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diff --git a/doc/manual-html/gimpprint_33.html b/doc/manual-html/gimpprint_33.html new file mode 100644 index 0000000..edf4627 --- /dev/null +++ b/doc/manual-html/gimpprint_33.html @@ -0,0 +1,247 @@ +<HTML> +<HEAD> +<!-- This HTML file has been created by texi2html 1.51 + from .././gimpprint.texi on 11 June 2004 --> + +<TITLE>GIMP-Print - Oversampling</TITLE> +</HEAD> +<BODY> +Go to the <A HREF="gimpprint_1.html">first</A>, <A HREF="gimpprint_32.html">previous</A>, <A HREF="gimpprint_34.html">next</A>, <A HREF="gimpprint_47.html">last</A> section, <A HREF="gimpprint_toc.html">table of contents</A>. +<P><HR><P> + + +<H3><A NAME="SEC48" HREF="gimpprint_toc.html#TOC48">B.2.5 Oversampling</A></H3> +<P> +<A NAME="IDX189"></A> + +</P> +<P> +By oversampling, we mean printing on the same row more than once. +There are two reasons for oversampling: to increase the horizontal +resolution of the printout and to reduce banding. + +</P> +<P> +Oversampling to increase horizontal resolution is necessary because, +although the printer might be able to position an ink drop to, for +example, 1/1440" horizontally, it may not be able to lay down two such +drops 1/1440" apart. If it can print two drops 1/720" apart, 2x +oversampling will be necessary to get a 1/1440" horizontal resolution. +If it can only print two drops 1/360" apart, 4x oversampling will be +necessary for a 1/1440" horizontal resolution. The printer enforces +this "drop spacing" by only accepting raster passes with a horizontal +resolution matching the spacing with which it can print dots, so we +must print passes at different horizontal positions if we are to +obtain a higher horizontal resolution. (Another reason it does this +may be to reduce the amount of memory needed in the printer.) + +</P> +<P> +Oversampling can also be done to decrease the banding apparent in an +image. By splitting a row into two or more sets of dots ("lines") and +printing each line on the same row, but with a different nozzle for +each line, we can get a smoother print. + +</P> +<P> +To quantify these two kinds of oversampling, we'll introduce two new +constants: @math{H} shows how many different horizontal offsets we want +to print at (the "horizontal oversampling") while @math{O} shows how +many times we want to print each row, over and above the number of times +necessary for horizontal oversampling (the "extra oversampling"). + +</P> +<P> +It is necessary for all the lines printed by a given pass to have the +same horizontal offset, but there need not be any relation between +them in terms of extra oversampling. For the moment, however, we will +treat all oversampling as potentially requiring this alignment; all +lines in one pass must be derived from the original row data in the +same way. Thus, we'll assume @math{O=1} for now. + +</P> +<P> +So, how do we do this oversampling? In fact, it can be done easily: +advance the paper by a factor of @math{H} less between each pass. We'll +define a new variable, @math{A}, to show how much we advance the paper +between passes. Previously, we'd have defined @math{A=J}; we now let +@math{A=J/H}. This also affects our pass blocks. Printing one pass +block used to involve advancing the paper @math{S*J} rows; it now +advances the paper @math{S*J/H} rows. We therefore name a group of +@math{H} pass blocks a "band". Printing one band involves advancing +the paper @math{S*J} rows, as a pass block did before. + +</P> +<P> +To keep our weave pattern working correctly, so that overprinting does +not occur within a pass block, we also have to redefine @math{G} as +@math{GCD(S,A)}. Here's an example of an oversampled weave pattern: + +</P> +<P> +@math{S=4}, @math{J=10}, @math{H=2}, @math{A=J/H=10/2=5}, +@math{G=GCD(4,5)=1}, +<BR>passesperblock=@math{S}=4, +<BR>passespersubblock=@math{S/G}=4/1=4: + +</P> + +<PRE> +0 *---*---*---*---*---*---*---*---*---* +1 *---*---*---*---*---*---*---*---*---* +2 *---*---*---*---*---*---*---*---*---* +3 *---*---*---*---*---*---*---*---*---* +4 *---*---*---*---*---*---*---*---*---* +5 *---*---*---*---*---*---*---*---*---* +6 *---*---*---*---*---*---*---*---*---* +7 *---*---*---*---*---*---*---*---*---* +8 *---*---*---*---*---*---*---*---*---* +9 *---*---*---*---*---*---*---*---* +10 *---*---*---*---*---*---*--- +11 *---*---*---*---*---*-- +12 *---*---*---*---*- +13 *---*---*---* +14 *---*--- +15 *-- +</PRE> + +<P> +Now we have to determine which line is printed by each jet on each +pass. If we number each line generated as we split up a row, we can +use these numbers. We'll number the lines in our diagram by replacing +the <SAMP>`*'</SAMP>s with integers in the range [0...@math{H-1}]. + +</P> +<P> +Overprinting occurs once per pass block, so we can simply print pass +block 0 with line 0, pass block 1 with line 1, pass block 2 with line +2, etc, wrapping to 0 when we've run out of lines: + +</P> + +<PRE> +0 0--0---0--0---0--0---0--0---0--0 +1 0--0---0--0---0--0---0--0---0--0 +2 0--0---0--0---0--0---0--0---0--0 +3 0--0---0--0---0--0---0--0---0--0 +4 1--1---1--1---1--1---1--1---1--1 +5 1--1---1--1---1--1---1--1---1--1 +6 1--1---1--1---1--1---1--1---1--1 +7 1--1---1--1---1--1---1--1---1--1 +8 0--0---0--0---0--0---0--0---0--0 +9 0--0---0--0---0--0---0--0---0 +10 0--0---0--0---0--0---0--- +11 0--0---0--0---0--0-- +12 1--1---1--1---1- +13 1--1---1--1 +14 1--1--- +15 1-- +</PRE> + +<P> +@math{S=4}, @math{J=12}, @math{H=2}, @math{A=J/H=12/2=6}, @math{G=GCD(4,6)=2}, +<BR>passesperblock=@math{S}=4, +<BR>passespersubblock=@math{S/G}=4/2=2: + +</P> + +<PRE> +0 0--0---0--0---0--0---0--0---0--0---0--0 +1 0--0---0--0---0--0---0--0---0--0---0--0 +2 0--0---0--0---0--0---0--0---0--0---0--0 +3 0--0---0--0---0--0---0--0---0--0---0--0 +4 1--1---1--1---1--1---1--1---1--1---1--1 +5 1--1---1--1---1--1---1--1---1--1---1--1 +6 1--1---1--1---1--1---1--1---1--1---1 +7 1--1---1--1---1--1---1--1---1-- +8 0--0---0--0---0--0---0--0- +9 0--0---0--0---0--0--- +10 0--0---0--0---0 +11 0--0---0-- +12 1--1- +</PRE> + +<P> +But what do we do if @math{J} is not an exact multiple of @math{H}? +This is a difficult problem, which I struggled with for quite a few days +before giving in and taking the easy (but less elegant) way out. The +easy solution is to round @math{J/H} down, then add on the accumulated +error at the end of each band. + +</P> +<P> +@math{S=4}, @math{J=11}, @math{H=2} @math{A=floor(J/H)=floor(11/2)=5}, @math{G=GCD(4,5)}, +<BR>passesperblock=@math{S}=4, +<BR>passespersubblock=@math{S/G}=4/1=4 + +</P> + +<PRE> +Band 0: +0 0--0---0--0---0--0---0--0---0--0---0 +1 0--0---0--0---0--0---0--0---0--0---0 +2 0--0---0--0---0--0---0--0---0--0---0 +3 0--0---0--0---0--0---0--0---0--0---0 +4 1--1---1--1---1--1---1--1---1--1---1 +5 1--1---1--1---1--1---1--1---1--1---1 +6 1--1---1--1---1--1---1--1---1--1---1 +7 1--1---1--1---1--1---1--1---1--1--- + +Band 1: +8 | 0--0---0--0---0--0---0--0---0- +9 \-----------------------------------------/ 0--0---0--0---0--0---0--0 +10 S*J rows 0--0---0--0---0--0--- +11 0--0---0--0---0-- +12 1--1---1--1- +13 1--1---1 +14 1--- +</PRE> + +<P> +We can calculate the starting row and subpass number of a given pass +in this scheme as follows: + +</P> + +<PRE> +A = floor(J / H) +subblocksperblock = gcd(S, A) +subpassblock = floor((p % S) * subblocksperblock / S) +if subpassblock * 2 < subblocksperblock + subblockoffset = 2*subpassblock +else + subblockoffset = 2*(subblocksperblock-subpassblock)-1 +band = floor(P / (S * H)) +passinband = P % (S * H) +startingrow = band * S * J + passinband * A + subblockoffset +subpass = passinband / S +</PRE> + +<P> +So the row number of jet @math{j} of pass @math{p} is + +</P> + +<PRE> +A = floor(J / H) +subblocksperblock = gcd(S, A) + +subblockoffset(p) + = 2*subpassblock , if subpassblock * 2 < subblocksperblock + = 2*(subblocksperblock-subpassblock)-1 , otherwise + where + subpassblock = floor((p % S) * subblocksperblock / S) + +band(p) = floor(p / (S * H)) +passinband(p) = p % (S * H) + +row(j, p) = band(p) * S * J + passinband(p) * A + subblockoffset(p) + j * S +row(j, p) = p * J + subblockoffset(p) + j * S +</PRE> + +<P> +To be continued@enddots{} +<P><HR><P> +Go to the <A HREF="gimpprint_1.html">first</A>, <A HREF="gimpprint_32.html">previous</A>, <A HREF="gimpprint_34.html">next</A>, <A HREF="gimpprint_47.html">last</A> section, <A HREF="gimpprint_toc.html">table of contents</A>. +</BODY> +</HTML> |