I used to sleep a lot in math class... For this question https://groups.google.com/forum/m/#!topic/comp.lang.tcl/iOedyEIUC4E%|%Calculating Distance from a Point to a Plane
%|%I can answer... Maybe there’s a faster way to calculate...

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namespace eval Vector3D {

    namespace export *

    proc sub_v3v3 {v0 v1} {

    lassign $v0 v0x v0y v0z
    lassign $v1 v1x v1y v1z

    return [list [expr {$v0x - $v1x}] \
                 [expr {$v0y - $v1y}] \
                 [expr {$v0z - $v1z}]]

    }

    proc dot_v3v3 {v0 v1} {

        lassign $v0 v0x v0y v0z
        lassign $v1 v1x v1y v1z

        return [expr {($v0x * $v1x) + ($v0y * $v1y) +  ($v0z * $v1z)}]

    }

    proc cross_v3v3 {v0 v1} {

        lassign $v0 vx0 vy0 vz0
        lassign $v1 vx1 vy1 vz1

        return [list [expr {($vy0 * $vz1) - ($vy1 * $vz0)}] \
                     [expr {($vz0 * $vx1) - ($vx0 * $vz1)}] \
                     [expr {($vx0 * $vy1) - ($vy0 * $vx1)}]]

    }

    proc norm {v} {

        lassign $v vx vy vz

        return [expr {sqrt($vx**2 + $vy**2 + $vz**2)}]

    }

    proc unit {v} {

        set n [norm $v]

        if {$n == 0} {
            error "Must be greatest than 0..."
        }

        lassign $v x y z

        return [list [expr {$x / double($n)}] \
                     [expr {$y / double($n)}] \
                     [expr {$z / double($n)}]]
        
    }


}
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   * Utilisation :

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namespace import Vector3D::*

set plan {{-10 -10 10} {10 -10 10} {0 10 10}} ; # 3 points on plan (3d)
set point {0 0 12} ; # point (3d)

lassign $plan v0 v1 v2

set u [sub_v3v3 $v1 $v0]
set v [sub_v3v3 $v2 $v0]
set normal [unit [cross_v3v3 $u $v]] ; # normal to plane

set sub [sub_v3v3 $point $v0]
set dist [dot_v3v3 $normal $sub]

puts "Distance 3D = $dist" 
# Distance 3D = 2.0
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