bezier-sandwich proposals

[Mark Polesky]

Here's the ps draw_bezier_sandwich routine from line 127 of
music-drawing-routines.ps. I've annotated it to show how it
pulls "thickness controls" off the stack. I put periods 
between some values to simplify reading (they're not part of
the stack). Currently there are 17 "thickness controls":

/draw_bezier_sandwich  % thickness controls
{ % x4 y4 x5 y5 x0 y0 . x3 y3 . x1 y1 x2 y2 x3 y3 . x0 y0 . linewidth
  gsave
  currentpoint translate
    % round ending and round beginning
    1 setlinejoin 1 setlinecap
  setlinewidth % x4 y4 x5 y5 x0 y0 . x3 y3 . x1 y1 x2 y2 x3 y3 . x0 y0
  moveto       % x4 y4 x5 y5 x0 y0 . x3 y3 . x1 y1 x2 y2 x3 y3
  curveto      % x4 y4 x5 y5 x0 y0 . x3 y3
  lineto       % x4 y4 x5 y5 x0 y0
  curveto      % (clear)
  closepath
  stroke_and_fill
  grestore
} bind def

I've noticed a couple of things:

1. the lineto command is redundant.

   the currentpoint just before is x3 y3, and lineto
   draws a "line" to the same point. Sometimes in ps
   this is a way of making sure you get the right
   linejoin (round here), but in this case the next
   curveto takes care of that.

2. P(x0,y0) is included twice.

   ps-commands copy and roll can take care of that.

____________________________________

So the number of thickness controls could be cut down
from 17 to 13 if draw_bezier_sandwich was defined as:

/draw_bezier_sandwich  % thickness controls
{ % x4 y4 x5 y5 . x1 y1 x2 y2 x3 y3 . x0 y0 . linewidth
  gsave
  currentpoint translate
    % round ending and round beginning
    1 setlinejoin 1 setlinecap
  setlinewidth % x4 y4 x5 y5 . x1 y1 x2 y2 x3 y3 . x0 y0
  2 copy       % x4 y4 x5 y5 . x1 y1 x2 y2 x3 y3 . x0 y0 . x0 y0
  10 2 roll    % x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3 . x0 y0
  moveto       % x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3
  curveto      % x4 y4 x5 y5 x0 y0
  curveto      % (empty)
  closepath
  stroke_and_fill
  grestore
} bind def


If anyone wanted the order of thickness controls to be
more intuitive, such as:

% linewidth . x0 y0 . x1 y1 x2 y2 x3 y3 . x4 y4 x5 y5

the routine could be defined like this:

/draw_bezier_sandwich  % thickness controls
{                 % linewidth . x0 y0 . x1 y1 x2 y2 x3 y3 . x4 y4 x5 y5
  12 4 roll       % linewidth . x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3
  7 index 7 index % linewidth . x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3 . x0 y0
  15 -1 roll      % x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3 . x0 y0 . linewidth
  gsave
  currentpoint translate
    % round ending and round beginning
    1 setlinejoin 1 setlinecap
  setlinewidth % x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3 . x0 y0
  moveto       % x4 y4 x5 y5 x0 y0 . x1 y1 x2 y2 x3 y3
  curveto      % x4 y4 x5 y5 x0 y0
  curveto      % (empty)
  closepath
  stroke_and_fill
  grestore
} bind def


- Mark