[Arjen Markus] (18 december 2002) The script below is a first (well, second) attempt to render mathematical formulae in a canvas. It is far from complete, and if I ever finish it, it will probably
end up totally differently, but it works to a certain degree with a certain class of formulae.

Several people, among whom [Lars Hellstrom] and [Kevin Kenny], provided useful information on existing algorithms, such as the one used in [TeX], and pointers to articles by [Brian Kernighan]   [http://citeseer.nj.nec.com/kernighan75system.html].

See also: [Binomial coefficients] for a quick-and-dirty solution.
----
 # mathform.tcl -- 
 #    Simple script to render mathematical formulae
 #

 namespace eval ::MathFormula:: {
    variable poshoriz   0
    variable offhoriz   0
    variable posvert    0
    variable offvert    0
    variable offset_add 0
 }

 # drawFormula --
 #    Draw the formula at a given position (lower-left)
 #
 # Arguments:
 #    canvas   The canvas to use
 #    xpos     X-position to start
 #    ypos     Y-position to start
 #    formula  String holding the formula
 #
 # Result:
 #    None
 #
 # Side effect:
 #    The formula is rendered on the screen
 #
 #
 proc ::MathFormula::drawFormula {canvas xpos ypos formula} {
    variable poshoriz
    variable offhoriz
    variable posvert
    variable offvert
    variable offset_add

    set poshoriz   $xpos
    set posvert    $ypos
    set offhoriz   0
    set offvert    0
    set offset_add 0

    set tokens [analyseFormula $formula]
    foreach {token xp yp advance} $tokens {
       renderToken $canvas $token $xp $yp $advance
    }
 }

 # renderToken --
 #    Render the given token
 #
 # Arguments:
 #    canvas   Canvas in which to draw
 #    token    Token to be drawn
 #    xp       X-position relative to current drawing position
 #    yp       Y-position relative to current drawing position
 #
 # Result:
 #    None
 #
 # Side effect:
 #    The token is drawn on the canvas
 #
 proc ::MathFormula::renderToken {canvas token xp yp advance} {
    variable poshoriz
    variable posvert
    variable offhoriz
    variable offvert

    set xpos [expr {$poshoriz+$xp}]
    set ypos [expr {$posvert+$yp}]

    switch -- $token {
    "INT" { # Integral
          set item [$canvas create line -3  9 -1 10 0 0 1 -10 3 -9 -width 1 -fill black -smooth 1]
          $canvas move $item $xpos $ypos
          incr xpos 5
        }
    "SUM" { # Sum
          set item [$canvas create line  8  2  0  2  5 -4  0 -9  8 -9 -width 1 -fill black]
          $canvas move $item $xpos $ypos
          incr xpos 8
       }
    "Inf" { # Infinity
          set item1 [$canvas create oval -5 -2  0  2  -outline black]
          set item2 [$canvas create oval  0 -2  5  2  -outline black]
          $canvas move $item1 $xpos $ypos
          $canvas move $item2 $xpos $ypos
       }
    default { # Letters
          set item [$canvas create text $xpos $ypos -text $token -fill black -anchor w -font "Times 12"]
          set bbox [$canvas bbox $item]
          set width [expr {[lindex $bbox 2]-[lindex $bbox 0]}]
          set xp   $width
          set xpos [expr {$xpos+$width}]
       }
    }
 
    if { $advance } {
       set poshoriz $xpos
    } else {
       set offhoriz [expr {$xp>$offhoriz? $xp : $offhoriz}]
    }
 }

 # analyseFormula --
 #    Analyse the formula and determine the positions of the tokens
 #
 # Arguments:
 #    formula  Formula to be drawn
 #
 # Result:
 #    List of tokens with relative positions and advancing information
 #
 proc ::MathFormula::analyseFormula {formula} {

    set result  [list]
    set advance 1
    set xp      0
    set yp      0

    foreach token $formula {
       switch -- $token {
       "_" { # Subscript
             set yp 5
             set advance 0
             continue
           }
       "^" { # Superscript
             set yp -3
             set advance 0
             continue
           }
       "~" { # Force space
             set token   " "
             set advance 1
           }
       "`" { # Force extra space
             incr xp     1
             set advance 1
             continue
           }
       "INT" { # Integral
             set xp  0
             set yp  0
             set advance 1
           }
       "SUM" { # Sum
             set xp  0
             set yp  2
             set advance 1
           }
       "from" { # Lower bound
             set xp -10
             set yp  14
             set advance 0
             continue
           }
       "to" { # Upper bound
             set xp    1
             set yp  -10
             set advance 0
             continue
           }
       "Inf" { # Infinity
             incr yp     -2  ;# Increase, not set!
             set advance  1
           }
       default { # Letters
             set advance 1
          }
       }
       lappend result $token $xp $yp $advance
       if { $advance } {
          set xp 0
          set yp 0
       }
    }

    return $result
 }

 # Main -- 
 #   Set up a canvas, analyse the formula and draw it
 #

 canvas .c -background white
 pack   .c -fill both

 set pi    "\u3c0"
 set alpha "\u3b1"
 set DELTA "\u394"
 set omega "\u3c9"
 set string "SUM from i=0 to Inf ~ A _ i ~ = ~ INT from 0 to $pi cos ^ 2 x dx"

 ::MathFormula::drawFormula .c 10 20  "Not ~ p ` erfect ~ yet, ~ but ..."
 ::MathFormula::drawFormula .c 10 60  $string
 ::MathFormula::drawFormula .c 10 100 "0.1 = e ^ -kT90"
 ::MathFormula::drawFormula .c 10 140 "f(x) = x ^ 3 - x ^ 2 + x - 1"
 ::MathFormula::drawFormula .c 10 180 "h(t) = cos( $omega t - $alpha )" 

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[[
[Category Mathematics] |
[Category Graphics]
]]