Plot parametric equation of rotated ellipse

img_rotate_ellipse1 GS(20190309) : A simple example to show how to rotate an ellipse on canvas.

# EllipseRotate.tcl
# Author:      Gerard Sookahet
# Date:        09 March 2019
# Version:     0.1
# Description: Simple graphical example of parametric equation of rotated ellipse
# xo,yo : center of the ellipse
# angle : rotation angle from 0 to 7 with the scalebar
# a : major radius
# b : minor radius
# t : parameter

package require tk
bind all <Escape> {exit}

proc EllipseRotate {xo yo a b angle t} {

 set cosa [expr {cos($angle)}]
 set sina [expr {sin($angle)}]
 set cost [expr {cos($t)}]
 set sint [expr {sin($t)}]
 set x [expr {$xo + $a*$cosa*$cost - $b*$sina*$sint}]
 set y [expr {$yo + $a*$sina*$cost + $b*$cosa*$sint}]

 return [list $x $y]

proc EllipsePlot {w xo yo a b pi angle} {
 $w delete all

 lassign [EllipseRotate $xo $yo $a $b $angle 0] x2 y2

 for {set p 0} {$p <= 720} {incr p} {
    set t [expr {$pi*$p/360}]
    lassign [EllipseRotate $xo $yo $a $b $angle $t] x1 y1
    .c create line $x1 $y1 $x2 $y2 -fill blue -width 3
    set x2 $x1
    set y2 $y1

set width 600
set height 400
set pi 3.1415926
set xo [expr {$width/2}]
set yo [expr {$height/2}]
set a 200
set b 100
set angle [expr {$pi/6}]

pack [canvas .c -width $width -height $height -background black]
pack [scale .sc -from 0 -to 7 -length 240 -resolution .1 \
           -orient horiz -bd 1 -showvalue true -variable angle \
           -command {EllipsePlot .c $::xo $::yo $::a $::b $::pi}]