Difference between revisions of "Translation"
From Robotics
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[[File:translation1.png|right|250px]] | [[File:translation1.png|right|250px]] | ||
− | Translation is the easiest kind of transformation. Translating a point <math> | + | Translation is the easiest kind of transformation. Translating a point <math>q_0</math> means that it is shifted by a translation vector. So the translation vector <math>\vec{\mathbf{p}}</math> is added to the position vector <math>\vec{\mathbf{q}}_0</math> of <math>q_0</math>. The position vector <math>\vec{\mathbf{q}}_1</math> of the resulting transformed point <math>q_1</math> is calculated as follows:<br/> |
:<math> | :<math> | ||
− | \vec{\mathbf{ | + | \vec{\mathbf{q}}_1=\vec{\mathbf{q}}_0+\vec{\mathbf{p}} |
+ | </math> | ||
+ | The figure on the right shows an example in two-dimensional space. In robotics usually three dimensions are regarded. Considering the particular components of the vectors, a translation looks as follows:<br/> | ||
+ | :<math> | ||
+ | \left[\begin{array}{c} | ||
+ | x_1\\ | ||
+ | y_1\\ | ||
+ | z_1 | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{c} | ||
+ | x_0\\ | ||
+ | y_0\\ | ||
+ | z_0 | ||
+ | \end{array}\right]+ | ||
+ | \left[\begin{array}{c} | ||
+ | p_x\\ | ||
+ | p_y\\ | ||
+ | p_z | ||
+ | \end{array}\right]= | ||
+ | \left[\begin{array}{c} | ||
+ | x_0+p_x\\ | ||
+ | y_0+p_y\\ | ||
+ | z_0+p_z | ||
+ | \end{array}\right] | ||
</math> | </math> | ||
For further information about vector addition and examples, please have a look at the article about [[Simple arithmetic operations|simple arithmetic vector operations]]. | For further information about vector addition and examples, please have a look at the article about [[Simple arithmetic operations|simple arithmetic vector operations]]. | ||
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[[Category:Article]] | [[Category:Article]] | ||
[[Category:Transformations]] | [[Category:Transformations]] |
Latest revision as of 17:31, 24 November 2017
← Back: Transformations | Overview: Transformations | Next: Rotation → |
Translation is the easiest kind of transformation. Translating a point means that it is shifted by a translation vector. So the translation vector is added to the position vector of . The position vector of the resulting transformed point is calculated as follows:
The figure on the right shows an example in two-dimensional space. In robotics usually three dimensions are regarded. Considering the particular components of the vectors, a translation looks as follows:
For further information about vector addition and examples, please have a look at the article about simple arithmetic vector operations.