Line circle intersection: Difference between revisions
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*See [https://mathworld.wolfram.com/Circle-LineIntersection.html Wolfram] for the formulae needed.
=={{header|AutoHotkey}}==
<lang AutoHotkey>data := [[[3, -5], 3, [-10, 11], [10, -9], 0]
, [[3, -5], 3, [-10, 11], [-11, 12], 1]
, [[3, -5], 3, [3, -2], [7, -2], 1]
, [[0, 0], 4, [0, -3], [0, 6], 0]
, [[0, 0], 4, [0, -3], [0, 6], 1]
, [[4, 2], 5, [6, 3], [10, 7], 0]
, [[4, 2], 5, [7, 4], [11, 8], 1]]
Result := "Center`tRad`tP1`tP2`tSegment`tintersect 1`tIntersect 2`n"
for i, obj in data
{
x := Line_circle_intersection(center := obj.1, radius := obj.2, P1 := obj.3, P2 := obj.4, Segment := obj.5)
Result .= "[" center.1 "," center.2 "]`t" radius "`t[" p1.1 "," p1.2 "]`t[" p2.1 "," p2.2 "]`t" Segment
for i, v in x
Result .= "`t[" i "]"
Result .= "`n"
}
MsgBox % Result
return
Line_circle_intersection(c, r, p1, p2, segment:=0){
global result
p1.1 -= c.1, p2.1 -= c.1, p1.2 -= c.2, p2.2 -= c.2
dx := p2.1 - p1.1, dy := p2.2 - p1.2
dr := Sqrt(dx**2 + dy**2)
D := p1.1*p2.2 - p2.1*p1.2
x1 := (D * dy + sgn(dy) * dx * Sqrt(r**2 * dr**2 - D**2)) / dr**2
x2 := (D * dy - sgn(dy) * dx * Sqrt(r**2 * dr**2 - D**2)) / dr**2
y1 := (0-D * dx + Abs(dy) * Sqrt(r**2 * dr**2 - D**2)) / dr**2
y2 := (0-D * dx - Abs(dy) * Sqrt(r**2 * dr**2 - D**2)) / dr**2
p1.1 += c.1, p2.1 += c.1, p1.2 += c.2, p2.2 += c.2
x1 += c.1, x2 += c.1, y1 += c.2, y2 += c.2
res := []
if segment
{
if !((x1 < p1.1 && x1 < p2.1) || (x1 > p1.1 && x1 > p2.1)
|| (y1 < p1.2 && y1 < p2.2) || (y1 > p1.2 && y1 > p2.2))
res[x1 ", " y1] := true
if !((x2 < p1.1 && x2 < p2.1) || (x2 > p1.1 && x2 > p2.1)
|| (y2 < p1.2 && y2 < p2.2) || (y2 > p1.2 && y2 > p2.2))
res[x2 ", " y2] := true
}
else
res[x1 ", " y1] := true, res[x2 ", " y2] := true
return res
}
sgn(x){
return x<0?-1:1
}</lang>
{{out}}
<pre>Center Rad P1 P2 Segment intersect 1 Intersect 2
[3,-5] 3 [-10,11] [10,-9] 0 [3.000000, -2.000000] [6.000000, -5.000000]
[3,-5] 3 [-10,11] [-11,12] 1
[3,-5] 3 [3,-2] [7,-2] 1 [3.000000, -2.000000]
[0,0] 4 [0,-3] [0,6] 0 [0.000000, -4.000000] [0.000000, 4.000000]
[0,0] 4 [0,-3] [0,6] 1 [0.000000, 4.000000]
[4,2] 5 [6,3] [10,7] 0 [1.000000, -2.000000] [8.000000, 5.000000]
[4,2] 5 [7,4] [11,8] 1 [8.000000, 5.000000]</pre>
=={{header|C}}==
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