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Thread: Seeking advice on how to convert from Polar to Cartesian with angle offsets.

  1. #1
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    Seeking advice on how to convert from Polar to Cartesian with angle offsets.

    Hi there.


    I am aware of how to convert from Polar to Cartesian. However, the issue I am having is that for my intended application, the angles are offset and inverted to the usual Polar configuration. So 0 degrees begins at the top and runs clockwise around until it reaches 360/0degrees again...
    Seeking advice on how to convert from Polar to Cartesian with angle offsets.-screen-shot-2017-02-25-11.16.49.png
    Would anyone have an idea of a formula which would enable me to calculate the XY coordinates using this circle?

    I see that with polar coordinates, usually 0degrees begins to the right (where 90 degees is located in the above image). And there seems to be two systems, one rotates to 360/degrees anticlockwise and the other goes positive negative either side of 0 degrees. I find this a little confusing.

    Any help would be much appreciated!

    Many thanks!

    Martin
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  2. #2
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    Re: Seeking advice on how to convert from Polar to Cartesian with angle offsets.

    for $\theta$ measured clockwise from $0^\circ$ at the top ...

    $x = r\sin{\theta}$

    $y = r\cos{\theta}$
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    Re: Seeking advice on how to convert from Polar to Cartesian with angle offsets.

    Thanks so much, skeeter! Have you any idea how to do this the other way around now. Like if I have two XY coordinates to start with, how to work it out so that I get Polar coordinates specific to the above circle?

    My workings so far are way off!
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  4. #4
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    Re: Seeking advice on how to convert from Polar to Cartesian with angle offsets.

    $r=\sqrt{x^2+y^2}$

    $\theta = \arctan\left(\dfrac{x}{y}\right)$ for $0 < \theta < 90^\circ$ ... i.e. both x & y positive

    $\theta = 180^\circ + \arctan\left(\dfrac{x}{y}\right)$ for $90^\circ < \theta < 270^\circ$ ... i.e. y negative

    $\theta = 360^\circ + \arctan\left(\dfrac{x}{y}\right)$ for $270^\circ < \theta < 360^\circ$ ... i.e. x negative, y positive
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