Transformation matrix - Revision history

Vegard: /* See also */ add link

2020-02-25T14:51:39Z

Vegard: add link

2020-01-22T18:07:49Z

add link

← Older revision		Revision as of 18:07, 22 January 2020
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	Source: https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml		Source: https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

			== See also ==

			* https://math.stackexchange.com/questions/237369/given-this-transformation-matrix-how-do-i-decompose-it-into-translation-rotati/417813

	[[Category:Graphics programming]]		[[Category:Graphics programming]]

Vegard: new page

2020-01-17T09:00:12Z

new page

New page

== 2D ==

=== Rotation ===

<math>
\begin{pmatrix}
\cos \theta & -\sin \theta & 0 \\
\sin \theta & \cos \theta & 0 \\
0 & 0 & 1
\end{pmatrix}
</math>

Source: https://en.wikipedia.org/wiki/Rotation_matrix

== 3D ==

=== Translation ===

<math>
\begin{pmatrix}
1 & 0 & 0 & x \\
0 & 1 & 0 & y \\
0 & 0 & 1 & z \\
0 & 0 & 0 & 1
\end{pmatrix}
</math>

Source: https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glTranslate.xml

=== Scaling ===

<math>
\begin{pmatrix}
x & 0 & 0 & 0 \\
0 & y & 0 & 0 \\
0 & 0 & z & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
</math>

Source: https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glScale.xml

=== Rotation ===

<math>
\begin{pmatrix}
x^2 c' + c & xy c' - zs & xz c' + ys & 0 \\
yx c' + zs & y^2 c' + c & yz c' - xs & 0 \\
xz c' - ys & yz c' + xs & z^2 c' + c & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
</math>

with

<math>
\begin{align}
c &= \cos(\mathit{angle}) \\
c' &= 1 - c \\
s &= \sin(\mathit{angle})
\end{align}
</math>

Source: https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glRotate.xml

[[Category:Graphics programming]]
[[Category:Linear algebra]]

← Older revision		Revision as of 14:51, 25 February 2020
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	== See also ==		== See also ==

			* [[Homogeneous coordinates]]
	* https://math.stackexchange.com/questions/237369/given-this-transformation-matrix-how-do-i-decompose-it-into-translation-rotati/417813		* https://math.stackexchange.com/questions/237369/given-this-transformation-matrix-how-do-i-decompose-it-into-translation-rotati/417813