many-to-many-verbose.eps

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L3? dup dup{save exch}if

% languagelevel2 ONLY code goes here

/Range 0 def
/DataSource 0 def
/val 0 def
/nRange 0 def
/mulRange 0 def
/d0 0 def
/r0 0 def
/di 0 def
/ri 0 def
/a0 0 def
/a1 0 def
/r1 0 def
/r2 0 def
/dx 0 def
/Nsteps 0 def
/sh3tp 0 def
/ymax 0 def
/ymin 0 def
/xmax 0 def
/xmin 0 def

/setupFunEval % funDict -- 	% this calculates and sets up a function dict for evaulation.
{
    begin
	/nRange Range length 2 idiv store
	/mulRange   % precompute the range data needed to map a sample value from the table to a range value
		    % this data looks like [ range0mul range0min range1mul range1min ... rangeN-1mul rangeN-1min ]
	[ 
	    0 1 nRange 1 sub
	    { % index
		    2 mul/nDim2 xd		% 2*dimension# we are dealing with
		    Range nDim2 get		% ymin
		    Range nDim2 1 add get	% ymin ymax 
		    1 index sub			% ymin (ymax-ymin)
						% xmin = 0, xmax = 255 (2^bitspersample - 1)
		    255 div			% ymin (ymax-ymin)/(xmax - xmin)
		    exch			% (ymax-ymin)/(xmax - xmin) ymin
	    }for
	]store
    end
}bd

/FunEval % val1 fundict -> comp1 comp2 ... compN
{
    begin
	% the value passed in is the base index into the table
	nRange mul /val xd	% compute the actual index to the table
				% since there are nRange entries per base index
	0 1 nRange 1 sub
	{
	    dup 2 mul/nDim2 xd % dim
	    val	% base value to use to do our lookup
	    add DataSource exch get %  lookedupval
	    mulRange nDim2 get mul 	% lookedupval*(ymax-ymin)/(xmax-xmin)
	    mulRange nDim2 1 add get % lookedupval*(ymax-ymin)/(xmax-xmin) ymin
	    add % interpolated result
	}for	% comp1 comp2 ... compN
    end
}bd

/max % a b -> max(a, b)
{
	2 copy lt
	{exch pop}{pop}ifelse
}bd

/sh2
{	% emulation of shading type 2. Assumes shading dictionary is top dictionary on the dict stack
	/Coords load aload pop 	% x0 y0 x1 y1
	3 index 3 index translate	% origin is now at beginning point of shading
					% x0 y0 x1 y1
	3 -1 roll sub	% x0 x1 y1-y0
	3 1 roll exch 	% y1-y0 x1 x0
	sub				% y1-y0 x1-x0
	2 copy
	dup mul exch dup mul add sqrt	% length of segment between two points
	dup
	scale  
	atan	% atan (dy/dx)
	%dup (rotation angle = )print ==
	rotate		% now line between 0,0 and 1,0 is the line perpendicular to which the axial lines are drawn					
	
	/Function load setupFunEval	% may need to setup function dictionary by calling setupFunEval
	
	% this is now specific to axial shadings. Compute the maximum bounds to fill
	clippath {pathbbox}stopped {0 0 0 0}if newpath 	% x0 y0 x1 y1
	/ymax xs
	/xmax xs
	/ymin xs
	/xmin xs
	currentdict/Extend known
	{
		/Extend load 0 get
		{	
			0/Function load FunEval sc	% evaluate the function to get a color and set it
			xmin ymin xmin abs ymax ymin sub rectfill
		}if
	}if
	% paint the rects. The sampling frequency is that of our table
	/Nsteps/Function load/Size get 0 get 1 sub store
	/dx 1 Nsteps div store
	gsave
		/di ymax ymin sub store
		/Function load
		% loop Nsteps + 1 times, incrementing the index by 1 each time
		0 1 Nsteps
		{
			1 index FunEval sc
			0 ymin dx di rectfill
			dx 0 translate
		}for
		pop	% pop our function
	grestore	% origin is back to start point
	currentdict/Extend known
	{
		/Extend load 1 get
		{	
			Nsteps/Function load FunEval sc	% last element
			1 ymin xmax 1 sub abs ymax ymin sub rectfill
		}if
	}if
}bd

/shp	% this paints our shape for shading type 3
{	% x1 r1 x0 r0 -
	4 copy

	% fill interior arc
	dup 0 gt{
		0 exch a1 a0 arc
	}{
		pop 0 moveto
	}ifelse

	dup 0 gt{
		0 exch a0 a1 arcn
	}{
		pop 0 lineto
	}ifelse
	
	fill

	% fill exterior arc
	dup 0 gt{
		0 exch a0 a1 arc
	}{
		pop 0 moveto
	}ifelse

	dup 0 gt{
		0 exch a1 a0 arcn
	}{
		pop 0 lineto
	}ifelse
	
	fill
}bd

/calcmaxs
{	% calculate maximum distance vector from origin to corner points
	% of bbox
	xmin dup mul ymin dup mul add sqrt		% (xmin2 + ymin2)
	xmax dup mul ymin dup mul add sqrt		% (xmax2 + ymin2)
	xmin dup mul ymax dup mul add sqrt		% (xmin2 + ymax2)
	xmax dup mul ymax dup mul add sqrt		% (xmax2 + ymax2)
	max max max								% maximum value
}bd

/sh3
{	% emulation of shading type 3. Assumes shading dictionary is top dictionary on the dict stack
	/Coords load aload pop 	% x0 y0 r1 x1 y1 r2
	5 index 5 index translate	% origin is now at first circle origin
	3 -1 roll 6 -1 roll sub		% y0 r1 y1 r2 dx
	3 -1 roll 5 -1 roll sub		% r1 r2 dx dy
	2 copy dup mul exch dup mul add sqrt
	/dx xs						% r1 r2 dx dy
	2 copy 0 ne exch 0 ne or
	{
		% r1 r2 dx dy
		exch atan rotate	% we are now rotated so dy is zero and positive values of dx move us as expected
	}{
		pop pop
	}ifelse
	% r1 r2		
	/r2 xs
	/r1 xs
	/Function load 
	dup/Size get 0 get 1 sub	% this is the size of our table minus 1
	/Nsteps xs		% at some point we should optimize this better so NSteps is based on needed steps for the device
	setupFunEval		% may need to setup function dictionary by calling setupFunEval
	% determine the case:
	% case 0: circle1 inside circle2
	% case 1: circle 2 inside circle 1
	% case 2: r1 = r2 
	% case 3: r1 != r2
	dx r2 add r1 lt{
		% circle 2 inside of circle 1
		0 
	}{
		dx r1 add r2 le
		{ % circle 1 inside of circle 2
			1
		}{ % circles don't contain each other
			r1 r2 eq
			{	% equal
				2
			}{ % r1 != r2
				3
			}ifelse		
		}ifelse
	}ifelse
	/sh3tp xs		% sh3tp has the number of our different cases
	clippath {pathbbox}stopped {0 0 0 0}if 
	newpath 	% x0 y0 x1 y1
	/ymax xs
	/xmax xs
	/ymin xs
	/xmin xs

	% Arc angle atan( sqrt((dx*dx + dy*dy) - dr*dr), dr)
	dx dup mul r2 r1 sub dup mul sub dup 0 gt
	{
		sqrt r2 r1 sub atan
		/a0 exch 180 exch sub store 
		/a1 a0 neg store 
	}{
		pop
		/a0 0 store
		/a1 360 store		
	}ifelse		

	currentdict/Extend known
	{
		/Extend load 0 get r1 0 gt and	% no need to extend if the radius of the first end is 0
		{	
			0/Function load FunEval sc	% evaluate the function to get a color and set it
			% case 0: circle1 inside circle2
			% case 1: circle 2 inside circle 1
			% case 2: circles don't contain each other and r1 == r2
			% case 3: circles don't contain each other and r1 != r2
			{ 
				{	% case 0
					dx 0 r1 360 0 arcn
					xmin ymin moveto
					xmax ymin lineto
					xmax ymax lineto
					xmin ymax lineto
					xmin ymin lineto
					eofill		% for the bigger radius we fill everything except our circle
				}
				{	% case 1
					r1 0 gt{0 0 r1 0 360 arc fill}if
				}
				{	% case 2
					% r1 == r2, extend 0
					% r3 = r, x3 = -(abs(minx) + r), x1 = 0
				
					% x(i+1) r(i+1) x(i) r(i) shp
					0 r1 xmin abs r1 add neg r1 shp
				}
				{	% case 3
					% no containment, r1 != r2
				
					r2 r1 gt{	% the endpoint we are drawing is that with a circle of zero radius
						% x(i+1) r(i+1) x(i) r(i) shp
						0 r1
						r1 neg r2 r1 sub div dx mul	% this is point of beginning circle
						0	% point of ending circle
						shp	% takes x(i+1) r(i+1) x(i) r(i)
					}{	% the first circle is the bigger of the two
						% we find a circle on our line which is outside the bbox in the
						% negative direction
						% x(i+1) r(i+1) x(i) r(i) shp
						0 r1 calcmaxs	% 0 r1 maxs
						dup
						% calculating xs: (-(maxs+r2)*x2)/(x2-(r1-r2))
						r2 add dx mul dx r1 r2 sub sub div
						neg				% maxs xs'
						exch 1 index	% xs' maxs xs'
						abs exch sub
						shp
					}ifelse
				} 
			}sh3tp get exec	% execute the extend at beginning proc for our shading type
		}if
	}if

	% now do the shading
	/d0 0 store
	/r0 r1 store
	/di dx Nsteps div store
	/ri r2 r1 sub Nsteps div store 
	/Function load 
	0 1 Nsteps
	{	% function t(i)
		1 index FunEval sc
		d0 di add r0 ri add d0 r0 shp
		{
		% fill interior arc
		d0 0 r0 a1 a0 arc
		d0 di add 0 r0 ri add a0 a1 arcn
		fill
		
		% fill exterior arc
		d0 0 r0 a0 a1 arc
		d0 di add 0 r0 ri add a1 a0 arcn
		fill
		}pop
		
		% advance to next
		/d0 d0 di add store
		/r0 r0 ri add store
	}for
	pop	% pop our function dict

	% handle Extend
	currentdict/Extend known
	{
		/Extend load 1 get r2 0 gt and	% no need to extend if the radius of the last end is 0
		{	
			Nsteps/Function load FunEval sc	% last element
			% case 0: circle1 inside circle2
			% case 1: circle 2 inside circle 1
			% case 2: circles don't contain each other and r1 == r2
			% case 3: circles don't contain each other and r1 != r2
			{ 
				{
					dx 0 r2 0 360 arc fill
				} 
				{
					dx 0 r2 360 0 arcn
					xmin ymin moveto
					xmax ymin lineto
					xmax ymax lineto
					xmin ymax lineto
					xmin ymin lineto
					eofill		% for the bigger radius we fill everything except our circle
				} 
				{	% r1 == r2, extend 1
					% r3 = r, x3 = (abs(xmax) + r), x1 = dx
					% x(i+1) r(i+1) x(i) r(i) shp
					xmax abs r1 add r1 dx r1 shp
				}	
				{	% no containment, r1 != r2
			
					r2 r1 gt{
						% we find a circle on our line which is outside the bbox in the
						% positive direction
						% x(i+1) r(i+1) x(i) r(i) shp
						calcmaxs dup	% maxs maxs
						% calculating xs: ((maxs+r1)*x2)/(x2-(r2-r1))
						r1 add dx mul dx r2 r1 sub sub div	% maxs xs
						exch 1 index	% xs maxs xs
						exch sub
						dx r2
						shp
					}{	% the endpoint we are drawing is that with a circle of zero radius
						% x(i+1) r(i+1) x(i) r(i) shp
						r1 neg r2 r1 sub div dx mul	% this is point of ending circle
						0		% radius of ending circle
						dx 		% point of starting circle
						r2		% radius of starting circle
						shp
					}ifelse
				}
			}			
			sh3tp get exec	% execute the extend at end proc for our shading type
		}if
	}if
}bd
/sh		% emulation of shfill operator for type 2 and type 3 shadings based on type 0 functions
{	% shadingDict --
	begin
		/ShadingType load dup dup 2 eq exch 3 eq or
		{	% shadingtype
			gsave
				newpath
				/ColorSpace load scs
				currentdict/BBox known
				{
					/BBox load aload pop	% llx lly urx ury
					2 index sub				% llx lly urx ury-lly
					3 index					% llx lly urx ury-lly llx
					3 -1 roll exch sub 
					exch rectclip
				}if
				2 eq
				{sh2}{sh3}ifelse
			grestore
		}{
			% shadingtype
			pop 
			(DEBUG: shading type unimplemented\n)print flush
		}ifelse
	end
}bd

% end of language level 2 ONLY code

{restore}if not dup{save exch}if
% languagelevel3 ONLY code goes here
	L3?{	% we do these loads conditionally or else they will fail on a level 2 printer
		/sh/shfill ld
		/csq/clipsave ld
		/csQ/cliprestore ld
	}if
{restore}if

%currentdict dup maxlength exch length sub (number of extra slots in md = )print == flush	% *** how many entries are free
end
setpacking
% count 0 ne { pstack(***extras on stack during prolog execution***\n)print flush}if	% *** BARK if anything is left on stack
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00>] def
/CharStrings 19 dict dup begin
/.notdef 0 def
/C 1 def
/M 2 def
/U 3 def
/underscore 4 def
/a 5 def
/b 6 def
/c 7 def
/d 8 def
/e 9 def
/i 10 def
/l 11 def
/m 12 def
/n 13 def
/o 14 def
/r 15 def
/s 16 def
/t 17 def
/u 18 def
 end readonly def
currentdict dup/FontName get exch definefont pop end
%APLsfntEnd
42/FontType resourcestatus{pop pop true}{false}ifelse
{currentfile 0(%APLT1End\n)/SubFileDecode filter flushfile}if
/FontType 1 def
/FontMatrix [ 0.00048828125 0 0 0.00048828125 0 0 ] readonly def
/FontBBox {-1947 -985 2961 2297} readonly def
/UniqueID 4052586 def
currentdict end
currentfile eexec
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