Difference between revisions of "Translation"
From Robotics
Line 5: | Line 5: | ||
:<math> | :<math> | ||
\vec{\mathbf{q}}_1=\vec{\mathbf{q}}_0+\vec{\mathbf{p}} | \vec{\mathbf{q}}_1=\vec{\mathbf{q}}_0+\vec{\mathbf{p}} | ||
+ | </math> | ||
+ | Considering the particular components of the vectors, it 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]]. |
Revision as of 10:25, 27 May 2014
← 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:
Considering the particular components of the vectors, it looks as follows:
For further information about vector addition and examples, please have a look at the article about simple arithmetic vector operations.