
[P1, P2, Q]
[P1, P2, Q]
| xy
| xy
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elif distanceSquarePointToSegment(P3; P1; Q) <= EPS_SQUARE then true
elif distanceSquarePointToSegment(P3; P1; Q) <= EPS_SQUARE then true
else false
else false
end;</lang>
end;</syntaxhighlight>
'''Examples'''
'''Examples'''
<lang jq>def task1:
<syntaxhighlight lang="jq">def task1:
def pts: [ [0, 0], [0, 1], [3, 1]];
def pts: [ [0, 0], [0, 1], [3, 1]];
"Triangle is \(.)",
"Triangle is \(.)",
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([ [3/2, 12/5], [51/10, -31/10], [-19/5, 1.2] ] | task1), "",
([ [3/2, 12/5], [51/10, -31/10], [-19/5, 1.2] ] | task1), "",
([ [1/10, 1/9], [100/8, 100/3], [100/4, 100/9] ] | task2), "",
([ [1/10, 1/9], [100/8, 100/3], [100/4, 100/9] ] | task2), "",
([ [1/10, 1/9], [100/8, 100/3], [-100/8, 100/6] ] | task2)</lang>
([ [1/10, 1/9], [100/8, 100/3], [-100/8, 100/6] ] | task2)</syntaxhighlight>
{{out}}
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<pre>
<pre>
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{{trans|Python}}
{{trans|Python}}
Using the Wren examples.
Using the Wren examples.
<lang julia>Point(x, y) = [x, y]
<syntaxhighlight lang="julia">Point(x, y) = [x, y]
Triangle(a, b, c) = [a, b, c]
Triangle(a, b, c) = [a, b, c]
LEzero(x) = x < 0 || isapprox(x, 0, atol=0.00000001)
LEzero(x) = x < 0 || isapprox(x, 0, atol=0.00000001)
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end
end
end
end
</lang>{{out}}
</syntaxhighlight>{{out}}
<pre>
<pre>
Using triangle [[1.5, 2.4], [0.51, -0.31], [-0.38, 1.2]]:
Using triangle [[1.5, 2.4], [0.51, -0.31], [-0.38, 1.2]]:
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=={{header|Kotlin}}==
=={{header|Kotlin}}==
{{trans|Java}}
{{trans|Java}}
<lang scala>import kotlin.math.max
<syntaxhighlight lang="scala">import kotlin.math.max
import kotlin.math.min
import kotlin.math.min


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}
}
}
}
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle[(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
<pre>Triangle[(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
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=={{header|Lua}}==
=={{header|Lua}}==
{{trans|C++}}
{{trans|C++}}
<lang lua>EPS = 0.001
<syntaxhighlight lang="lua">EPS = 0.001
EPS_SQUARE = EPS * EPS
EPS_SQUARE = EPS * EPS


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test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, -12.5, 16.666666666666668, 5.414285714285714, 14.349206349206348)
test(0.1, 0.1111111111111111, 12.5, 33.333333333333336, -12.5, 16.666666666666668, 5.414285714285714, 14.349206349206348)
print()</lang>
print()</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
<pre>Triangle is [(1.5, 2.4), (5.1, -3.1), (-3.8, 1.2)]
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<lang Mathematica>RegionMember[Polygon[{{1, 2}, {3, 1}, {2, 4}}], {2, 2}]</lang>
<syntaxhighlight lang="mathematica">RegionMember[Polygon[{{1, 2}, {3, 1}, {2, 4}}], {2, 2}]</syntaxhighlight>
{{out}}
{{out}}
<pre>True</pre>
<pre>True</pre>
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=={{header|Nim}}==
=={{header|Nim}}==
{{trans|Kotlin}}
{{trans|Kotlin}}
<lang Nim>import strformat
<syntaxhighlight lang="nim">import strformat


const
const
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p3 = (-100 / 8, 100 / 6)
p3 = (-100 / 8, 100 / 6)
tri = initTriangle(p1, p2, p3)
tri = initTriangle(p1, p2, p3)
test(tri, pt)</lang>
test(tri, pt)</syntaxhighlight>


{{out}}
{{out}}
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=={{header|Perl}}==
=={{header|Perl}}==
Translate the Java program at [https://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html this blog post] and data set is taken from the [[Find_if_a_point_is_within_a_triangle#Raku|Raku]] entry.
Translate the Java program at [https://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html this blog post] and data set is taken from the [[Find_if_a_point_is_within_a_triangle#Raku|Raku]] entry.
<lang Perl># 20201123 added Perl programming solution
<syntaxhighlight lang="perl"># 20201123 added Perl programming solution


use strict;
use strict;
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while ( my @vertex = $iter->()) { print '(',join(',',@vertex),') ' }
while ( my @vertex = $iter->()) { print '(',join(',',@vertex),') ' }
print ': ',naivePointInTriangle (@DATA, @$point) ? 'True' : 'False', "\n" ;
print ': ',naivePointInTriangle (@DATA, @$point) ? 'True' : 'False', "\n" ;
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Point (0,0) is within triangle (1.5,2.4) (5.1,-3.1) (-3.8,0.5) : True
<pre>Point (0,0) is within triangle (1.5,2.4) (5.1,-3.1) (-3.8,0.5) : True
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=== using convex_hull ===
=== using convex_hull ===
Using convex_hull() from [[Convex_hull#Phix]]
Using convex_hull() from [[Convex_hull#Phix]]
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</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: #008080;">constant</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</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>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">inside</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">inside</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">inside</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">inside</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
<!--</syntaxhighlight>-->
{{out}}
{{out}}
<pre>
<pre>
Line 1,872: Line 1,872:
===trans python===
===trans python===
(same output)
(same output)
<!--<lang Phix>(phixonline)-->
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</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: #008080;">constant</span> <span style="color: #000000;">p0</span> <span style="color: #0000FF;">=</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>
Line 1,907: Line 1,907:
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">iswithin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">iswithin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">iswithin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">)})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"point %v is with triangle %v?:%t\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">iswithin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">triangle</span><span style="color: #0000FF;">)})</span>
<!--</lang>-->
<!--</syntaxhighlight>-->


=={{header|Python}}==
=={{header|Python}}==
<lang python>
<syntaxhighlight lang="python">
""" find if point is in a triangle """
""" find if point is in a triangle """


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isornot = "is" if iswithin(pnt, a, b, c) else "is not"
isornot = "is" if iswithin(pnt, a, b, c) else "is not"
print("Point", pnt, isornot, "within the triangle", TRI)
print("Point", pnt, isornot, "within the triangle", TRI)
</lang>{{out}}
</syntaxhighlight>{{out}}
<pre>
<pre>
Point Point2D(0, 0) is within the triangle Triangle(Point2D(3/2, 12/5), Point2D(51/10, -31/10), Point2D(-19/5, 1/2))
Point Point2D(0, 0) is within the triangle Triangle(Point2D(3/2, 12/5), Point2D(51/10, -31/10), Point2D(-19/5, 1/2))
Line 1,956: Line 1,956:
I would probably use the dot-product version, if only because it requires less (no) division.
I would probably use the dot-product version, if only because it requires less (no) division.


<lang racket>#lang racket/base
<syntaxhighlight lang="racket">#lang racket/base


(define-syntax-rule (all-between-0..1? x ...)
(define-syntax-rule (all-between-0..1? x ...)
Line 2,003: Line 2,003:
(run-tests point-in-triangle?/barycentric)
(run-tests point-in-triangle?/barycentric)
(run-tests point-in-triangle?/parametric)
(run-tests point-in-triangle?/parametric)
(run-tests point-in-triangle?/dot-product))</lang>
(run-tests point-in-triangle?/dot-product))</syntaxhighlight>


{{out}}
{{out}}
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Reusing code from the [[Convex_hull#Raku|Convex hull]] task and some logic from the [[Determine_if_two_triangles_overlap#Raku|Determine if two triangles overlap]] task.
Reusing code from the [[Convex_hull#Raku|Convex hull]] task and some logic from the [[Determine_if_two_triangles_overlap#Raku|Determine if two triangles overlap]] task.


<lang perl6>class Point {
<syntaxhighlight lang="raku" line>class Point {
has Real $.x is rw;
has Real $.x is rw;
has Real $.y is rw;
has Real $.y is rw;
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say "Point {$point.gist} is within triangle {join ', ', @triangle».gist}: ",
say "Point {$point.gist} is within triangle {join ', ', @triangle».gist}: ",
$point.&is-within: @triangle
$point.&is-within: @triangle
}</lang>
}</syntaxhighlight>
{{out}}
{{out}}
<pre>Point (0, 0) is within triangle (1.5, 2.4), (5.1, -3.1), (-3.8, 0.5): True
<pre>Point (0, 0) is within triangle (1.5, 2.4), (5.1, -3.1), (-3.8, 0.5): True
Line 2,050: Line 2,050:


<br>Extra certification code was added to verify that the &nbsp; '''X,Y''' &nbsp; coördinates for the points are not missing and are numeric.
<br>Extra certification code was added to verify that the &nbsp; '''X,Y''' &nbsp; coördinates for the points are not missing and are numeric.
<lang rexx>/*REXX program determines if a specified point is within a specified triangle. */
<syntaxhighlight lang="rexx">/*REXX program determines if a specified point is within a specified triangle. */
parse arg p a b c . /*obtain optional arguments from the CL*/
parse arg p a b c . /*obtain optional arguments from the CL*/
if p=='' | p=="," then p= '(0,0)' /*Not specified? Then use the default.*/
if p=='' | p=="," then p= '(0,0)' /*Not specified? Then use the default.*/
Line 2,066: Line 2,066:
y: procedure; parse arg ',' y ")"; return cert(y,"Y") /* " " Y " */
y: procedure; parse arg ',' y ")"; return cert(y,"Y") /* " " Y " */
$: parse arg aa,bb,cc; return (x(aa)-x(cc)) *(y(bb)-y(cc)) - (x(bb)-x(cc)) *(y(aa)-y(cc))
$: parse arg aa,bb,cc; return (x(aa)-x(cc)) *(y(bb)-y(cc)) - (x(bb)-x(cc)) *(y(aa)-y(cc))
?: #1=$(p,a,b); #2=$(p,b,c); #3=$(p,c,a); return (#1>=0&#2>=0&#3>=0) | (#1<=0&#2<=0&#3<=0)</lang>
?: #1=$(p,a,b); #2=$(p,b,c); #3=$(p,c,a); return (#1>=0&#2>=0&#3>=0) | (#1<=0&#2<=0&#3<=0)</syntaxhighlight>
{{out|output|text=&nbsp; when using the default triangle and the point at: &nbsp; <tt> (0,0) </tt>}}
{{out|output|text=&nbsp; when using the default triangle and the point at: &nbsp; <tt> (0,0) </tt>}}
<pre>
<pre>
Line 2,082: Line 2,082:
=={{header|Ruby}}==
=={{header|Ruby}}==
{{trans|Go}}
{{trans|Go}}
<lang ruby>EPS = 0.001
<syntaxhighlight lang="ruby">EPS = 0.001
EPS_SQUARE = EPS * EPS
EPS_SQUARE = EPS * EPS


Line 2,169: Line 2,169:
end
end


main()</lang>
main()</syntaxhighlight>
{{out}}
{{out}}
<pre>Triangle is [[1.5, 2.4], [5.1, -3.1], [-3.8, 1.2]]
<pre>Triangle is [[1.5, 2.4], [5.1, -3.1], [-3.8, 1.2]]
Line 2,184: Line 2,184:
=={{header|Vlang}}==
=={{header|Vlang}}==
{{trans|go}}
{{trans|go}}
<lang vlang>import math
<syntaxhighlight lang="vlang">import math


const eps = 0.001
const eps = 0.001
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within = accurate_point_in_triangle(x1, y1, x2, y2, x3, y3, x, y)
within = accurate_point_in_triangle(x1, y1, x2, y2, x3, y3, x, y)
println("Point $pt is within triangle ? $within")
println("Point $pt is within triangle ? $within")
}</lang>
}</syntaxhighlight>


{{out}}
{{out}}
Line 2,288: Line 2,288:
=={{header|Wren}}==
=={{header|Wren}}==
This is a translation of the ActionScript code for the 'accurate' method in the first referenced article above.
This is a translation of the ActionScript code for the 'accurate' method in the first referenced article above.
<lang ecmascript>var EPS = 0.001
<syntaxhighlight lang="ecmascript">var EPS = 0.001
var EPS_SQUARE = EPS * EPS
var EPS_SQUARE = EPS * EPS


Line 2,368: Line 2,368:
y3 = tri[2][1]
y3 = tri[2][1]
within = accuratePointInTriangle.call(x1, y1, x2, y2, x3, y3, x, y)
within = accuratePointInTriangle.call(x1, y1, x2, y2, x3, y3, x, y)
System.print("Point %(pt) is within triangle ? %(within)")</lang>
System.print("Point %(pt) is within triangle ? %(within)")</syntaxhighlight>


{{out}}
{{out}}
Line 2,385: Line 2,385:


=={{header|XPL0}}==
=={{header|XPL0}}==
<lang XPL0>func real Dot(W,X,Y,Z); \Return the dot product of two 2D vectors
<syntaxhighlight lang="xpl0">func real Dot(W,X,Y,Z); \Return the dot product of two 2D vectors
real W,X,Y,Z; \ (W-X) dot (Y-Z)
real W,X,Y,Z; \ (W-X) dot (Y-Z)
real WX(2), YZ(2);
real WX(2), YZ(2);
Line 2,408: Line 2,408:
Text(0, if PointInTri([-5.0,-2.2]) then "inside" else "outside"); CrLf(0);
Text(0, if PointInTri([-5.0,-2.2]) then "inside" else "outside"); CrLf(0);
Text(0, if PointInTri([10.5, 6.3]) then "inside" else "outside"); CrLf(0);
Text(0, if PointInTri([10.5, 6.3]) then "inside" else "outside"); CrLf(0);
]</lang>
]</syntaxhighlight>


{{out}}
{{out}}
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