Find the intersection of a line with a plane: Difference between revisions

</pre>

=={{header|AutoHotkey}}==

<lang AutoHotkey>/*

; https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection#Algebraic_form

l = line vector

lo = point on the line

n = plane normal vector

Po = point on the plane

if (l . n) = 0 ; line and plane are parallel.

if (Po - lo) . n = 0 ; line is contained in the plane.

(P - Po) . n = 0 ; vector equation of plane.

P = lo + l * d ; vector equation of line.

((lo + l * d) - Po) . n = 0 ; Substitute line into plane equation.

(l . n) * d + (lo - Po) . n = 0 ; Expanding.

d = ((Po - lo) . n) / (l . n) ; solving for d.

P = lo + l * ((Po - lo) . n) / (l . n) ; solving P.

*/

intersectPoint(l, lo, n, Pn ){

if (Vector_dot(Vector_sub(Pn, lo), n) = 0) ; line is contained in the plane

return [1]

if (Vector_dot(l, n) = 0) ; line and plane are parallel

return [0]

diff := Vector_Sub(Pn, lo) ; (Po - lo)

prod1 := Vector_Dot(diff, n) ; ((Po - lo) . n)

prod2 := Vector_Dot(l, n) ; (l . n)

d := prod1 / prod2 ; d = ((Po - lo) . n) / (l . n)

return Vector_Add(lo, Vector_Mul(l, d)) ; P = lo + l * d

}

Vector_Add(v, w){

return [v.1+w.1, v.2+w.2, v.3+w.3]

}

Vector_Sub(v, w){

return [v.1-w.1, v.2-w.2, v.3-w.3]

}

Vector_Mul(v, s){

return [s*v.1, s*v.2, s*v.3]

}

Vector_Dot(v, w){

return v.1*w.1 + v.2*w.2 + v.3*w.3

}</lang>

Examples:<lang AutoHotkey>; task

l1 := [0, -1, -1]

lo1 := [0, 0, 10]

n1 := [0, 0, 1]

Po1 := [0, 0, 5]

; line on plane

l2 := [1, 1, 0]

lo2 := [1, 1, 0]

n2 := [0, 0, 1]

Po2 := [5, 1, 0]

; line parallel to plane

l3 := [1, 1, 0]

lo3 := [1, 1, 1]

n3 := [0, 0, 1]

Po3 := [5, 1, 0]

output := ""

loop 3

{

result := ""

ip := intersectPoint(l%A_Index%, lo%A_Index%, n%A_Index%, Po%A_Index%)

for i, v in ip

result .= v ", "

output .= Trim(result, ", ") "`n"

}

MsgBox % output

return</lang>

{{out}}

<pre>0.000000, -5.000000, 5.000000

1 ; line on plane

0 ; line parallel to plane