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<refentry id="cairo-cairo-matrix-t">
<refmeta>
<refentrytitle role="top_of_page" id="cairo-cairo-matrix-t.top_of_page">cairo_matrix_t</refentrytitle>
<manvolnum>3</manvolnum>
<refmiscinfo>
CAIRO Library
</refmiscinfo>
</refmeta>
<refnamediv>
<refname>cairo_matrix_t</refname>
<refpurpose>Generic matrix operations</refpurpose>
</refnamediv>
<refsynopsisdiv id="cairo-cairo-matrix-t.synopsis" role="synopsis">
<title role="synopsis.title">Synopsis</title>
<synopsis> <link linkend="cairo-matrix-t">cairo_matrix_t</link>;
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-init">cairo_matrix_init</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> xx</parameter>,
<parameter><link linkend="double"><type>double</type></link> yx</parameter>,
<parameter><link linkend="double"><type>double</type></link> xy</parameter>,
<parameter><link linkend="double"><type>double</type></link> yy</parameter>,
<parameter><link linkend="double"><type>double</type></link> x0</parameter>,
<parameter><link linkend="double"><type>double</type></link> y0</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-init-identity">cairo_matrix_init_identity</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-init-translate">cairo_matrix_init_translate</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> tx</parameter>,
<parameter><link linkend="double"><type>double</type></link> ty</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-init-scale">cairo_matrix_init_scale</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> sx</parameter>,
<parameter><link linkend="double"><type>double</type></link> sy</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-init-rotate">cairo_matrix_init_rotate</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> radians</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-translate">cairo_matrix_translate</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> tx</parameter>,
<parameter><link linkend="double"><type>double</type></link> ty</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-scale">cairo_matrix_scale</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> sx</parameter>,
<parameter><link linkend="double"><type>double</type></link> sy</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-rotate">cairo_matrix_rotate</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> radians</parameter>);
<link linkend="cairo-status-t"><returnvalue>cairo_status_t</returnvalue></link> <link linkend="cairo-matrix-invert">cairo_matrix_invert</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-multiply">cairo_matrix_multiply</link> (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *result</parameter>,
<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *a</parameter>,
<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *b</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-transform-distance">cairo_matrix_transform_distance</link> (<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> *dx</parameter>,
<parameter><link linkend="double"><type>double</type></link> *dy</parameter>);
<link linkend="void"><returnvalue>void</returnvalue></link> <link linkend="cairo-matrix-transform-point">cairo_matrix_transform_point</link> (<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> *x</parameter>,
<parameter><link linkend="double"><type>double</type></link> *y</parameter>);
</synopsis>
</refsynopsisdiv>
<refsect1 id="cairo-cairo-matrix-t.description" role="desc">
<title role="desc.title">Description</title>
<para>
<link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> is used throughout cairo to convert between different
coordinate spaces. A <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> holds an affine transformation,
such as a scale, rotation, shear, or a combination of these.
The transformation of a point (<literal>x</literal>,<literal>y</literal>)
is given by:
</para>
<para>
<programlisting>
x_new = xx * x + xy * y + x0;
y_new = yx * x + yy * y + y0;
</programlisting>
</para>
<para>
The current transformation matrix of a <link linkend="cairo-t"><type>cairo_t</type></link>, represented as a
<link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>, defines the transformation from user-space
coordinates to device-space coordinates. See <link linkend="cairo-get-matrix"><function>cairo_get_matrix()</function></link> and
<link linkend="cairo-set-matrix"><function>cairo_set_matrix()</function></link>.
</para>
</refsect1>
<refsect1 id="cairo-cairo-matrix-t.details" role="details">
<title role="details.title">Details</title>
<refsect2 id="cairo-matrix-t" role="struct">
<title>cairo_matrix_t</title>
<indexterm zone="cairo-matrix-t"><primary sortas="matrix_t">cairo_matrix_t</primary></indexterm>
<programlisting>typedef struct {
double xx; double yx;
double xy; double yy;
double x0; double y0;
} cairo_matrix_t;
</programlisting>
<para>
A <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> holds an affine transformation, such as a scale,
rotation, shear, or a combination of those. The transformation of
a point (x, y) is given by:
<programlisting>
x_new = xx * x + xy * y + x0;
y_new = yx * x + yy * y + y0;
</programlisting>
</para><variablelist role="struct">
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.xx">xx</structfield>;</term>
<listitem><simpara>xx component of the affine transformation
</simpara></listitem>
</varlistentry>
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.yx">yx</structfield>;</term>
<listitem><simpara>yx component of the affine transformation
</simpara></listitem>
</varlistentry>
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.xy">xy</structfield>;</term>
<listitem><simpara>xy component of the affine transformation
</simpara></listitem>
</varlistentry>
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.yy">yy</structfield>;</term>
<listitem><simpara>yy component of the affine transformation
</simpara></listitem>
</varlistentry>
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.x0">x0</structfield>;</term>
<listitem><simpara>X translation component of the affine transformation
</simpara></listitem>
</varlistentry>
<varlistentry><term><link linkend="double"><type>double</type></link> <structfield id="cairo-matrix-t.y0">y0</structfield>;</term>
<listitem><simpara>Y translation component of the affine transformation
</simpara></listitem>
</varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-init" role="function">
<title>cairo_matrix_init ()</title>
<indexterm zone="cairo-matrix-init"><primary sortas="matrix_init">cairo_matrix_init</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_init (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> xx</parameter>,
<parameter><link linkend="double"><type>double</type></link> yx</parameter>,
<parameter><link linkend="double"><type>double</type></link> xy</parameter>,
<parameter><link linkend="double"><type>double</type></link> yy</parameter>,
<parameter><link linkend="double"><type>double</type></link> x0</parameter>,
<parameter><link linkend="double"><type>double</type></link> y0</parameter>);</programlisting>
<para>
Sets <parameter>matrix</parameter> to be the affine transformation given by
<parameter>xx</parameter>, <parameter>yx</parameter>, <parameter>xy</parameter>, <parameter>yy</parameter>, <parameter>x0</parameter>, <parameter>y0</parameter>. The transformation is given
by:
<programlisting>
x_new = xx * x + xy * y + x0;
y_new = yx * x + yy * y + y0;
</programlisting>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>xx</parameter> :</term>
<listitem><simpara>xx component of the affine transformation
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>yx</parameter> :</term>
<listitem><simpara>yx component of the affine transformation
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>xy</parameter> :</term>
<listitem><simpara>xy component of the affine transformation
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>yy</parameter> :</term>
<listitem><simpara>yy component of the affine transformation
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>x0</parameter> :</term>
<listitem><simpara>X translation component of the affine transformation
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>y0</parameter> :</term>
<listitem><simpara>Y translation component of the affine transformation
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-init-identity" role="function">
<title>cairo_matrix_init_identity ()</title>
<indexterm zone="cairo-matrix-init-identity"><primary sortas="matrix_init_identity">cairo_matrix_init_identity</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_init_identity (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>);</programlisting>
<para>
Modifies <parameter>matrix</parameter> to be an identity transformation.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-init-translate" role="function">
<title>cairo_matrix_init_translate ()</title>
<indexterm zone="cairo-matrix-init-translate"><primary sortas="matrix_init_translate">cairo_matrix_init_translate</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_init_translate (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> tx</parameter>,
<parameter><link linkend="double"><type>double</type></link> ty</parameter>);</programlisting>
<para>
Initializes <parameter>matrix</parameter> to a transformation that translates by <parameter>tx</parameter> and
<parameter>ty</parameter> in the X and Y dimensions, respectively.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>tx</parameter> :</term>
<listitem><simpara>amount to translate in the X direction
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>ty</parameter> :</term>
<listitem><simpara>amount to translate in the Y direction
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-init-scale" role="function">
<title>cairo_matrix_init_scale ()</title>
<indexterm zone="cairo-matrix-init-scale"><primary sortas="matrix_init_scale">cairo_matrix_init_scale</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_init_scale (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> sx</parameter>,
<parameter><link linkend="double"><type>double</type></link> sy</parameter>);</programlisting>
<para>
Initializes <parameter>matrix</parameter> to a transformation that scales by <parameter>sx</parameter> and <parameter>sy</parameter>
in the X and Y dimensions, respectively.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>sx</parameter> :</term>
<listitem><simpara>scale factor in the X direction
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>sy</parameter> :</term>
<listitem><simpara>scale factor in the Y direction
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-init-rotate" role="function">
<title>cairo_matrix_init_rotate ()</title>
<indexterm zone="cairo-matrix-init-rotate"><primary sortas="matrix_init_rotate">cairo_matrix_init_rotate</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_init_rotate (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> radians</parameter>);</programlisting>
<para>
Initialized <parameter>matrix</parameter> to a transformation that rotates by <parameter>radians</parameter>.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>radians</parameter> :</term>
<listitem><simpara>angle of rotation, in radians. The direction of rotation
is defined such that positive angles rotate in the direction from
the positive X axis toward the positive Y axis. With the default
axis orientation of cairo, positive angles rotate in a clockwise
direction.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-translate" role="function">
<title>cairo_matrix_translate ()</title>
<indexterm zone="cairo-matrix-translate"><primary sortas="matrix_translate">cairo_matrix_translate</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_translate (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> tx</parameter>,
<parameter><link linkend="double"><type>double</type></link> ty</parameter>);</programlisting>
<para>
Applies a translation by <parameter>tx</parameter>, <parameter>ty</parameter> to the transformation in
<parameter>matrix</parameter>. The effect of the new transformation is to first translate
the coordinates by <parameter>tx</parameter> and <parameter>ty</parameter>, then apply the original transformation
to the coordinates.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>tx</parameter> :</term>
<listitem><simpara>amount to translate in the X direction
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>ty</parameter> :</term>
<listitem><simpara>amount to translate in the Y direction
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-scale" role="function">
<title>cairo_matrix_scale ()</title>
<indexterm zone="cairo-matrix-scale"><primary sortas="matrix_scale">cairo_matrix_scale</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_scale (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> sx</parameter>,
<parameter><link linkend="double"><type>double</type></link> sy</parameter>);</programlisting>
<para>
Applies scaling by <parameter>sx</parameter>, <parameter>sy</parameter> to the transformation in <parameter>matrix</parameter>. The
effect of the new transformation is to first scale the coordinates
by <parameter>sx</parameter> and <parameter>sy</parameter>, then apply the original transformation to the coordinates.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>sx</parameter> :</term>
<listitem><simpara>scale factor in the X direction
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>sy</parameter> :</term>
<listitem><simpara>scale factor in the Y direction
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-rotate" role="function">
<title>cairo_matrix_rotate ()</title>
<indexterm zone="cairo-matrix-rotate"><primary sortas="matrix_rotate">cairo_matrix_rotate</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_rotate (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> radians</parameter>);</programlisting>
<para>
Applies rotation by <parameter>radians</parameter> to the transformation in
<parameter>matrix</parameter>. The effect of the new transformation is to first rotate the
coordinates by <parameter>radians</parameter>, then apply the original transformation
to the coordinates.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>radians</parameter> :</term>
<listitem><simpara>angle of rotation, in radians. The direction of rotation
is defined such that positive angles rotate in the direction from
the positive X axis toward the positive Y axis. With the default
axis orientation of cairo, positive angles rotate in a clockwise
direction.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-invert" role="function">
<title>cairo_matrix_invert ()</title>
<indexterm zone="cairo-matrix-invert"><primary sortas="matrix_invert">cairo_matrix_invert</primary></indexterm>
<programlisting><link linkend="cairo-status-t"><returnvalue>cairo_status_t</returnvalue></link> cairo_matrix_invert (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>);</programlisting>
<para>
Changes <parameter>matrix</parameter> to be the inverse of its original value. Not
all transformation matrices have inverses; if the matrix
collapses points together (it is <firstterm>degenerate</firstterm>),
then it has no inverse and this function will fail.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><emphasis>Returns</emphasis> :</term><listitem><simpara> If <parameter>matrix</parameter> has an inverse, modifies <parameter>matrix</parameter> to
be the inverse matrix and returns <link linkend="CAIRO-STATUS-SUCCESS:CAPS"><literal>CAIRO_STATUS_SUCCESS</literal></link>. Otherwise,
returns <link linkend="CAIRO-STATUS-INVALID-MATRIX:CAPS"><literal>CAIRO_STATUS_INVALID_MATRIX</literal></link>.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-multiply" role="function">
<title>cairo_matrix_multiply ()</title>
<indexterm zone="cairo-matrix-multiply"><primary sortas="matrix_multiply">cairo_matrix_multiply</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_multiply (<parameter><link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *result</parameter>,
<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *a</parameter>,
<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *b</parameter>);</programlisting>
<para>
Multiplies the affine transformations in <parameter>a</parameter> and <parameter>b</parameter> together
and stores the result in <parameter>result</parameter>. The effect of the resulting
transformation is to first apply the transformation in <parameter>a</parameter> to the
coordinates and then apply the transformation in <parameter>b</parameter> to the
coordinates.
</para>
<para>
It is allowable for <parameter>result</parameter> to be identical to either <parameter>a</parameter> or <parameter>b</parameter>.
</para><variablelist role="params">
<varlistentry><term><parameter>result</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> in which to store the result
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>a</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>b</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-transform-distance" role="function">
<title>cairo_matrix_transform_distance ()</title>
<indexterm zone="cairo-matrix-transform-distance"><primary sortas="matrix_transform_distance">cairo_matrix_transform_distance</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_transform_distance (<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> *dx</parameter>,
<parameter><link linkend="double"><type>double</type></link> *dy</parameter>);</programlisting>
<para>
Transforms the distance vector (<parameter>dx</parameter>,<parameter>dy</parameter>) by <parameter>matrix</parameter>. This is
similar to <link linkend="cairo-matrix-transform-point"><function>cairo_matrix_transform_point()</function></link> except that the translation
components of the transformation are ignored. The calculation of
the returned vector is as follows:
</para>
<para>
<programlisting>
dx2 = dx1 * a + dy1 * c;
dy2 = dx1 * b + dy1 * d;
</programlisting>
</para>
<para>
Affine transformations are position invariant, so the same vector
always transforms to the same vector. If (<parameter>x1</parameter>,<parameter>y1</parameter>) transforms
to (<parameter>x2</parameter>,<parameter>y2</parameter>) then (<parameter>x1</parameter>+<parameter>dx1</parameter>,<parameter>y1</parameter>+<parameter>dy1</parameter>) will transform to
(<parameter>x1</parameter>+<parameter>dx2</parameter>,<parameter>y1</parameter>+<parameter>dy2</parameter>) for all values of <parameter>x1</parameter> and <parameter>x2</parameter>.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>dx</parameter> :</term>
<listitem><simpara>X component of a distance vector. An in/out parameter
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>dy</parameter> :</term>
<listitem><simpara>Y component of a distance vector. An in/out parameter
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2 id="cairo-matrix-transform-point" role="function">
<title>cairo_matrix_transform_point ()</title>
<indexterm zone="cairo-matrix-transform-point"><primary sortas="matrix_transform_point">cairo_matrix_transform_point</primary></indexterm>
<programlisting><link linkend="void"><returnvalue>void</returnvalue></link> cairo_matrix_transform_point (<parameter>const <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link> *matrix</parameter>,
<parameter><link linkend="double"><type>double</type></link> *x</parameter>,
<parameter><link linkend="double"><type>double</type></link> *y</parameter>);</programlisting>
<para>
Transforms the point (<parameter>x</parameter>, <parameter>y</parameter>) by <parameter>matrix</parameter>.
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>a <link linkend="cairo-matrix-t"><type>cairo_matrix_t</type></link>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>x</parameter> :</term>
<listitem><simpara>X position. An in/out parameter
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>y</parameter> :</term>
<listitem><simpara>Y position. An in/out parameter
</simpara></listitem></varlistentry>
</variablelist></refsect2>
</refsect1>
<refsect1 id="cairo-cairo-matrix-t.see-also">
<title>See Also</title>
<link linkend="cairo-t"><type>cairo_t</type></link>
</refsect1>
</refentry>