tuliskan rumus Transformasi Geometriberikut ini-translasi-refleksi-rotasi-dilatasi.... Question from @Alam2010

Alam2010 @Alam2010

August 2022 1 10 Report

tuliskan rumus Transformasi Geometri
berikut ini

-translasi
-refleksi
-rotasi
-dilatasi

ridhovictor4

Jawab:

Penjelasan dengan langkah-langkah:

- Translasi:

$\bold{T}(T_x,T_y) = \left[\begin{array}{ccc}1&0&T_x\\0&1&T_y\\0&0&1\end{array}\right]$

- Rotasi :

$\bold{R}(\theta) = \left[\begin{array}{ccc}\cos(\theta)&-\sin(\theta)&0\\\sin(\theta)&\cos(\theta)&0\\0&0&1\end{array}\right]$

- Rotasi dengan pusat (a,b):

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- Refleksi

(terhadap garis y = tan(Ψ)x , tan(Ψ) = m = gradien garis refleksi) :

$\bold{Rf}(\tan(\psi)x) = \left[\begin{array}{ccc}\cos(\psi)&-\sin(\psi)&0\\\sin(\psi)&\cos(\psi)&0\\0&0&1\end{array}\right]$

- Refleksi (terhadap garis y = tan(Ψ)x + c) :

$\bold{Rf}(\tan(\psi)x+c) = \bold{T}(0,c)\cdot\bold{R}(\psi)\cdot\bold{T}(0,-c)\\\bold{Rf}(\tan(\psi)x+c) = \left[\begin{array}{ccc}1&0&0\\0&1&c\\0&0&1\end{array}\right]\left[\begin{array}{ccc}\cos(\psi)&-\sin(\psi)&0\\\sin(\psi)&\cos(\psi)&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&-c\\0&0&1\end{array}\right]$

$\bold{R}(\theta,(a,b)) = \left[\begin{array}{ccc}\cos(\psi)&-\sin(\psi)&c\sin(\psi)\\\sin(\theta)&\cos(\theta)&c(1-\cos(\psi))\\0&0&1\end{array}\right]$

- Dilatasi :

$\bold{S}(k) = \left[\begin{array}{ccc}k&0&0\\0&k&0\\0&0&1\end{array}\right]$

- Dilatasi dengan pusat (a,b):

$\bold{S}(k,(a,b)) = \bold{T}(a,b)\cdot\bold{S}(k)\cdot\bold{T}(-a,-b)\\\bold{S}(k,(a,b)) =\left[\begin{array}{ccc}1&0&a\\0&1&b\\0&0&1\end{array}\right]\left[\begin{array}{ccc}k&0&0\\0&k&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&-a\\0&1&-b\\0&0&1\end{array}\right]$
$\bold{S}(k,(a,b)) =\left[\begin{array}{ccc}k&0&a(1-k)\\0&k&b(1-k)\\0&0&1\end{array}\right]$