</listitem>

<listitem>

<para>

Removebtree index. It was used to cluster the index.

RemoveB-tree index. It was used to cluster the index.

</para>

</listitem>

<listitem>

<para>

Constructors within <application>pgSphere</application> are

functions needed to create spherical data types from other data

types.In usage, there isn't a differencefrom

types.For actual use, there isn't a differenceto

<emphasis>usual</emphasis> <application>PostgreSQL</application>

functions. <application>pgSphere</application> constructor

functions are named by returned data type. Constructor functions

Euler transformation

</title>

<para>

There are two constructor functions fora Euler transformation:

There are two constructor functions foran Euler transformation:

</para>

<funcsynopsis>

<funcprototype>

For more information about that parameter, see <xref linkend="dt.strans"/>.

</para>

<example>

<title>Createa Euler transformation object</title>

<title>Createan Euler transformation object</title>

<simpara>

Create a transformation object to rotate a spherical object

counterclockwise, first 20&deg; around

Otherwise, this function returns an error.

</para>

<example>

<title>A circle around theNoth Pole</title>

<title>A circle around thenorth pole</title>

<simpara>

Get a spherical circle around the North Pole with a radius

of 30&deg;.

The input of spherical lines using Euler transformation and

length is quite circumstantial (see <xref linkend="dt.sline"/>).

For short lines it is easier to input a line specifying the

begining and the end of the line.

beginning and the end of the line.

</para>

<funcsynopsis>

<funcprototype>

<para>or</para>

<synopsis> object + strans (&ohgr;, i, &OHgr;)</synopsis>

<example>

<title>Perihel andaphel coordinates of a comet orbit</title>

<title>perihelion andaphelion coordinates of a comet's orbit</title>

<simpara>

We are assuming the orbital elements of a comet are

&OHgr;=30&deg;, i=60&deg; and &ohgr;=90&deg;. We get the

spherical position ofperihel andaphel with:

spherical position ofperihelion andaphelion with:

</simpara>

<programlisting>

<![CDATA[sql> SELECT set_sphere_output('DEG');]]>

<![CDATA[ SET DEG]]>

<![CDATA[(1 row)]]>

<![CDATA[]]>

<![CDATA[sql> SELECT spoint '(0,0)' + strans '90d,60d,30d' ASperihel;]]>

<![CDATA[perihel]]>

<![CDATA[sql> SELECT spoint '(0,0)' + strans '90d,60d,30d' ASperihelion;]]>

<![CDATA[perihelion]]>

<![CDATA[--------------]]>

<![CDATA[ (120d , 60d)]]>

<![CDATA[(1 row)]]>

<![CDATA[]]>

<![CDATA[sql> SELECT spoint '(180d,0)' + strans '90d,60d,30d' ASaphel;]]>

<![CDATA[aphel]]>

<![CDATA[sql> SELECT spoint '(180d,0)' + strans '90d,60d,30d' ASaphelion;]]>

<![CDATA[aphelion]]>

<![CDATA[---------------]]>

<![CDATA[ (300d , -60d)]]>

<![CDATA[(1 row)]]>

</funcprototype>

</funcsynopsis>

<para>

return thecartesian

return theCartesian

<literal>x</literal>, <literal>y</literal> or

<literal>z</literal> value of a spherical position

<parameter>p</parameter>. The returned values are always

between <literal>-1.0</literal> and <literal>+1.0</literal>.

</para>

<example>

<title>

Get thecartesian <literal>z</literal>-value

Get theCartesian <literal>z</literal>-value

of a spherical point

</title>

<programlisting>

</programlisting>

</example>

<para>

You can get a <type>float8</type> array ofcartesian values using the function

You can get a <type>float8</type> array ofCartesian values using the function

</para>

<funcsynopsis>

<funcprototype>

</funcsynopsis>

<example>

<title>

Get thecartesian values of a spherical point

Get theCartesian values of a spherical point

</title>

<programlisting>

<![CDATA[sql> SELECT xyz ( spoint '(0d,0d)' ) AS cart;]]>

<para>

Using the function

<function>strans_zxz(strans),</function> you can convert

a Euler transformation to <literal>ZXZ</literal>-axes

an Euler transformation to <literal>ZXZ</literal>axes

transformation.

</para>

<example>

<title>Change the transformation axes to <literal>ZXZ</literal></title>

<simpara>

Convert the transformation <literal>strans '20d, -270d, 70.5d,

XZY'</literal> to a <literal>ZXZ</literal>-transformation.

XZY'</literal> to a <literal>ZXZ</literal>transformation.

</simpara>

<programlisting>

<![CDATA[sql> SELECT strans_zxz ( strans '20d, -270d, 70.5d, XZY' );]]>

</title>

<sect3 id="funcs.spoly.npts">

<title>

Cnunt of edges

Count of edges

</title>

<para>

Similar to an <type>spath</type> (<xref linkend="funcs.spath.npts"/>),

</title>

<para>

<application>pgSphere</application> uses <literal>GiST</literal>

to create spherical indices. An index speeds up theexecutation

to create spherical indices. An index speeds up theexecution

time of operators <link

linkend="op.over"><literal>@</literal></link>, <link

linkend="op.over"><literal>&amp;&amp;</literal></link>, <link

Then, change into <filename>POSTGRESQL_SRC/src/contrib</filename>.

If the sources are not yet installed and the directory

<filename>pg_sphere</filename> does not exist, take the

gzipped <application>pgSphere</application> sources ( e.g.,

gzipped <application>pgSphere</application> sources ( e.g.,

<filename>pg_sphere_xxx.tgz</filename> ) and run:

</para>

<programlisting>

</title>

<para>

The length/circumference operator <literal>@-@</literal> is

a non-boolean unary operator returning thecirumference or

a non-boolean unary operator returning thecircumference or

length of an object. In the current implementation,

<application>pgSphere</application> supports only

circumferences of circles, polygons, and boxes. It supports

<para>

The unary operator <literal>-</literal> changes the

direction of <type>sline</type> or <type>spath</type>

objects. You can use it witha Euler transformation object

objects. You can use it withan Euler transformation object

in the figurative sense, too (<xref linkend="op.trans"/>).

</para>

<example>

</imageobject>

</mediaobject>

A spherical point is an object without expanse

but with a position.Usage cases are:

but with a position.Use cases are:

</para>

<itemizedlist>

<listitem>

<imagedata fileref="&graph1003;" width="160px" format="JPEG"/>

</imageobject>

</mediaobject>

A Euler transformation is done with three counterclockwise

An Euler transformation is done with three counterclockwise

object rotations around following the axes:

<literal>x</literal>-axis, <literal>y</literal>-axis, or

<literal>z</literal>-axis.Usage cases are:

<literal>z</literal>-axis.Use cases are:

</para>

<itemizedlist>

<listitem>

</listitem>

</itemizedlist>

<para>

The input syntax ofa Euler transformation is:

The input syntax ofan Euler transformation is:

</para>

<synopsis>angle1, angle2, angle3 &lsqb;, axes &rsqb;</synopsis>

<para>

</mediaobject>

A spherical circle is an area

around a point, where all points inside the circle have a

distance less than or equal to the radius of the circle.Usage

distance less than or equal to the radius of the circle.Use

cases are:

</para>

<itemizedlist>

</imageobject>

</mediaobject>

A spherical line is part of a great circle (meridian) that has

a beginning and an end and hence, a direction.Usage cases are:

a beginning and an end and hence, a direction.Use cases are:

</para>

<itemizedlist>

<listitem>

A general located line with a length

<parameter>length</parameter> is defined as a line starting at

position <literal>(0d,0d)</literal> and ending at position

<literal>(length,0d)</literal> transformed witha Euler

<literal>(length,0d)</literal> transformed withan Euler

transformation <parameter>euler</parameter>. The input syntax

is :

</para>

<listitem>

<para>

The transformation <parameter>euler</parameter>

will always be converted toa Euler

will always be converted toan Euler

transformation using axes <literal>Z</literal>,

<literal>X</literal>, and <literal>Z</literal>.

</para>

</para>

</blockquote>

<para>

Usage cases are:

Use cases are:

</para>

<itemizedlist>

<listitem>

</imageobject>

</mediaobject>

A spherical path is a

concatination of spherical lines.Usage cases are:

concatenation of spherical lines.Use cases are:

</para>

<itemizedlist>

<listitem>

<para>

A spherical polygon is a

closed spherical path where line segments cannot be crossed.

One mainusage case are areas on the earth and sky sphere.

One mainuse case are areas on the earth and sky sphere.

Polygons within <application>pgSphere</application>

have the same input syntax as paths:

</para>