## SYNOPSIS

This document describes the geometry of regions available for spatial filtering in \s-1IRAF/PROS\s0 analysis.

## DESCRIPTION

Geometric shapes

Several geometric shapes are used to describe regions. The valid shapes are:

```  shape:        arguments:
-----         ----------------------------------------
BOX           xcenter ycenter xwidth yheight (angle)
ELLIPSE       xcenter ycenter xwidth yheight (angle)
FIELD         none
LINE          x1 y1 x2 y2
PIE           xcenter ycenter angle1 angle2
POINT         x1 y1
POLYGON       x1 y1 x2 y2 ... xn yn
```

All arguments are real values; integer values are automatically converted to real where necessary. All angles are in degrees and specify angles that run counter-clockwise from the positive y\-axis.

Shapes can be specified using \*(L"command\*(R" syntax:

[shape] arg1 arg2 ...

or using \*(L"routine\*(R" syntax:

[shape](arg1, arg2, ...)

or by any combination of the these. (Of course, the parentheses must balance and there cannot be more commas than necessary.) The shape keywords are case\-insensitive. Furthermore, any shape can be specified by a three-character unique abbreviation. For example, one can specify three circular regions as:

"foo.fits[CIRCLE 512 512 50;CIR(128 128, 10);cir(650,650,20)]"

(Quotes generally are required to protect the region descriptor from being processed by the Unix shell.)

The annulus shape specifies annuli, centered at xcenter, ycenter, with inner and outer radii (r1, r2). For example,

ANNULUS 25 25 5 10

specifies an annulus centered at 25.0 25.0 with an inner radius of 5.0 and an outer radius of 10. Assuming (as will be done for all examples in this document, unless otherwise noted) this shape is used in a mask of size 40x40, it will look like this:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:....................111111111........... 33:...................11111111111.......... 32:.................111111111111111........ 31:.................111111111111111........ 30:................11111111111111111....... 29:...............1111111.....1111111...... 28:...............111111.......111111...... 27:...............11111.........11111...... 26:...............11111.........11111...... 25:...............11111.........11111...... 24:...............11111.........11111...... 23:...............11111.........11111...... 22:...............111111.......111111...... 21:...............1111111.....1111111...... 20:................11111111111111111....... 19:.................111111111111111........ 18:.................111111111111111........ 17:...................11111111111.......... 16:....................111111111........... 15:........................................ 14:........................................ 13:........................................ 12:........................................ 11:........................................ 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The box shape specifies an orthogonally oriented box, centered at xcenter, ycenter, of size xwidth, yheight. It requires four arguments and accepts an optional fifth argument to specify a rotation angle. When the rotation angle is specified (in degrees), the box is rotated by an angle that runs counter-clockwise from the positive y\-axis.

The box shape specifies a rotated box, centered at xcenter, ycenter, of size xwidth, yheight. The box is rotated by an angle specified in degrees that runs counter-clockwise from the positive y\-axis. If the angle argument is omitted, it defaults to 0.

The circle shape specifies a circle, centered at xcenter, ycenter, of radius r. It requires three arguments.

The ellipse shape specifies an ellipse, centered at xcenter, ycenter, with y\-axis width a and the y\-axis length b defined such that:

x**2/a**2 + y**2/b**2 = 1

Note that a can be less than, equal to, or greater than b. The ellipse is rotated the specified number of degrees. The rotation is done according to astronomical convention, counter-clockwise from the positive y\-axis. An ellipse defined by:

ELLIPSE 20 20 5 10 45

will look like this:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:........................................ 33:........................................ 32:........................................ 31:........................................ 30:........................................ 29:........................................ 28:........................................ 27:............111111...................... 26:............11111111.................... 25:............111111111................... 24:............11111111111................. 23:............111111111111................ 22:............111111111111................ 21:.............111111111111............... 20:.............1111111111111.............. 19:..............111111111111.............. 18:...............111111111111............. 17:...............111111111111............. 16:................11111111111............. 15:..................111111111............. 14:...................11111111............. 13:.....................111111............. 12:........................................ 11:........................................ 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The field shape specifies the entire field as a region. It is not usually specified explicitly, but is used implicitly in the case where no regions are specified, that is, in cases where either a null string or some abbreviation of the string \*(L"none\*(R" is input. Field takes no arguments.

The pie shape specifies an angular wedge of the entire field, centered at xcenter, ycenter. The wedge runs between the two specified angles. The angles are given in degrees, running counter-clockwise from the positive x\-axis. For example,

PIE 20 20 90 180

defines a region from 90 degrees to 180 degrees, i.e., quadrant 2 of the Cartesian plane. The display of such a region looks like this:

1234567890123456789012345678901234567890 ---------------------------------------- 40:11111111111111111111.................... 39:11111111111111111111.................... 38:11111111111111111111.................... 37:11111111111111111111.................... 36:11111111111111111111.................... 35:11111111111111111111.................... 34:11111111111111111111.................... 33:11111111111111111111.................... 32:11111111111111111111.................... 31:11111111111111111111.................... 30:11111111111111111111.................... 29:11111111111111111111.................... 28:11111111111111111111.................... 27:11111111111111111111.................... 26:11111111111111111111.................... 25:11111111111111111111.................... 24:11111111111111111111.................... 23:11111111111111111111.................... 22:11111111111111111111.................... 21:11111111111111111111.................... 20:........................................ 19:........................................ 18:........................................ 17:........................................ 16:........................................ 15:........................................ 14:........................................ 13:........................................ 12:........................................ 11:........................................ 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The pie slice specified is always a counter-clockwise sweep between the angles, starting at the first angle and ending at the second. Thus:

PIE 10 15 30 60

describes a 30 degree sweep from 2 o'clock to 1 o'clock, while:

PIE 10 15 60 30

describes a 330 degree counter-clockwise sweep from 1 o'clock to 2 o'clock passing through 12 o'clock (0 degrees). Note in both of these examples that the center of the slice can be anywhere on the plane. The second mask looks like this:

1234567890123456789012345678901234567890 ---------------------------------------- 40:111111111111111111111111................ 39:11111111111111111111111................. 38:11111111111111111111111................. 37:1111111111111111111111.................. 36:1111111111111111111111.................. 35:111111111111111111111................... 34:11111111111111111111.................... 33:11111111111111111111.................... 32:1111111111111111111....................1 31:1111111111111111111..................111 30:111111111111111111.................11111 29:111111111111111111................111111 28:11111111111111111...............11111111 27:1111111111111111..............1111111111 26:1111111111111111.............11111111111 25:111111111111111............1111111111111 24:111111111111111..........111111111111111 23:11111111111111.........11111111111111111 22:11111111111111........111111111111111111 21:1111111111111.......11111111111111111111 20:111111111111......1111111111111111111111 19:111111111111....111111111111111111111111 18:11111111111....1111111111111111111111111 17:11111111111..111111111111111111111111111 16:1111111111.11111111111111111111111111111 15:1111111111111111111111111111111111111111 14:1111111111111111111111111111111111111111 13:1111111111111111111111111111111111111111 12:1111111111111111111111111111111111111111 11:1111111111111111111111111111111111111111 10:1111111111111111111111111111111111111111 9:1111111111111111111111111111111111111111 8:1111111111111111111111111111111111111111 7:1111111111111111111111111111111111111111 6:1111111111111111111111111111111111111111 5:1111111111111111111111111111111111111111 4:1111111111111111111111111111111111111111 3:1111111111111111111111111111111111111111 2:1111111111111111111111111111111111111111 1:1111111111111111111111111111111111111111

The pie slice goes to the edge of the field. To limit its scope, pie usually is is combined with other shapes, such as circles and annuli, using boolean operations. (See below and in \*(L"help regalgebra\*(R").

Pie Performance Notes:

Pie region processing time is proportional to the size of the image, and not the size of the region. This is because the pie shape is the only infinite length shape, and we essentially must check all y rows for inclusion (unlike other regions, where the y limits can be calculated beforehand). Thus, pie can run very slowly on large images. In particular, it will run \s-1MUCH\s0 more slowly than the panda shape in image-based region operations (such as funcnts). We recommend use of panda over pie where ever possible.

If you must use pie, always try to put it last in a boolean && expression. The reason for this is that the filter code is optimized to exit as soon as the result is know. Since pie is the slowest region, it is better to avoid executing it if another region can decide the result. Consider, for example, the difference in time required to process a Chandra \s-1ACIS\s0 file when a pie and circle are combined in two different orders:

time ./funcnts nacis.fits "circle 4096 4096 100 && pie 4096 4096 10 78" 2.87u 0.38s 0:35.08 9.2%

time ./funcnts nacis.fits "pie 4096 4096 10 78 && circle 4096 4096 100 " 89.73u 0.36s 1:03.50 141.8%

Black-magic performance note:

Panda region processing uses a quick test pie region instead of the normal pie region when combining its annulus and pie shapes. This qtpie shape differs from the normal pie in that it utilizes the y limits from the previous region with which it is combined. In a panda shape, which is a series of annuli combined with pies, the processing time is thus reduced to that of the annuli.

You can use the qtpie shape instead of pie in cases where you are combining pie with another shape using the && operator. This will cause the pie limits to be set using limits from the other shape, and will speed up the processing considerably. For example, the above execution of funcnts can be improved considerably using this technique:

time ./funcnts nacis.fits "circle 4096 4096 100 && qtpie 4096 4096 10 78" 4.66u 0.33s 0:05.87 85.0%

We emphasize that this is a quasi-documented feature and might change in the future. The qtpie shape is not recognized by ds9 or other programs.

The line shape allows single pixels in a line between (x1,y1) and (x2,y2) to be included or excluded. For example:

LINE (5,6, 24,25)

displays as:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:........................................ 33:........................................ 32:........................................ 31:........................................ 30:........................................ 29:........................................ 28:........................................ 27:........................................ 26:........................................ 25:.......................1................ 24:......................1................. 23:.....................1.................. 22:....................1................... 21:...................1.................... 20:..................1..................... 19:.................1...................... 18:................1....................... 17:...............1........................ 16:..............1......................... 15:.............1.......................... 14:............1........................... 13:...........1............................ 12:..........1............................. 11:.........1.............................. 10:........1............................... 9:.......1................................ 8:......1................................. 7:.....1.................................. 6:....1................................... 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The point shape allows single pixels to be included or excluded. Although the (x,y) values are real numbers, they are truncated to integer and the corresponding pixel is included or excluded, as specified.

Several points can be put in one region declaration; unlike the original \s-1IRAF\s0 implementation, each now is given a different region mask value. This makes it easier, for example, for funcnts to determine the number of photons in the individual pixels. For example,

POINT (5,6, 10,11, 20,20, 35,30)

will give the different region mask values to all four points, as shown below:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:........................................ 33:........................................ 32:........................................ 31:........................................ 30:..................................4..... 29:........................................ 28:........................................ 27:........................................ 26:........................................ 25:........................................ 24:........................................ 23:........................................ 22:........................................ 21:........................................ 20:...................3.................... 19:........................................ 18:........................................ 17:........................................ 16:........................................ 15:........................................ 14:........................................ 13:........................................ 12:........................................ 11:.........2.............................. 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:....1................................... 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The polygon shape specifies a polygon with vertices (x1, y1) ... (xn, yn). The polygon is closed automatically: one should not specify the last vertex to be the same as the first. Any number of vertices are allowed. For example, the following polygon defines a right triangle as shown below:

POLYGON (10,10, 10,30, 30,30)

looks like this:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:........................................ 33:........................................ 32:........................................ 31:........................................ 30:..........11111111111111111111.......... 29:..........1111111111111111111........... 28:..........111111111111111111............ 27:..........11111111111111111............. 26:..........1111111111111111.............. 25:..........111111111111111............... 24:..........11111111111111................ 23:..........1111111111111................. 22:..........111111111111.................. 21:..........11111111111................... 20:..........1111111111.................... 19:..........111111111..................... 18:..........11111111...................... 17:..........1111111....................... 16:..........111111........................ 15:..........11111......................... 14:..........1111.......................... 13:..........111........................... 12:..........11............................ 11:..........1............................. 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

Note that polygons can get twisted upon themselves if edge lines cross. Thus:

POL (10,10, 20,20, 20,10, 10,20)

will produce an area which is two triangles, like butterfly wings, as shown below:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:........................................ 33:........................................ 32:........................................ 31:........................................ 30:........................................ 29:........................................ 28:........................................ 27:........................................ 26:........................................ 25:........................................ 24:........................................ 23:........................................ 22:........................................ 21:........................................ 20:........................................ 19:..........1........1.................... 18:..........11......11.................... 17:..........111....111.................... 16:..........1111..1111.................... 15:..........1111111111.................... 14:..........1111..1111.................... 13:..........111....111.................... 12:..........11......11.................... 11:..........1........1.................... 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

The following are combinations of pie with different shapes (called \*(L"panda\*(R" for \*(L"Pie \s-1AND\s0 Annulus\*(R") allow for easy specification of radial sections:

shape: arguments: ----- --------- PANDA xcen ycen ang1 ang2 nang irad orad nrad # circular CPANDA xcen ycen ang1 ang2 nang irad orad nrad # circular BPANDA xcen ycen ang1 ang2 nang xwlo yhlo xwhi yhhi nrad (ang) # box EPANDA xcen ycen ang1 ang2 nang xwlo yhlo xwhi yhhi nrad (ang) # ellipse

The panda (Pies \s-1AND\s0 Annuli) shape can be used to create combinations of pie and annuli markers. It is analogous to a Cartesian product on those shapes, i.e., the result is several shapes generated by performing a boolean \s-1AND\s0 between pies and annuli. Thus, the panda and cpanda specify combinations of annulus and circle with pie, respectively and give identical results. The bpanda combines box and pie, while epanda combines ellipse and pie.

Consider the example shown below:

PANDA(20,20, 0,360,3, 0,15,4)

Here, 3 pie slices centered at 20, 20 are combined with 4 annuli, also centered at 20, 20. The result is a mask with 12 regions (displayed in base 16 to save characters):

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:..............44444444444............... 33:............444444444444444............. 32:...........88444444444444444............ 31:.........888844443333344444444.......... 30:........88888833333333333444444......... 29:........88888733333333333344444......... 28:.......8888877733333333333344444........ 27:......888887777332222233333344444....... 26:......888877777622222222333334444....... 25:.....88887777766622222222333334444...... 24:.....88887777666622222222233334444...... 23:.....88887777666651111222233334444...... 22:.....88877776666551111122223333444...... 21:.....88877776666555111122223333444...... 20:.....888777766665559999aaaabbbbccc...... 19:.....888777766665559999aaaabbbbccc...... 18:.....888777766665599999aaaabbbbccc...... 17:.....88887777666659999aaaabbbbcccc...... 16:.....888877776666aaaaaaaaabbbbcccc...... 15:.....888877777666aaaaaaaabbbbbcccc...... 14:......8888777776aaaaaaaabbbbbcccc....... 13:......888887777bbaaaaabbbbbbccccc....... 12:.......88888777bbbbbbbbbbbbccccc........ 11:........888887bbbbbbbbbbbbccccc......... 10:........888888bbbbbbbbbbbcccccc......... 9:.........8888ccccbbbbbcccccccc.......... 8:...........88ccccccccccccccc............ 7:............ccccccccccccccc............. 6:..............ccccccccccc............... 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

Several regions with different mask values can be combined in the same mask. This supports comparing data from the different regions. (For information on how to combine different shapes into a single region, see \*(L"help regalgebra\*(R".) For example, consider the following set of regions:

ANNULUS 25 25 5 10 ELLIPSE 20 20 5 10 315 BOX 15 15 5 10

The resulting mask will look as follows:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........................................ 35:........................................ 34:....................111111111........... 33:...................11111111111.......... 32:.................111111111111111........ 31:.................111111111111111........ 30:................11111111111111111....... 29:...............1111111.....1111111...... 28:...............111111.......111111...... 27:...............11111.222222..11111...... 26:...............111112222222..11111...... 25:...............111112222222..11111...... 24:...............111112222222..11111...... 23:...............111112222222..11111...... 22:...............111111222222.111111...... 21:..............211111112222.1111111...... 20:............322211111111111111111....... 19:............32222111111111111111........ 18:............22222111111111111111........ 17:............222222211111111111.......... 16:............22222222111111111........... 15:............222222222................... 14:............22222222.................... 13:............222222...................... 12:............33333....................... 11:............33333....................... 10:........................................ 9:........................................ 8:........................................ 7:........................................ 6:........................................ 5:........................................ 4:........................................ 3:........................................ 2:........................................ 1:........................................

Note that when a pixel is in 2 or more regions, it is arbitrarily assigned to a one of the regions in question (often based on how a give C compiler optimizes boolean expressions).

Region accelerators

Two types of \fBaccelerators, to simplify region specification, are provided as natural extensions to the ways shapes are described. These are: extended lists of parameters, specifying multiple regions, valid for annulus, box, circle, ellipse, pie, and points; and n=, valid for annulus, box, circle, ellipse, and pie (not point). In both cases, one specification is used to define several different regions, that is, to define shapes with different mask values in the region mask.

The following regions accept accelerator syntax:

shape arguments ----- ------------------------------------------ ANNULUS xcenter ycenter radius1 radius2 ... radiusn ANNULUS xcenter ycenter inner_radius outer_radius n=[number] BOX xcenter ycenter xw1 yh1 xw2 yh2 ... xwn yhn (angle) BOX xcenter ycenter xwlo yhlo xwhi yhhi n=[number] (angle) CIRCLE xcenter ycenter r1 r2 ... rn # same as annulus CIRCLE xcenter ycenter rinner router n=[number] # same as annulus ELLIPSE xcenter ycenter xw1 yh1 xw2 yh2 ... xwn yhn (angle) ELLIPSE xcenter ycenter xwlo yhlo xwhi yhhi n=[number] (angle) PIE xcenter ycenter angle1 angle2 (angle3) (angle4) (angle5) ... PIE xcenter ycenter angle1 angle2 (n=[number]) POINT x1 y1 x2 y2 ... xn yn

Note that the circle accelerators are simply aliases for the annulus accelerators.

For example, several annuli at the same center can be specified in one region expression by specifying more than two radii. If N radii are specified, then N\-1 annuli result, with the outer radius of each preceding annulus being the inner radius of the succeeding annulus. Each annulus is considered a separate region, and is given a separate mask value. For example,

ANNULUS 20 20 0 2 5 10 15 20

specifies five different annuli centered at 20 20, and is equivalent to:

ANNULUS 20.0 20.0 0 2 ANNULUS 20.0 20.0 2 5 ANNULUS 20.0 20.0 5 10 ANNULUS 20.0 20.0 10 15 ANNULUS 20.0 20.0 15 20

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:.............5555555555555.............. 38:...........55555555555555555............ 37:.........555555555555555555555.......... 36:........55555555555555555555555......... 35:......555555555555555555555555555....... 34:.....55555555544444444444555555555...... 33:....5555555544444444444444455555555..... 32:....5555555444444444444444445555555..... 31:...555555444444444444444444444555555.... 30:..55555544444444444444444444444555555... 29:..55555544444443333333334444444555555... 28:.5555554444444333333333334444444555555.. 27:.5555544444433333333333333344444455555.. 26:555555444444333333333333333444444555555. 25:555554444443333333333333333344444455555. 24:555554444433333332222233333334444455555. 23:555554444433333322222223333334444455555. 22:555554444433333222222222333334444455555. 21:555554444433333222111222333334444455555. 20:555554444433333222111222333334444455555. 19:555554444433333222111222333334444455555. 18:555554444433333222222222333334444455555. 17:555554444433333322222223333334444455555. 16:555554444433333332222233333334444455555. 15:555554444443333333333333333344444455555. 14:555555444444333333333333333444444555555. 13:.5555544444433333333333333344444455555.. 12:.5555554444444333333333334444444555555.. 11:..55555544444443333333334444444555555... 10:..55555544444444444444444444444555555... 9:...555555444444444444444444444555555.... 8:....5555555444444444444444445555555..... 7:....5555555544444444444444455555555..... 6:.....55555555544444444444555555555...... 5:......555555555555555555555555555....... 4:........55555555555555555555555......... 3:.........555555555555555555555.......... 2:...........55555555555555555............ 1:.............5555555555555..............

For boxes and ellipses, if an odd number of arguments is specified, then the last argument is assumed to be an angle. Otherwise, the angle is assumed to be zero. For example:

ellipse 20 20 3 5 6 10 9 15 12 20 45

specifies an 3 ellipses at a 45 degree angle:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:........................................ 38:........................................ 37:........................................ 36:........33333333........................ 35:......333333333333...................... 34:.....3333333333333333................... 33:....333333333333333333.................. 32:....33333332222233333333................ 31:...3333332222222222333333............... 30:...33333222222222222233333.............. 29:...333332222222222222223333............. 28:...3333222222211112222223333............ 27:...33332222211111111222223333........... 26:...333322222111111111122223333.......... 25:...3333222211111111111122223333......... 24:....3332222111111..1111122223333........ 23:....333322211111.....11112222333........ 22:....33332222111.......11112223333....... 21:.....33322221111.......11122223333...... 20:.....33332221111.......11112223333...... 19:.....33332222111.......11112222333...... 18:......33332221111.......11122223333..... 17:.......33322221111.....111112223333..... 16:.......3333222211111..1111112222333..... 15:........3333222211111111111122223333.... 14:.........333322221111111111222223333.... 13:..........33332222211111111222223333.... 12:...........3333222222111122222223333.... 11:............333322222222222222233333.... 10:.............33333222222222222233333.... 9:..............3333332222222222333333.... 8:...............33333333222223333333..... 7:.................333333333333333333..... 6:..................3333333333333333...... 5:.....................333333333333....... 4:.......................33333333......... 3:........................................ 2:........................................ 1:........................................

Note in the above example that the lower limit is not part of the region for boxes, circles, and ellipses. This makes circles and annuli equivalent, i.e.:

circle 20 20 5 10 15 20 annulus 20 20 5 10 15 20

both give the following region mask:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........................................ 39:.............3333333333333.............. 38:...........33333333333333333............ 37:.........333333333333333333333.......... 36:........33333333333333333333333......... 35:......333333333333333333333333333....... 34:.....33333333322222222222333333333...... 33:....3333333322222222222222233333333..... 32:....3333333222222222222222223333333..... 31:...333333222222222222222222222333333.... 30:..33333322222222222222222222222333333... 29:..33333322222221111111112222222333333... 28:.3333332222222111111111112222222333333.. 27:.3333322222211111111111111122222233333.. 26:333333222222111111111111111222222333333. 25:333332222221111111111111111122222233333. 24:33333222221111111.....11111112222233333. 23:3333322222111111.......1111112222233333. 22:333332222211111.........111112222233333. 21:333332222211111.........111112222233333. 20:333332222211111.........111112222233333. 19:333332222211111.........111112222233333. 18:333332222211111.........111112222233333. 17:3333322222111111.......1111112222233333. 16:33333222221111111.....11111112222233333. 15:333332222221111111111111111122222233333. 14:333333222222111111111111111222222333333. 13:.3333322222211111111111111122222233333.. 12:.3333332222222111111111112222222333333.. 11:..33333322222221111111112222222333333... 10:..33333322222222222222222222222333333... 9:...333333222222222222222222222333333.... 8:....3333333222222222222222223333333..... 7:....3333333322222222222222233333333..... 6:.....33333333322222222222333333333...... 5:......333333333333333333333333333....... 4:........33333333333333333333333......... 3:.........333333333333333333333.......... 2:...........33333333333333333............ 1:.............3333333333333..............

As a final example, specifying several angles in one pie slice expression is equivalent to specifying several separate slices with the same center. As with the annulus, if N angles are specified, then N\-1 slices result, with the ending angle of each preceding slice being the starting angle of the succeeding slice. Each slice is considered a separate region, and is given a separate mask value. For example,

PIE 12 12 315 45 115 270

specifies three regions as shown below:

1234567890123456789012345678901234567890 ---------------------------------------- 40:2222222222222222222222222222222222222222 39:2222222222222222222222222222222222222221 38:2222222222222222222222222222222222222211 37:2222222222222222222222222222222222222111 36:2222222222222222222222222222222222221111 35:3222222222222222222222222222222222211111 34:3222222222222222222222222222222222111111 33:3322222222222222222222222222222221111111 32:3322222222222222222222222222222211111111 31:3332222222222222222222222222222111111111 30:3332222222222222222222222222221111111111 29:3333222222222222222222222222211111111111 28:3333222222222222222222222222111111111111 27:3333322222222222222222222221111111111111 26:3333322222222222222222222211111111111111 25:3333322222222222222222222111111111111111 24:3333332222222222222222221111111111111111 23:3333332222222222222222211111111111111111 22:3333333222222222222222111111111111111111 21:3333333222222222222221111111111111111111 20:3333333322222222222211111111111111111111 19:3333333322222222222111111111111111111111 18:3333333332222222221111111111111111111111 17:3333333332222222211111111111111111111111 16:3333333333222222111111111111111111111111 15:3333333333222221111111111111111111111111 14:3333333333322211111111111111111111111111 13:3333333333322111111111111111111111111111 12:33333333333.1111111111111111111111111111 11:3333333333331111111111111111111111111111 10:333333333333.111111111111111111111111111 9:333333333333..11111111111111111111111111 8:333333333333...1111111111111111111111111 7:333333333333....111111111111111111111111 6:333333333333.....11111111111111111111111 5:333333333333......1111111111111111111111 4:333333333333.......111111111111111111111 3:333333333333........11111111111111111111 2:333333333333.........1111111111111111111 1:333333333333..........111111111111111111

The annulus, box, circle, ellipse, and pie shapes also accept an n=[int] syntax for specifying multiple regions. The n=[int]syntax interprets the previous (shape\-dependent) arguments as lower and upper limits for the region and creates n shapes with evenly spaced boundaries. For example, if n=[int] is specified in an annulus, the two immediately preceding radii (rn and rm) are divided into int annuli, such that the inner radius of the first is rn and the outer radius of the last is rm. For example,

ANNULUS 20 20 5 20 n=3

is equivalent to:

ANNULUS 20 20 5 10 15 20

If this syntax is used with an ellipse or box, then the two preceding pairs of values are taken to be lower and upper limits for a set of ellipses or boxes. A circle uses the two preceding arguments for upper and lower radii. For pie, the two preceding angles are divided into n wedges such that the starting angle of the first is the lower bound and the ending angle of the last is the upper bound. In all cases, the n=[int] syntax allows any single alphabetic character before the \*(L"=\*(R", i.e, i=3, z=3, etc. are all equivalent.

Also note that for boxes and ellipses, the optional angle argument is always specified after the n=[int] syntax. For example:

ellipse 20 20 4 6 16 24 n=3 45

specifies 3 elliptical regions at an angle of 45 degrees:

1234567890123456789012345678901234567890 ---------------------------------------- 40:........33333333........................ 39:.....33333333333333..................... 38:....33333333333333333................... 37:...33333333333333333333................. 36:..33333333333333333333333............... 35:.3333333333222223333333333.............. 34:3333333322222222222233333333............ 33:33333332222222222222223333333........... 32:333333222222222222222222333333.......... 31:3333322222222222222222222333333......... 30:33333222222222111122222222333333........ 29:333332222222111111112222222333333....... 28:3333222222211111111111222222333333...... 27:3333222222111111111111112222233333...... 26:33332222221111111111111112222233333..... 25:33332222211111111.111111112222233333.... 24:333322222111111......111111222223333.... 23:333322222111111.......111112222233333... 22:33333222221111.........11111222223333... 21:333332222211111.........11112222233333.. 20:.33332222211111.........11111222223333.. 19:.33333222221111.........111112222233333. 18:..33332222211111.........11112222233333. 17:..333332222211111.......111111222233333. 16:...333322222111111......111111222223333. 15:...333332222211111111.111111112222233333 14:....333332222211111111111111122222233333 13:.....33333222221111111111111122222233333 12:.....33333322222211111111111222222233333 11:......3333332222222111111112222222333333 10:.......333333222222221111222222222333333 9:........33333322222222222222222222333333 8:.........333333222222222222222222333333. 7:..........33333332222222222222223333333. 6:...........3333333322222222222233333333. 5:.............3333333333222223333333333.. 4:..............33333333333333333333333... 3:................33333333333333333333.... 2:..................33333333333333333..... 1:....................33333333333333......

Both the variable argument syntax and the n=[int] syntax must occur alone in a region descriptor (aside from the optional angle for boxes and ellipses). They cannot be combined. Thus, it is not valid to precede or follow an n=[int] accelerator with more angles or radii, as in this example:

# INVALID -- one too many angles before a=5 ... # and no angles are allowed after a=5 PIE 12 12 10 25 50 a=5 85 135

Instead, use three separate specifications, such as:

PIE 12 12 10 25 PIE 12 12 25 50 a=5 PIE 12 12 85 135

The original (\s-1IRAF\s0) implementation of region filtering permitted this looser syntax, but we found it caused more confusion than it was worth and therefore removed it.

\s-1NB:\s0 Accelerators may be combined with other shapes in a boolean expression in any order. (This is a change starting with funtools v1.1.1. Prior to this release, the accelerator shape had to be specified last). The actual region mask id values returned depend on the order in which the shapes are specified, although the total number of pixels or rows that pass the filter will be consistent. For this reason, use of accelerators in boolean expressions is discouraged in programs such as funcnts, where region mask id values are used to count events or image pixels.

[All region masks displayed in this document were generated using the fundisp routine and the undocumented \*(L"mask=all\*(R" argument (with spaced removed using sed ):

fundisp "funtools/funtest/test40.fits[ANNULUS 25 25 5 10]" mask=all |\ sed 's/ //g'

Note that you must supply an image of the appropriate size \*(-- in this case, a \s-1FITS\s0 image of dimension 40x40 is used.]

## RELATED TO reggeometry…

See funtools(7) for a list of Funtools help pages