Difference between revisions of "Transformations"
From Robotics
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{{Navigation|before=[[Adjugate Formula]]|overview=[[Transformations]]|next=[[Translation]]}} | {{Navigation|before=[[Adjugate Formula]]|overview=[[Transformations]]|next=[[Translation]]}} | ||
| − | In this article general transformations used in the context of robotics and the underlying mathematics are described. The different types of transformations are presented in the following subarticles: | + | In this article general transformations used in the context of robotics and the underlying mathematics are described. All types of transformations can be achieved by [[Multiplication of matrices|matrix multiplication]]. Basis is at first the multiplication of a vector with the respective identity matrix. The identity matrix corresponds to an empty transformation. So a multiplication with an identity matrix results in the original vector, for example in two-dimensional space:<br/> |
| + | :<math> | ||
| + | \vec{\mathbf{p}}_1=\mathbf{I}_2\cdot\vec{\mathbf{p}}_0= | ||
| + | \left[\begin{array}{cc} | ||
| + | 1&0\\ | ||
| + | 0&1 | ||
| + | \end{array}\right] | ||
| + | \cdot | ||
| + | \left[\begin{array}{c} | ||
| + | x_0\\ | ||
| + | y_0 | ||
| + | \end{array}\right] | ||
| + | </math> | ||
| + | |||
| + | The different types of transformations are presented in the following subarticles: | ||
# [[Translation]] | # [[Translation]] | ||
Revision as of 13:59, 26 May 2014
| ← Back: Adjugate Formula | Overview: Transformations | Next: Translation → |
In this article general transformations used in the context of robotics and the underlying mathematics are described. All types of transformations can be achieved by matrix multiplication. Basis is at first the multiplication of a vector with the respective identity matrix. The identity matrix corresponds to an empty transformation. So a multiplication with an identity matrix results in the original vector, for example in two-dimensional space:
![\vec{\mathbf{p}}_1=\mathbf{I}_2\cdot\vec{\mathbf{p}}_0=
\left[\begin{array}{cc}
1&0\\
0&1
\end{array}\right]
\cdot
\left[\begin{array}{c}
x_0\\
y_0
\end{array}\right]](/wiki/robotics/images/math/e/4/e/e4e61043a50198396bfd13ac65639777.png)
The different types of transformations are presented in the following subarticles:
