I used to sleep a lot in math class... For this question Calculating Distance from a Point to a Plane I can answer... Maybe there’s a faster way to calculate...
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)}]]
}
}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