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<?xml version="1.0" encoding="UTF-8" ?>
<!DOCTYPE refentry PUBLIC "-//OASIS//DTD DocBook XML V4.1.2//EN"
"http://www.oasis-open.org/docbook/xml/4.1.2/docbookx.dtd">
<refentry id="libgimpmath-GimpMatrix">
<refmeta>
<refentrytitle>GimpMatrix</refentrytitle>
<manvolnum>3</manvolnum>
<refmiscinfo>LIBGIMPMATH Library</refmiscinfo>
</refmeta>
<refnamediv>
<refname>GimpMatrix</refname><refpurpose>Utilities to set up and manipulate 3x3 transformation matrices.</refpurpose>
</refnamediv>
<refsynopsisdiv><title>Synopsis</title>
<synopsis>
<link linkend="GimpMatrix2">GimpMatrix2</link>;
<link linkend="GimpMatrix3">GimpMatrix3</link>;
<link linkend="GimpMatrix4">GimpMatrix4</link>;
<link linkend="void">void</link> <link linkend="gimp-matrix2-identity">gimp_matrix2_identity</link> (<link linkend="GimpMatrix2">GimpMatrix2</link> *matrix);
<link linkend="void">void</link> <link linkend="gimp-matrix2-mult">gimp_matrix2_mult</link> (const <link linkend="GimpMatrix2">GimpMatrix2</link> *matrix1,
<link linkend="GimpMatrix2">GimpMatrix2</link> *matrix2);
<link linkend="void">void</link> <link linkend="gimp-matrix3-identity">gimp_matrix3_identity</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="void">void</link> <link linkend="gimp-matrix3-mult">gimp_matrix3_mult</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix1,
<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix2);
<link linkend="void">void</link> <link linkend="gimp-matrix3-translate">gimp_matrix3_translate</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y);
<link linkend="void">void</link> <link linkend="gimp-matrix3-scale">gimp_matrix3_scale</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y);
<link linkend="void">void</link> <link linkend="gimp-matrix3-rotate">gimp_matrix3_rotate</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> theta);
<link linkend="void">void</link> <link linkend="gimp-matrix3-xshear">gimp_matrix3_xshear</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> amount);
<link linkend="void">void</link> <link linkend="gimp-matrix3-yshear">gimp_matrix3_yshear</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> amount);
<link linkend="void">void</link> <link linkend="gimp-matrix3-affine">gimp_matrix3_affine</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> a,
<link linkend="gdouble">gdouble</link> b,
<link linkend="gdouble">gdouble</link> c,
<link linkend="gdouble">gdouble</link> d,
<link linkend="gdouble">gdouble</link> e,
<link linkend="gdouble">gdouble</link> f);
<link linkend="void">void</link> <link linkend="gimp-matrix3-transform-point">gimp_matrix3_transform_point</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y,
<link linkend="gdouble">gdouble</link> *newx,
<link linkend="gdouble">gdouble</link> *newy);
<link linkend="gdouble">gdouble</link> <link linkend="gimp-matrix3-determinant">gimp_matrix3_determinant</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="void">void</link> <link linkend="gimp-matrix3-invert">gimp_matrix3_invert</link> (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="gboolean">gboolean</link> <link linkend="gimp-matrix3-is-diagonal">gimp_matrix3_is_diagonal</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="gboolean">gboolean</link> <link linkend="gimp-matrix3-is-identity">gimp_matrix3_is_identity</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="gboolean">gboolean</link> <link linkend="gimp-matrix3-is-simple">gimp_matrix3_is_simple</link> (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);
<link linkend="void">void</link> <link linkend="gimp-matrix4-to-deg">gimp_matrix4_to_deg</link> (const <link linkend="GimpMatrix4">GimpMatrix4</link> *matrix,
<link linkend="gdouble">gdouble</link> *a,
<link linkend="gdouble">gdouble</link> *b,
<link linkend="gdouble">gdouble</link> *c);
</synopsis>
</refsynopsisdiv>
<refsect1>
<title>Description</title>
<para>
When doing image manipulation you will often need 3x3 transformation
matrices that define translation, rotation, scaling, shearing and
arbitrary perspective transformations using a 3x3 matrix. Here you'll
find a set of utility functions to set up those matrices and to perform
basic matrix manipulations and tests.
</para>
</refsect1>
<refsect1>
<title>Details</title>
<refsect2>
<title><anchor id="GimpMatrix2"/>GimpMatrix2</title>
<indexterm><primary>GimpMatrix2</primary></indexterm><programlisting>typedef struct {
gdouble coeff[2][2];
} GimpMatrix2;
</programlisting>
<para>
A two by two matrix.
</para></refsect2>
<refsect2>
<title><anchor id="GimpMatrix3"/>GimpMatrix3</title>
<indexterm><primary>GimpMatrix3</primary></indexterm><programlisting>typedef struct {
gdouble coeff[3][3];
} GimpMatrix3;
</programlisting>
<para>
A three by three matrix.
</para></refsect2>
<refsect2>
<title><anchor id="GimpMatrix4"/>GimpMatrix4</title>
<indexterm><primary>GimpMatrix4</primary></indexterm><programlisting>typedef struct {
gdouble coeff[4][4];
} GimpMatrix4;
</programlisting>
<para>
A four by four matrix.
</para></refsect2>
<refsect2>
<title><anchor id="gimp-matrix2-identity"/>gimp_matrix2_identity ()</title>
<indexterm><primary>gimp_matrix2_identity</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix2_identity (<link linkend="GimpMatrix2">GimpMatrix2</link> *matrix);</programlisting>
<para>
Sets the matrix to the identity matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> A matrix.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix2-mult"/>gimp_matrix2_mult ()</title>
<indexterm><primary>gimp_matrix2_mult</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix2_mult (const <link linkend="GimpMatrix2">GimpMatrix2</link> *matrix1,
<link linkend="GimpMatrix2">GimpMatrix2</link> *matrix2);</programlisting>
<para>
Multiplies two matrices and puts the result into the second one.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix1</parameter> :</term>
<listitem><simpara> The first input matrix.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>matrix2</parameter> :</term>
<listitem><simpara> The second input matrix which will be overwritten by the result.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-identity"/>gimp_matrix3_identity ()</title>
<indexterm><primary>gimp_matrix3_identity</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_identity (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Sets the matrix to the identity matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> A matrix.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-mult"/>gimp_matrix3_mult ()</title>
<indexterm><primary>gimp_matrix3_mult</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_mult (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix1,
<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix2);</programlisting>
<para>
Multiplies two matrices and puts the result into the second one.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix1</parameter> :</term>
<listitem><simpara> The first input matrix.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>matrix2</parameter> :</term>
<listitem><simpara> The second input matrix which will be overwritten by the result.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-translate"/>gimp_matrix3_translate ()</title>
<indexterm><primary>gimp_matrix3_translate</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_translate (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y);</programlisting>
<para>
Translates the matrix by x and y.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be translated.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>x</parameter> :</term>
<listitem><simpara> Translation in X direction.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>y</parameter> :</term>
<listitem><simpara> Translation in Y direction.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-scale"/>gimp_matrix3_scale ()</title>
<indexterm><primary>gimp_matrix3_scale</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_scale (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y);</programlisting>
<para>
Scales the matrix by x and y</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be scaled.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>x</parameter> :</term>
<listitem><simpara> X scale factor.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>y</parameter> :</term>
<listitem><simpara> Y scale factor.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-rotate"/>gimp_matrix3_rotate ()</title>
<indexterm><primary>gimp_matrix3_rotate</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_rotate (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> theta);</programlisting>
<para>
Rotates the matrix by theta degrees.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be rotated.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>theta</parameter> :</term>
<listitem><simpara> The angle of rotation (in radians).
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-xshear"/>gimp_matrix3_xshear ()</title>
<indexterm><primary>gimp_matrix3_xshear</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_xshear (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> amount);</programlisting>
<para>
Shears the matrix in the X direction.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be sheared.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>amount</parameter> :</term>
<listitem><simpara> X shear amount.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-yshear"/>gimp_matrix3_yshear ()</title>
<indexterm><primary>gimp_matrix3_yshear</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_yshear (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> amount);</programlisting>
<para>
Shears the matrix in the Y direction.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be sheared.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>amount</parameter> :</term>
<listitem><simpara> Y shear amount.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-affine"/>gimp_matrix3_affine ()</title>
<indexterm><primary>gimp_matrix3_affine</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_affine (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> a,
<link linkend="gdouble">gdouble</link> b,
<link linkend="gdouble">gdouble</link> c,
<link linkend="gdouble">gdouble</link> d,
<link linkend="gdouble">gdouble</link> e,
<link linkend="gdouble">gdouble</link> f);</programlisting>
<para>
Applies the affine transformation given by six values to <parameter>matrix</parameter>.
The six values form define an affine transformation matrix as
illustrated below:
</para>
<para>
( a c e )
( b d f )
( 0 0 1 )</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The input matrix.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>a</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>b</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>c</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>d</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>e</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>f</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-transform-point"/>gimp_matrix3_transform_point ()</title>
<indexterm><primary>gimp_matrix3_transform_point</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_transform_point (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix,
<link linkend="gdouble">gdouble</link> x,
<link linkend="gdouble">gdouble</link> y,
<link linkend="gdouble">gdouble</link> *newx,
<link linkend="gdouble">gdouble</link> *newy);</programlisting>
<para>
Transforms a point in 2D as specified by the transformation matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The transformation matrix.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>x</parameter> :</term>
<listitem><simpara> The source X coordinate.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>y</parameter> :</term>
<listitem><simpara> The source Y coordinate.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>newx</parameter> :</term>
<listitem><simpara> The transformed X coordinate.
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>newy</parameter> :</term>
<listitem><simpara> The transformed Y coordinate.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-determinant"/>gimp_matrix3_determinant ()</title>
<indexterm><primary>gimp_matrix3_determinant</primary></indexterm><programlisting><link linkend="gdouble">gdouble</link> gimp_matrix3_determinant (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Calculates the determinant of the given matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The input matrix.
</simpara></listitem></varlistentry>
<varlistentry><term><emphasis>Returns</emphasis> :</term><listitem><simpara> The determinant.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-invert"/>gimp_matrix3_invert ()</title>
<indexterm><primary>gimp_matrix3_invert</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix3_invert (<link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Inverts the given matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be inverted.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-is-diagonal"/>gimp_matrix3_is_diagonal ()</title>
<indexterm><primary>gimp_matrix3_is_diagonal</primary></indexterm><programlisting><link linkend="gboolean">gboolean</link> gimp_matrix3_is_diagonal (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Checks if the given matrix is diagonal.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be tested.
</simpara></listitem></varlistentry>
<varlistentry><term><emphasis>Returns</emphasis> :</term><listitem><simpara> TRUE if the matrix is diagonal.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-is-identity"/>gimp_matrix3_is_identity ()</title>
<indexterm><primary>gimp_matrix3_is_identity</primary></indexterm><programlisting><link linkend="gboolean">gboolean</link> gimp_matrix3_is_identity (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Checks if the given matrix is the identity matrix.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be tested.
</simpara></listitem></varlistentry>
<varlistentry><term><emphasis>Returns</emphasis> :</term><listitem><simpara> TRUE if the matrix is the identity matrix.
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix3-is-simple"/>gimp_matrix3_is_simple ()</title>
<indexterm><primary>gimp_matrix3_is_simple</primary></indexterm><programlisting><link linkend="gboolean">gboolean</link> gimp_matrix3_is_simple (const <link linkend="GimpMatrix3">GimpMatrix3</link> *matrix);</programlisting>
<para>
Checks if we'll need to interpolate when applying this matrix as
a transformation.</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara> The matrix that is to be tested.
</simpara></listitem></varlistentry>
<varlistentry><term><emphasis>Returns</emphasis> :</term><listitem><simpara> TRUE if all entries of the upper left 2x2 matrix are either
0 or 1
</simpara></listitem></varlistentry>
</variablelist></refsect2>
<refsect2>
<title><anchor id="gimp-matrix4-to-deg"/>gimp_matrix4_to_deg ()</title>
<indexterm><primary>gimp_matrix4_to_deg</primary></indexterm><programlisting><link linkend="void">void</link> gimp_matrix4_to_deg (const <link linkend="GimpMatrix4">GimpMatrix4</link> *matrix,
<link linkend="gdouble">gdouble</link> *a,
<link linkend="gdouble">gdouble</link> *b,
<link linkend="gdouble">gdouble</link> *c);</programlisting>
<para>
</para>
<para>
</para><variablelist role="params">
<varlistentry><term><parameter>matrix</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>a</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>b</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
<varlistentry><term><parameter>c</parameter> :</term>
<listitem><simpara>
</simpara></listitem></varlistentry>
</variablelist></refsect2>
</refsect1>
<refsect1>
<title>See Also</title>
<para>
<link linkend="GimpVector2"><type>GimpVector2</type></link>
</para>
<para>
<link linkend="GimpVector3"><type>GimpVector3</type></link>
</para>
<para>
<link linkend="GimpVector4"><type>GimpVector4</type></link>
</para>
</refsect1>
</refentry>
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