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-Drawing geometric figures - the result of airplane travel.
The example script shows the use of canvas and geometric figues -(regular, convex polygons) with different number of edges based on -trigonometric functions.
-gustaf neumann (Aug 2, 2013)
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package require Tk -package require nx
Class Canvas is a simple convenience wrapper for the tk canvas, -which packs itself.
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nx::Class create Canvas { - :property {canvas .canvas} - :property {bg beige} - :property {height 500} - :property {width 500} - - :method init {} { - canvas ${:canvas} -bg ${:bg} -height ${:height} -width ${:width} - pack ${:canvas} - } -}
Class Area provides a center point (x, y) and a radius
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nx::Class create Area { - :property {canvas .canvas} - :property {x 250} - :property {y 250} - :property {radius 200} - - :variable pi [expr {acos(-1)}] - - :method degree {d} { - # - # return a coordinate pair on a circle around the center point with - # :radius at the provided degrees (0..360) - # - set x [expr {$d*${:pi}/180.0 - ${:pi}/2.0}] - set x0 [expr {cos($x)*${:radius}+${:x}}] - set y0 [expr {sin($x)*${:radius}+${:y}}] - list $x0 $y0 - } - - :method n-tangle {n} { - # - # Draw a regular n-tangle (e.g. when n==3, a triangle) inscribed to - # a circle with radius :radius - # - for {set i 0} {$i < $n} {incr i} { - set p($i) [:degree [expr {$i*360/$n}]] - } - lassign $p(0) x0 y0 - for {set i 1} {$i < $n} {incr i} { - lassign $p($i) x1 y1 - ${:canvas} create line $x0 $y0 $x1 $y1 - lassign $p($i) x0 y0 - } - lassign $p(0) x1 y1 - ${:canvas} create line $x0 $y0 $x1 $y1 - } -}
Class Inscribe draws multiple n-tangles with the came center point.
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nx::Class create Inscribe -superclass Area { - :property {count 4} - :property {edges 3} - :method init {} { - for {set i 0} {$i < ${:count}} {incr i} { - ${:canvas} create oval \ - [expr {${:x}-${:radius}}] [expr {${:y}-${:radius}}] \ - [expr {${:x}+${:radius}}] [expr {${:y}+${:radius}}] - :n-tangle ${:edges} - set :radius [expr {${:radius}/2.0}] - } - } -}
Class Hull creates an n-tangle with :density hull lines between -neighboring edges
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nx::Class create Hull -superclass Area { - :property {edges 3} - :property {density 10} - - :method n-tangle {n} { - for {set i 0} {$i < $n} {incr i} { - set p($i) [:degree [expr {$i*360/$n}]] - } - lassign $p(0) x0 y0 - for {set i 1} {$i < $n} {incr i} { - lassign $p($i) x1 y1 - set line($i) [list $x0 $y0 $x1 $y1] - ${:canvas} create line $x0 $y0 $x1 $y1 - lassign $p($i) x0 y0 - } - lassign $p(0) x1 y1 - ${:canvas} create line $x0 $y0 $x1 $y1 - set line(0) [list $x0 $y0 $x1 $y1] - set line($n) [list $x0 $y0 $x1 $y1] - - for {set i 0} {$i < $n} {incr i} { - lassign $line($i) x0 y0 x1 y1 - lassign $line([expr {$i+1}]) x2 y2 x3 y3 - set dx1 [expr {($x0 - $x1)*1.0/${:density}}] - set dy1 [expr {($y0 - $y1)*1.0/${:density}}] - set dx2 [expr {($x2 - $x3)*1.0/${:density}}] - set dy2 [expr {($y2 - $y3)*1.0/${:density}}] - for {set j 1} {$j < ${:density}} {incr j} { - ${:canvas} create line [expr {$x0-$dx1*$j}] [expr {$y0-$dy1*$j}] \ - [expr {$x2-$dx2*$j}] [expr {$y2-$dy2*$j}] - } - } - } - - :method init {} { - :n-tangle ${:edges} - } -}
Draw either one larger figure with inner figures -or a series of smaller figures next to each other.
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set multiple 0 - -if {$multiple} { - # Draw a series of figures next to each other - set c [::Canvas new -width 650 -height 750 -bg white] - ::Inscribe new -canvas [$c cget -canvas] -x 100 -y 100 -radius 80 -count 7 - ::Inscribe new -canvas [$c cget -canvas] -x 300 -y 100 -radius 80 -count 7 -edges 4 - ::Inscribe new -canvas [$c cget -canvas] -x 500 -y 100 -radius 80 -count 7 -edges 5 - ::Hull new -canvas [$c cget -canvas] -x 100 -y 300 -radius 80 -edges 3 -density 10 - ::Hull new -canvas [$c cget -canvas] -x 300 -y 300 -radius 80 -edges 4 -density 10 - ::Hull new -canvas [$c cget -canvas] -x 500 -y 300 -radius 80 -edges 5 -density 10 - ::Hull new -canvas [$c cget -canvas] -x 300 -y 600 -radius 200 -edges 3 -density 40 -} else { - # Draw a several series of figures with the same center - set c [::Canvas new -width 650 -height 650 -bg white] - ::Hull new -canvas [$c cget -canvas] -x 300 -y 320 -radius 300 -edges 5 -density 40 - ::Hull new -canvas [$c cget -canvas] -x 300 -y 320 -radius 150 -edges 4 -density 20 - ::Hull new -canvas [$c cget -canvas] -x 300 -y 320 -radius 75 -edges 3 -density 10 - ::Hull new -canvas [$c cget -canvas] -x 300 -y 320 -radius 30 -edges 5 -density 5 -}