MS: This is a version of Recursive curves that avoids floating point operations:

- as all segments drawn have one of two lengths, these lengths are precomputed, as well as the depth at which a segment is drawn. The depth is hence kept in an integer.
- as all angles are multiples of $pi/4, the angle is kept by the integer number of $pi/4 rotations
- the angle-dependent values are precomputed in a table, for the 8 possible values of ($angle%8)

Additional optimisations:

- the second recursion is tail-optimised using while
- avoiding variable accesses by reusing returns of set and incr
- calling lappend with single element to append (bytecompiled)

This does not make for particularly readable code :(

Note that this is a great example of **senseless overoptimisation** - the extra optimisation is not relevant here; there is not much further improvement from the original version as the app is I/O bound (drawing on the canvas). Even without drawing, the speedup is only about 20%.

Also note that this implementation makes additional assumptions:

- the initial angle is 0
- (dragon only) the initial value of s is 1

proc main {} { pack [canvas .c -width 240 -height 280] set ::points {150 190} # ETFS configurability: uncomment what you want set t [time {ccurve .c 120 0 2}] #set t [time {dragon .c 160 0 1 2.4}] wm title . "[expr {[lindex $t 0]/1000000.}] sec" bind . <Return> {exec wish $argv0 &; exit} } # This just sets up the parameters for # table-based ops; we assume here that # the initial angle is 0. proc setParams {len angle minlen} { global parList set maxDepth [expr {(1+floor(2*log($len/$minlen)/log(2)))}] set minlen [expr {$len/pow(sqrt(2),$maxDepth)}] set minlen0 [expr {$minlen/sqrt(2)}] set parList {} lappend parList [list 0.0 $minlen ];# 0 lappend parList [list $minlen0 $minlen0];# 1 lappend parList [list $minlen 0.0 ];# 2 lappend parList [list $minlen0 -$minlen0];# 3 lappend parList [list 0.0 -$minlen ];# 4 lappend parList [list -$minlen0 -$minlen0];# 5 lappend parList [list -$minlen 0.0 ];# 6 lappend parList [list -$minlen0 $minlen0];# 7 return [expr {int($maxDepth)}] } # C curve drawer: assumes initial angle 0 proc ccurve {w len angle minlen} { set maxDepth [setParams $len $angle $minlen] ccurveInt $w [incr maxDepth] $angle } proc ccurveInt {w depth angle} { while {[incr depth -1]} { ccurveInt $w $depth [expr {[incr angle -1] + 2}] } plotline $w $angle } # Dragon curve drawer: assumes initial angle 0, initial s 1 proc dragon {w len angle s minlen} { set maxDepth [setParams $len $angle $minlen] dragonInt $w [incr maxDepth] $angle $s } proc dragonInt {w depth angle s} { while {[incr depth -1]} { if {$s == 1} { dragonInt $w $depth [expr {[incr angle -1] + 2}] 1 set s -1 } else { dragonInt $w $depth [expr {[incr angle 1] - 2}] 1 } } plotline $w $angle } # Plot a line from last end point in specified direction and length proc plotline {w ang} { global ::points # Note that '$ang % 8' and '$ang & 7' give the same result foreach {xadd yadd} [lindex $::parList [expr {$ang & 7}]] { lappend points [expr {[lindex $points end-1]-$xadd}] lappend points [expr {[lindex $points end-1]-$yadd}] } if {[llength $points]>200} { $w create line $points set points [lrange $points end-1 end] update } } # Let's go! main