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Geodézia I. - NymE GEO portál

Geodézia I. - NymE GEO portál

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Síkbeli koordináta transzformációk - hasonlósági transzformáció-<br />

⎡Y⎤<br />

⎢ ⎥<br />

⎣X⎦<br />

=<br />

⎡cosα<br />

s ⋅ ⎢<br />

⎣ sinα<br />

− sinα<br />

cosα<br />

⎤<br />

⎥ ⋅<br />

⎦<br />

⎡Y'<br />

⎤<br />

⎢ ⎥<br />

⎣X'<br />

⎦<br />

⇒<br />

Y<br />

=<br />

s ⋅R<br />

⋅ Y'<br />

Forgató mátrix tulajdonságai:<br />

1.<br />

R<br />

=<br />

cosα<br />

− sinα<br />

2<br />

= cosα ⋅cosα −<br />

sinα<br />

cosα<br />

2<br />

( − sinα) ⋅ sinα = cos α + sin α = 1<br />

− −1<br />

T ⎡ cosα<br />

sinα<br />

⎤<br />

⇒ R = R = ⎢<br />

⎥<br />

⎣−<br />

sinα<br />

cosα<br />

⎦<br />

R = R<br />

1 T<br />

2.<br />

12

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