Difference between revisions of "Scaling"
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\end{array}\right] | \end{array}\right] | ||
</math> | </math> | ||
− | + | The computation of scaling looks as follows in component notation:<br/> | |
:<math> | :<math> | ||
\vec{\mathbf{q}}_1=\mathbf{T}_s\cdot\vec{\mathbf{q}}_0= | \vec{\mathbf{q}}_1=\mathbf{T}_s\cdot\vec{\mathbf{q}}_0= | ||
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\end{array}\right] | \end{array}\right] | ||
</math> | </math> | ||
− | Several different cases can be considered:<br/> | + | So the values <math>a</math> and <math>d</math> act as factors for the x- and the y-component of the vector. Several different cases <math>a</math> and <math>d</math> can be considered, for example:<br/> |
:<table> | :<table> |
Revision as of 16:13, 27 May 2014
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Scaling shifts coordinates similar to translation. The difference is, that translation is independent of the current coordinates. Scaling however shifts the coordinates depending on the current values. So the same trnasformation matrix has various effects on different vectors.
For the sake of simplicity scaling is explained for two-dimensional space. But the behavior of the parameters is the same for an additional third dimension. Scaling is achieved by modifying the components and on the first diagonal of the transformation matrix , while the other components are zero:
The computation of scaling looks as follows in component notation:
So the values and act as factors for the x- and the y-component of the vector. Several different cases and can be considered, for example:
▪ is the identity matrix → no effect
▪ x-component is scaled up → vector shifted to positive x-direction