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diff --git a/funtools/doc/regalgebra.html b/funtools/doc/regalgebra.html new file mode 100644 index 0000000..c31dbf7 --- /dev/null +++ b/funtools/doc/regalgebra.html @@ -0,0 +1,278 @@ +<!-- =defdoc regalgebra regalgebra n --> +<HTML> +<HEAD> +<TITLE>Region Algebra</TITLE> +</HEAD> +<BODY> + +<!-- =section regalgebra NAME --> +<H2><A NAME="regalgebra">RegAlgebra: Boolean Algebra on Spatial Regions</A></H2> + +<!-- =section regalgebra SYNOPSIS --> +<H2>Summary</H2> +<P> +This document describes the boolean arithmetic defined for +region expressions. + +<!-- =section regalgebra DESCRIPTION --> +<H2>Description</H2> +<P> +When defining a region, several shapes can be combined using boolean +operations. The boolean operators are (in order of precedence): +<PRE> + Symbol Operator Associativity + ------ -------- ------------- + ! not right to left + & and left to right + ^ exclusive or left to right + | inclusive or left to right + +</PRE> +For example, to create a mask consisting of a large circle with a +smaller box removed, one can use the <B>and</B> and <B>not</B> +operators: +<PRE> + CIRCLE(11,11,15) & !BOX(11,11,3,6) +</PRE> + +and the resulting mask is: +<PRE> + 1234567890123456789012345678901234567890 + ---------------------------------------- + 1:1111111111111111111111.................. + 2:1111111111111111111111.................. + 3:11111111111111111111111................. + 4:111111111111111111111111................ + 5:111111111111111111111111................ + 6:1111111111111111111111111............... + 7:1111111111111111111111111............... + 8:1111111111111111111111111............... + 9:111111111...1111111111111............... + 10:111111111...1111111111111............... + 11:111111111...1111111111111............... + 12:111111111...1111111111111............... + 13:111111111...1111111111111............... + 14:111111111...1111111111111............... + 15:1111111111111111111111111............... + 16:1111111111111111111111111............... + 17:111111111111111111111111................ + 18:111111111111111111111111................ + 19:11111111111111111111111................. + 20:1111111111111111111111.................. + 21:1111111111111111111111.................. + 22:111111111111111111111................... + 23:..11111111111111111..................... + 24:...111111111111111...................... + 25:.....11111111111........................ + 26:........................................ + 27:........................................ + 28:........................................ + 29:........................................ + 30:........................................ + 31:........................................ + 32:........................................ + 33:........................................ + 34:........................................ + 35:........................................ + 36:........................................ + 37:........................................ + 38:........................................ + 39:........................................ + 40:........................................ +</PRE> +A three-quarter circle can be defined as: +<PRE> + CIRCLE(20,20,10) & !PIE(20,20,270,360) +</PRE> + +and looks as follows: +<PRE> + + 1234567890123456789012345678901234567890 + ---------------------------------------- + 1:........................................ + 2:........................................ + 3:........................................ + 4:........................................ + 5:........................................ + 6:........................................ + 7:........................................ + 8:........................................ + 9:........................................ + 10:........................................ + 11:...............111111111................ + 12:..............11111111111............... + 13:............111111111111111............. + 14:............111111111111111............. + 15:...........11111111111111111............ + 16:..........1111111111111111111........... + 17:..........1111111111111111111........... + 18:..........1111111111111111111........... + 19:..........1111111111111111111........... + 20:..........1111111111111111111........... + 21:..........1111111111.................... + 22:..........1111111111.................... + 23:..........1111111111.................... + 24:..........1111111111.................... + 25:...........111111111.................... + 26:............11111111.................... + 27:............11111111.................... + 28:..............111111.................... + 29:...............11111.................... + 30:........................................ + 31:........................................ + 32:........................................ + 33:........................................ + 34:........................................ + 35:........................................ + 36:........................................ + 37:........................................ + 38:........................................ + 39:........................................ + 40:........................................ +</PRE> +Two non-intersecting ellipses can be made into the same region: +<PRE> + ELL(20,20,10,20,90) | ELL(1,1,20,10,0) +</PRE> + +and looks as follows: +<PRE> + 1234567890123456789012345678901234567890 + ---------------------------------------- + 1:11111111111111111111.................... + 2:11111111111111111111.................... + 3:11111111111111111111.................... + 4:11111111111111111111.................... + 5:1111111111111111111..................... + 6:111111111111111111...................... + 7:1111111111111111........................ + 8:111111111111111......................... + 9:111111111111............................ + 10:111111111............................... + 11:...........11111111111111111............ + 12:........111111111111111111111111........ + 13:.....11111111111111111111111111111...... + 14:....11111111111111111111111111111111.... + 15:..11111111111111111111111111111111111... + 16:.1111111111111111111111111111111111111.. + 17:111111111111111111111111111111111111111. + 18:111111111111111111111111111111111111111. + 19:111111111111111111111111111111111111111. + 20:111111111111111111111111111111111111111. + 21:111111111111111111111111111111111111111. + 22:111111111111111111111111111111111111111. + 23:111111111111111111111111111111111111111. + 24:.1111111111111111111111111111111111111.. + 25:..11111111111111111111111111111111111... + 26:...11111111111111111111111111111111..... + 27:.....11111111111111111111111111111...... + 28:.......111111111111111111111111......... + 29:...........11111111111111111............ + 30:........................................ + 31:........................................ + 32:........................................ + 33:........................................ + 34:........................................ + 35:........................................ + 36:........................................ + 37:........................................ + 38:........................................ + 39:........................................ + 40:........................................ +</PRE> +You can use several boolean operations in a single region expression, +to create arbitrarily complex regions. With the important exception +below, you can apply the operators in any order, using parentheses if +necessary to override the natural precedences of the operators. + +<P> +NB: Using a panda shape is always much more efficient than explicitly +specifying "pie & annulus", due to the ability of panda to place a +limit on the number of pixels checked in the pie shape. If you are +going to specify the intersection of pie and annulus, use panda +instead. + +<P> +As described in "help regreometry", the <B>PIE</B> slice goes to the +edge of the field. To limit its scope, <B>PIE</B> usually is is +combined with other shapes, such as circles and annuli, using boolean +operations. In this context, it is worth noting that that there is a +difference between <B>-PIE</B> and <B>&!PIE</B>. The former is a +global exclude of all pixels in the <B>PIE</B> slice, while the latter +is a local excludes of pixels affecting only the region(s) with which +the <B>PIE</B> is combined. For example, the following region uses +<B>&!PIE</B> as a local exclude of a single circle. Two other circles +are also defined and are unaffected by the local exclude: +<PRE> + + CIRCLE(1,8,1) + CIRCLE(8,8,7)&!PIE(8,8,60,120)&!PIE(8,8,240,300) + CIRCLE(15,8,2) + + 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 + - - - - - - - - - - - - - - - + 15: . . . . . . . . . . . . . . . + 14: . . . . 2 2 2 2 2 2 2 . . . . + 13: . . . 2 2 2 2 2 2 2 2 2 . . . + 12: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 11: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 10: . . . . 2 2 2 2 2 2 2 . . . . + 9: . . . . . . 2 2 2 . . . . 3 3 + 8: 1 . . . . . . . . . . . . 3 3 + 7: . . . . . . 2 2 2 . . . . 3 3 + 6: . . . . 2 2 2 2 2 2 2 . . . . + 5: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 4: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 3: . . . 2 2 2 2 2 2 2 2 2 . . . + 2: . . . . 2 2 2 2 2 2 2 . . . . + 1: . . . . . . . . . . . . . . . + +</PRE> +Note that the two other regions are not affected by the <B>&!PIE</B>, +which only affects the circle with which it is combined. + +<P> +On the other hand, a <B>-PIE</B> is an global exclude that does +affect other regions with which it overlaps: +<PRE> + + CIRCLE(1,8,1) + CIRCLE(8,8,7) + -PIE(8,8,60,120) + -PIE(8,8,240,300) + CIRCLE(15,8,2) + + 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 + - - - - - - - - - - - - - - - + 15: . . . . . . . . . . . . . . . + 14: . . . . 2 2 2 2 2 2 2 . . . . + 13: . . . 2 2 2 2 2 2 2 2 2 . . . + 12: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 11: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 10: . . . . 2 2 2 2 2 2 2 . . . . + 9: . . . . . . 2 2 2 . . . . . . + 8: . . . . . . . . . . . . . . . + 7: . . . . . . 2 2 2 . . . . . . + 6: . . . . 2 2 2 2 2 2 2 . . . . + 5: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 4: . . 2 2 2 2 2 2 2 2 2 2 2 . . + 3: . . . 2 2 2 2 2 2 2 2 2 . . . + 2: . . . . 2 2 2 2 2 2 2 . . . . + 1: . . . . . . . . . . . . . . . + +</PRE> +The two smaller circles are entirely contained within the two exclude +<B>PIE</B> slices and therefore are excluded from the region. + +<!-- =section regalgebra SEE ALSO --> +<!-- =text See funtools(n) for a list of Funtools help pages --> +<!-- =stop --> + +<P> +<A HREF="./help.html">Go to Funtools Help Index</A> + +<H5>Last updated: November 17, 2005</H5> + +</BODY> +</HTML> |