Difference between revisions of "ApplyMatrix Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|vector-matrix}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|vector-matrix}} | ||
| − | ; ApplyMatrix( < | + | ; ApplyMatrix( <[[Matrices|Matrix]]>, <[[Geometric Objects|Object]]> ): Transforms the object ''O'' so that point ''P'' of ''O'' is mapped to: |
* point ''M*P'', if ''P'' is a ''2D'' point and ''M'' is a 2 x 2 matrix | * point ''M*P'', if ''P'' is a ''2D'' point and ''M'' is a 2 x 2 matrix | ||
:{{example|1= Let <code>M={{cos(π/2),-sin(π/2)}, {sin(π/2), cos(π/2)}}</code> be the transformation matrix and <code>u = (2,1)</code> a given vector (object). <code>ApplyMatrix(M,u)</code> yields the vector ''u'=(-1,2)'', i.e. the result of a mathematically positive rotation by 90° of vector ''u''.}} | :{{example|1= Let <code>M={{cos(π/2),-sin(π/2)}, {sin(π/2), cos(π/2)}}</code> be the transformation matrix and <code>u = (2,1)</code> a given vector (object). <code>ApplyMatrix(M,u)</code> yields the vector ''u'=(-1,2)'', i.e. the result of a mathematically positive rotation by 90° of vector ''u''.}} | ||
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* point ''M*P'', if ''P'' is a ''3D'' point and ''M'' a 3 x 3 matrix | * point ''M*P'', if ''P'' is a ''3D'' point and ''M'' a 3 x 3 matrix | ||
* point ''N*P'', if ''P'' is a ''3D'' point and ''M'' a 2 x 2 matrix: the matrix ''N'' is the ''completion or order 3'' of ''M'': given ''M'' = <math>\begin{pmatrix}a&b\\ c&d \end{pmatrix}</math> then ''N'' = <math>\begin{pmatrix}a&b&0\\ c&d&0\\0&0&1 \end{pmatrix}</math> | * point ''N*P'', if ''P'' is a ''3D'' point and ''M'' a 2 x 2 matrix: the matrix ''N'' is the ''completion or order 3'' of ''M'': given ''M'' = <math>\begin{pmatrix}a&b\\ c&d \end{pmatrix}</math> then ''N'' = <math>\begin{pmatrix}a&b&0\\ c&d&0\\0&0&1 \end{pmatrix}</math> | ||
| − | :{{note| 1=This command also works | + | :{{note| 1=This command also works with quadrics and [[Images|images]]: it will return "undefined" when the determinant of the transformation matrix is 0.}} |
Latest revision as of 14:52, 19 June 2023
- point M*P, if P is a 2D point and M is a 2 x 2 matrix
- Example: Let
M={{cos(π/2),-sin(π/2)}, {sin(π/2), cos(π/2)}}be the transformation matrix andu = (2,1)a given vector (object).ApplyMatrix(M,u)yields the vector u'=(-1,2), i.e. the result of a mathematically positive rotation by 90° of vector u.
- point project(M*(x(P), y(P), 1)), if P is a 2D point and M a 3 x 3 matrix: project is a projection, mapping point (x, y, z) to (x/z, y/z).
- Example: Let
M={{1,1,0},{0,1,1},{1,0,1}}be a matrix andu=(2,1)a given vector.ApplyMatrix(M,u)yields vector u'=(1,0.67). In effect \begin{pmatrix}1&1&0\\ 0&1&1\\1&0&1 \end{pmatrix} \begin{pmatrix}2\\ 1\\1 \end{pmatrix} = \begin{pmatrix}3\\ 2\\3 \end{pmatrix}, and (3/3 = 1, 2/3 ≈ 0.67) (rounding to 2 decimal places)
- point M*P, if P is a 3D point and M a 3 x 3 matrix
- point N*P, if P is a 3D point and M a 2 x 2 matrix: the matrix N is the completion or order 3 of M: given M = \begin{pmatrix}a&b\\ c&d \end{pmatrix} then N = \begin{pmatrix}a&b&0\\ c&d&0\\0&0&1 \end{pmatrix}
- Note: This command also works with quadrics and images: it will return "undefined" when the determinant of the transformation matrix is 0.
