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  • Calculation example – Similarity Transformation in 2-D space

Calculation example – Similarity Transformation in 2-D space

Written by  TheCivilEngineer.org

Calculate the coordinates of a known point P in an orthogonal coordinate system to a reference orthogonal coordinate system preserving shapes (angles) during transformation, in 2-D space.

 

Calculation example – Similarity Transformation in 2-D space

Known values: Point P coordinates x, y on initial coordinate system, translation vector parameters ΔΧ , ΔΥ between origin centers of the two coordinate systems, scale factor s, rotation angle a.

 

Solution: Point P coordinates X, Y on reference coordinate system.

From the geometry of the scene applies:

X=s⋅(x⋅cosa-y⋅sina)+ΔΧ

Υ=s⋅(x⋅sina+y⋅cosa)+ΔΥ

 

*Rotation angle a is measured counterclockwise from reference coordinate system XY to initial coordinate system xy.

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Read 1272 times Last modified on Tuesday, 13 February 2018 15:47
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