<HTML> <HEAD> <!-- This HTML file has been created by texi2html 1.51 from .././gimpprint.texi on 22 January 2003 --> <TITLE>GIMP-Print - Simple weaving algorithms</TITLE> </HEAD> <BODY> Go to the <A HREF="gimpprint_1.html">first</A>, <A HREF="gimpprint_28.html">previous</A>, <A HREF="gimpprint_30.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="SEC44" HREF="gimpprint_toc.html#TOC44">B.2.1 Simple weaving algorithms</A></H3> <P> The initial problem is to calculate the starting position of each pass; the row number of the printer's top jet when printing that pass. Since we assume the paper cannot be reverse-fed, the print head must, for each pass, start either further down the page than the previous pass or at the same position. Each pass's start point is therefore at a non-negative offset from the previous pass's start point. </P> <P> Once we have a formula for the starting row of each pass, we then turn that "inside out" to get a formula for the pass number containing each row. </P> <P> First, let's define how our printer works. We measure vertical position on the paper in "rows"; the resolution with which the printer can position the paper vertically. The print head contains @math{J} ink jets, which are spaced @math{S} rows apart. </P> <P> Consider a very simple case: we want to print a page as quickly as possible, and we mostly don't care how sparse the printing is, so long as it's fairly even. </P> <P> It's pretty obvious how to do this. We make one pass with the print head, printing @math{J} lines of data, each line @math{S} rows after the previous one. We then advance the paper by @math{S*J} rows and print the next row. For example, if @math{J=7} and @math{S=4}, this method can be illustrated like this: </P> <PRE> pass number | row number-------> | | 111111111122222222223333333333444444444455555555556666666666 | 0123456789012345678901234567890123456789012345678901234567890123456789 0 *---*---*---*---*---*---* 1 *---*---*---*---*---*---* 2 \-----------------------/ *---*---*---*---*---*- 7 jets \---/ 4 rows offset from one jet to the next \---------------------------/ 7*4=28 rows offset from one pass to the next </PRE> <P> In these examples, the vertical axis can be thought of as the time axis, with the pass number shown at the left margin, while the row number runs horizontally. A <SAMP>`*'</SAMP> shows each row printed by a pass, and a row of <SAMP>`-'</SAMP> is used to link together the rows printed by one pass of the print head. The first pass is numbered <SAMP>`0'</SAMP> and starts at row 0. Each subsequent pass @math{p} starts at row @math{p*S*J}. Each pass prints @math{J} lines, each line being @math{S} rows after the previous one. (For ease of viewing this file on a standard terminal, I'm clipping the examples at column 80.) </P> <P> This method covers the whole page with lines printed evenly @math{S} rows apart. However, we want to fill in all the other rows with printing to get a full-density page (we're ignoring oversampling at this stage). Where we have previously printed a single pass, we'll now print a "pass block": we print extra passes to fill in the empty rows. A naive implementation might look like this: </P> <PRE> 0 *---*---*---*---*---*---* 1 *---*---*---*---*---*---* 2 *---*---*---*---*---*---* 3 *---*---*---*---*---*---* 4 *---*---*---*---*---*---* 5 *---*---*---*---*---*---* 6 *---*---*---*---*---*---* 7 *---*---*---*---*---*---* 8 *---*---*---*---*---*- 9 *---*---*---*---*---* 10 *---*---*---*---*--- 11 *---*---*---*---*-- </PRE> <P> (Now you can see why this process is called "weaving"!) </P> <P><HR><P> Go to the <A HREF="gimpprint_1.html">first</A>, <A HREF="gimpprint_28.html">previous</A>, <A HREF="gimpprint_30.html">next</A>, <A HREF="gimpprint_47.html">last</A> section, <A HREF="gimpprint_toc.html">table of contents</A>. </BODY> </HTML>