'''Purpose:''' Show how to convert between rectangular and polar co-ordinates in Tcl.

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If you have rectangular co-ordinates $x and $y, and you need polar co-ordinates $r and $theta, you can use the following:

 proc rect_to_polar {x y} {
     list [expr {hypot($y, $x)}]\
          [expr {atan2($y, $x)}]
 }

 lassign [rect_to_polar $x $y] r theta 

Note the use of [hypot] and [atan2] in the code above.  These functions are much more robust than any corresponding code using [atan] and [sqrt].

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If you have polar co-ordinates $r and $theta, and you need rectangular co-ordinates $x and $y, you can use the following:

 proc polar_to_rect {r theta} {
     list [expr {$r * cos($theta)}]\
          [expr {$r * sin($theta)}]
 }

 lassign [polar_to_rect $r $theta] x y

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[[Next up:  three-dimensional (x, y, z) <-> (r, theta, phi)
Maybe cylindrical, after that ...]]

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[KPV] - Hey, I'll take up the hard task of converting cylindrical (r, theta, z) to rectangular (x, y, z).

 proc rect_to_cylindrical {x y z} {
    list {*}[rect_to_polar $x $y] $z
 }
 proc cylindrical_to_rect {r theta z} {
    list {*}[polar_to_rect $r $theta] $z
 }

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%| [Category Mathematics] |%
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