Purpose: Show how to convert between rectangular and polar co-ordinates in Tcl.
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 } {
set r [expr { hypot( $x, $y ) }]
set theta [expr { atan2( $y, $x ) }]
return [list $r $theta]
}
foreach { r theta } [rect_to_polar $x $y] breakNote the use of hypot and atan2 in the code above. These functions are much more robust than any corresponding code using atan and sqrt.
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 } {
set x [expr { $r * cos($theta) }]
set y [expr { $r * sin($theta) }]
return [list $x $y]
}
foreach { x y } [polar_to_rect $r $theta] break[Next up: three-dimensional (x, y, z) <-> (r, theta, phi) Maybe cylindrical, after that ...]