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Doc: improve description of geometric multiplication/division.

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David Johnston reminded me that the per-point calculations being done
by these operators are equivalent to complex multiplication/division.
(Once I would've recognized that immediately, but it's been too long
since I did any of that sort of math.)

Also put in a footnote mentioning that "rotation" of a box doesn't do
what you might expect, as I'd griped about in the referenced thread.

Discussion: https://postgr.es/m/158110996889.1089.4224139874633222837@wrigleys.postgresql.org
This commit is contained in:
Tom Lane 2020-04-22 21:32:38 -04:00
parent 48107e396f
commit 1cc34640ca
1 changed files with 17 additions and 29 deletions
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46
doc/src/sgml/func.sgml
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@ -9506,21 +9506,19 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
<returnvalue><replaceable>geometric_type</replaceable></returnvalue> <returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?> <?br?>
Multiplies each point of the first argument by the second Multiplies each point of the first argument by the second
<type>point</type><footnote><para>For this purpose, the <type>point</type> (treating a point as being a complex number
product of two points represented by real and imaginary parts, and performing standard
(<replaceable>x1</replaceable>,<replaceable>y1</replaceable>) and complex multiplication). If one interprets
(<replaceable>x2</replaceable>,<replaceable>y2</replaceable>) is the second <type>point</type> as a vector, this is equivalent to
defined as
(<replaceable>x1</replaceable>*<replaceable>x2</replaceable> -
<replaceable>y1</replaceable>*<replaceable>y2</replaceable>,
<replaceable>x1</replaceable>*<replaceable>y2</replaceable> +
<replaceable>y1</replaceable>*<replaceable>x2</replaceable>).</para></footnote>.
Interpreting the <type>point</type> as a vector, this is equivalent to
scaling the object's size and distance from the origin by the length scaling the object's size and distance from the origin by the length
of the vector, and rotating it counterclockwise around the origin by of the vector, and rotating it counterclockwise around the origin by
the vector's angle from the <replaceable>x</replaceable> axis. the vector's angle from the <replaceable>x</replaceable> axis.
Available for <type>point</type>, <type>box</type>, <type>path</type>, Available for <type>point</type>, <type>box</type>,<footnote
<type>circle</type>. id="functions-geometry-rotation-fn"><para><quote>Rotating</quote> a
box with these operators only moves its corner points: the box is
still considered to have sides parallel to the axes. Hence the box's
size is not preserved, as a true rotation would do.</para></footnote>
<type>path</type>, <type>circle</type>.
<?br?> <?br?>
<literal>path '((0,0),(1,0),(1,1))' * point '(3.0,0)'</literal> <literal>path '((0,0),(1,0),(1,1))' * point '(3.0,0)'</literal>
<returnvalue>((0,0),(3,0),(3,3))</returnvalue> <returnvalue>((0,0),(3,0),(3,3))</returnvalue>
@ -9535,26 +9533,16 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
<replaceable>geometric_type</replaceable> <literal>/</literal> <type>point</type> <replaceable>geometric_type</replaceable> <literal>/</literal> <type>point</type>
<returnvalue><replaceable>geometric_type</replaceable></returnvalue> <returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?> <?br?>
Divides each point of the first argument by the Divides each point of the first argument by the second
second <type>point</type><footnote><para>For this purpose, the <type>point</type> (treating a point as being a complex number
quotient of two points represented by real and imaginary parts, and performing standard
(<replaceable>x1</replaceable>,<replaceable>y1</replaceable>) and complex division). If one interprets
(<replaceable>x2</replaceable>,<replaceable>y2</replaceable>) is the second <type>point</type> as a vector, this is equivalent to
defined as
((<replaceable>x1</replaceable>*<replaceable>x2</replaceable> +
<replaceable>y1</replaceable>*<replaceable>y2</replaceable>) /
<replaceable>L</replaceable>,
(<replaceable>y1</replaceable>*<replaceable>x2</replaceable> -
<replaceable>x1</replaceable>*<replaceable>y2</replaceable>) /
<replaceable>L</replaceable>),
where <replaceable>L</replaceable> =
<replaceable>x2</replaceable>*<replaceable>x2</replaceable> +
<replaceable>y2</replaceable>*<replaceable>y2</replaceable>.</para></footnote>.
Interpreting the <type>point</type> as a vector, this is equivalent to
scaling the object's size and distance from the origin down by the scaling the object's size and distance from the origin down by the
length of the vector, and rotating it clockwise around the origin by length of the vector, and rotating it clockwise around the origin by
the vector's angle from the <replaceable>x</replaceable> axis. the vector's angle from the <replaceable>x</replaceable> axis.
Available for <type>point</type>, <type>box</type>, <type>path</type>, Available for <type>point</type>, <type>box</type>,<footnoteref
linkend="functions-geometry-rotation-fn"/> <type>path</type>,
<type>circle</type>. <type>circle</type>.
<?br?> <?br?>
<literal>path '((0,0),(1,0),(1,1))' / point '(2.0,0)'</literal> <literal>path '((0,0),(1,0),(1,1))' / point '(2.0,0)'</literal>