关于矢量的基础函数

proc calculate {points} {    set num_points [llength $points]    if {$num_points < 2 || $num_points > 4} {        return -code error "Invalid number of points. Must be 2, 3, or 4."    }    set last_point [lindex $points end]    switch $num_points {        2 {            set point1 [lindex $points 0]            set point2 [lindex $points 1]            set vector [vecsub $point2 $point1]            set normalized_vector [vecnormalize $vector]            return [list $normalized_vector $point2]        }        3 - 4 {            set point1 [lindex $points 0]            set point2 [lindex $points 1]            set point3 [lindex $points 2]            set vector1 [vecsub $point2 $point1]            set vector2 [vecsub $point3 $point1]            set normal [veccross $vector1 $vector2]            set normalized_normal [vecnormalize $normal]            return [list $normalized_normal $last_point]        }    }}
proc vecsub {v1 v2} {    set result [list]    foreach i $v1 j $v2 {        lappend result [expr {$j - $i}]    }    return $result}
proc vecnormalize {v} {    set length 0    foreach i $v {        set length [expr {$length + $i*$i}]    }    set length [expr {sqrt($length)}]    set result [list]    foreach i $v {        lappend result [expr {$i / $length}]    }    return $result}
proc veccross {v1 v2} {    set x [expr {[lindex $v1 1]*[lindex $v2 2] - [lindex $v1 2]*[lindex $v2 1]}]    set y [expr {[lindex $v1 2]*[lindex $v2 0] - [lindex $v1 0]*[lindex $v2 2]}]    set z [expr {[lindex $v1 0]*[lindex $v2 1] - [lindex $v1 1]*[lindex $v2 0]}]    return [list $x $y $z]}
calculate {{-65.0463 -298.55 -61.6646 } {38.73903 -207.005 -48.1097} }
calculate {{-65.0463 -298.55 -61.6646 } {38.73903 -207.005 -48.1097} {-51.713 -230.822 -49.622}}
calculate {{-65.0463 -298.55 -61.6646 } {38.73903 -207.005 -48.1097} {-51.713 -230.822 -49.622} {-44.304 -262.711 -49.416} }