[Keith Vetter] 2003-03-24 : as I was writing [TkGoldberg], I found
it difficult dealing with complex canvas objects that were composed
of arcs and polygons. These objects were hard to fill with a color,
especially if the arc is a concave part of the object. Also, arcs
don't rotate well (see [Canvas Rotation]).

I realize now that if I could have decomposed the complex object 
into one polygon then both of my problems would have
been solved. But to do that I would need to convert arc into a
vertex list. 

The code below does just that. It is a generalization of 
[Regular polygons] in that it takes "-start", "-extent" and "-sides"
as optional addition paramters. 
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''[escargo] 24 Mar 2003'' - There's a little glitch that appears on
a seven-sided figure. If start is set to zero, the glitch appears on
the far right-hand side....

[KPV] oops, step size should have been a double, not an int.

----
 proc rp2 {x0 y0 x1 y1 args} {
    
    array set V {-sides 0 -start 90 -extent 360} ;# Default values
    foreach {a value} $args {
        if {! [info exists V($a)]} {error "unknown option $a"}
        if {$value == {}} {error "value of \"$a\" missing"}
        set V($a) $value
    }
    if {$V(-extent) == 0} {return {}}
    
    set xm [expr {($x0+$x1)/2.}]
    set ym [expr {($y0+$y1)/2.}]
    set rx [expr {$xm-$x0}]
    set ry [expr {$ym-$y0}]
 
    set n $V(-sides)
    if {$n == 0} {                              ;# 0 sides => circle
        set n [expr {round(($rx+$ry)*0.5)}]
        if {$n < 2} {set n 4}
    }
    
    set dir [expr {$V(-extent) < 0 ? -1 : 1}]   ;# Extent can be negative
    if {abs($V(-extent)) > 360} {
        set V(-extent) [expr {$dir * (abs($V(-extent)) % 360)}]
    }
    set step [expr {$dir * 360.0 / $n}]
    set numsteps [expr {1 + double($V(-extent)) / $step}]
                              
    set xy {}
    set DEG2RAD [expr {4*atan(1)*2/360}]
                              
    for {set i 0} {$i < int($numsteps)} {incr i} {
        set rad [expr {($V(-start) - $i * $step) * $DEG2RAD}]
        set x [expr {$rx*cos($rad)}]
        set y [expr {$ry*sin($rad)}]
        lappend xy [expr {$xm + $x}] [expr {$ym - $y}]
    }
 
    # Figure out where last segment should end
    if {$numsteps != int($numsteps)} {
        # Vecter V1 is last drawn vertext (x,y) from above
        # Vector V2 is the edge of the polygon
        set rad2 [expr {($V(-start) - int($numsteps) * $step) * $DEG2RAD}]
        set x2 [expr {$rx*cos($rad2) - $x}]
        set y2 [expr {$ry*sin($rad2) - $y}]
 
        # Vector V3 is unit vector in direction we end at
        set rad3 [expr {($V(-start) - $V(-extent)) * $DEG2RAD}]
        set x3 [expr {cos($rad3)}]
        set y3 [expr {sin($rad3)}]
 
        # Find where V3 crosses V1+V2 => find j s.t.  V1 + kV2 = jV3
        set j [expr {($x*$y2 - $x2*$y) / ($x3*$y2 - $x2*$y3)}]
 
        lappend xy [expr {$xm + $j * $x3}] [expr {$ym - $j * $y3}]
    }
    return $xy
 }
 
 # Now for code to demonstrate and test it
 proc DrawIt {args} {
    global S
    
    foreach {x0 y0 x1 y1} [.c cget -scrollregion] break
    set bbox [list 20 20 [incr x1 -20] [incr y1 -20]]
    
    .c delete poly
    set xy [eval rp2 $bbox -sides $S(sides) -start $S(start) -extent 360]
    .c create poly $xy -fill {} -outline black -width 2 -dash - -tag poly
    set xy [eval rp2 $bbox -sides $S(sides) -start $S(start) -extent $S(extent)]
    .c create poly $xy -fill red -outline {} -tag poly
    .c create line $xy -fill red -fill black -width 3 -tag poly
 }
 
 pack [frame .bottom] -side bottom -fill x
 pack [canvas .c -width 500 -height 500 -bd 2 -relief raised] -fill both -expand 1
 bind .c <Configure> {%W config -scrollregion [list 0 0 %w %h] ; DrawIt}
 
 scale .sides -variable S(sides) -orient h -from 0 -to 10 -label Sides -relief ridge
 scale .start -variable S(start) -orient h -from 0 -to 360 -label Start -relief ridge
 scale .extent -variable S(extent) -orient h -from -360 -to 360 -label Extent -relief ridge
 
 pack .sides .start .extent -side left -in .bottom
 array set S {extent 135 sides 4 start 0}
 trace variable S w DrawIt

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[Category Graphics]