Difference between revisions of "ApplyMatrix Command"
From GeoGebra Manual
| Line 4: | Line 4: | ||
* point ''M*P'' (with matrix ''M'') in case M is a 2x2 matrix or | * point ''M*P'' (with matrix ''M'') in case M is a 2x2 matrix or | ||
* point ''project(M*(x(P), y(P), 1))'' where ''project'' is a projection mapping point ''(x,y,z)'' to ''(x/z, y/z)'' in case of 3x3 matrix. | * point ''project(M*(x(P), y(P), 1))'' where ''project'' is a projection mapping point ''(x,y,z)'' to ''(x/z, y/z)'' in case of 3x3 matrix. | ||
| − | |||
:{{example|1=<div> Let ''M={{cos(<math>\frac{π}{2} </math>),-sin(<math>\frac{π}{2} </math>)},{sin(<math>\frac{π}{2} </math>),cos(<math>\frac{π}{2} </math>)}}'' be the transformation matrix and ''u=(2,1)'' a given vector (object). <code><nowiki>ApplyMatrix[M,u]</nowiki></code> yields the 90 degrees rotated (with mathematicaly positiv sense of rotation) vector ''u´=(-1,2)''.</div>}} | :{{example|1=<div> Let ''M={{cos(<math>\frac{π}{2} </math>),-sin(<math>\frac{π}{2} </math>)},{sin(<math>\frac{π}{2} </math>),cos(<math>\frac{π}{2} </math>)}}'' be the transformation matrix and ''u=(2,1)'' a given vector (object). <code><nowiki>ApplyMatrix[M,u]</nowiki></code> yields the 90 degrees rotated (with mathematicaly positiv sense of rotation) vector ''u´=(-1,2)''.</div>}} | ||
| − | |||
:{{note| 1=This command also works for [[Images|images]].}} | :{{note| 1=This command also works for [[Images|images]].}} | ||
Revision as of 15:49, 8 July 2013
- point M*P (with matrix M) in case M is a 2x2 matrix or
- point project(M*(x(P), y(P), 1)) where project is a projection mapping point (x,y,z) to (x/z, y/z) in case of 3x3 matrix.
- Example:Let M={{cos(\frac{π}{2} ),-sin(\frac{π}{2} )},{sin(\frac{π}{2} ),cos(\frac{π}{2} )}} be the transformation matrix and u=(2,1) a given vector (object).
ApplyMatrix[M,u]yields the 90 degrees rotated (with mathematicaly positiv sense of rotation) vector u´=(-1,2).
- Note: This command also works for images.
