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Thread: help with points on a circle

  1. #1
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    help with points on a circle

    If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?


    thanks
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  2. #2
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    Re: help with points on a circle

    As you are seeking a pair of co-ordinates $\displaystyle \left(x_2,\;y_2\right)$

    you could set up a pair of equations in 2 unknowns.

    If the circle centre is the origin, then

    $\displaystyle \left(x_2\right)^2+\left(y_2 \right)^2=\left(x_1 \right)^2+\left(y_1 \right)^2=r^2$

    where the other co-ordinates are known.

    Then the area of the triangle between the origin and the 2 points is

    $\displaystyle 0.5r^2sin\theta$

    and so, your 2nd equation is, using the area of a triangle for which one vertex is the origin

    $\displaystyle 0.5r^2sin\theta=0.5|x_1y_2-x_2y_1|$

    However, a trigonometric solution will be much simpler.

    If you label the acute angle between the negative part of the x-axis, the origin and the red dot "A",
    your given angle "B",
    and the obtuse angle between the positive part of the x-axis and the blue dot "C",
    then use the given co-ordinates to calculate the circle radius and the angle "A",
    then calculate "C" and use

    $\displaystyle x=rcosC,\;\;y=rsinC$
    Last edited by Archie Meade; Jul 5th 2011 at 04:07 PM.
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  3. #3
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    Re: help with points on a circle

    Quote Originally Posted by Sneaky View Post
    If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?


    thanks
    p-radius(not x, for this matter)

    x=pcos (a)
    y=psin(a)

    you have red point, (x1,y1) put it above, find angle a.

    blue point is:

    x=pcos (a-b)
    y=psin(a-b)

    b is your rotation angle.

    I think that would work...
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  4. #4
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    Re: help with points on a circle

    Quote Originally Posted by Sneaky View Post
    If I know a coordinate of a point (red dot on image) of a circle with radius x and i want to rotate it y degrees to the right, how do I get the coordinate of the new point (blue dot on image) ?
    Let's change some of the notation here. Say that the the coordinates of the red point are $\displaystyle (x,y)$ then the coordinates of the blue point $\displaystyle \left( {x',y'} \right)$ can be found using:
    $\displaystyle \begin{array}{*{20}c}{x' = x\cos ( - \phi ) - y\sin ( - \phi )} \\ {y' = x\sin ( - \phi ) + y\cos ( - \phi )} \\ \end{array} $

    NOTE. I have changed the notation. $\displaystyle \phi$ is the angle you have called $\displaystyle y$. Also note that you said that you know $\displaystyle \color{red}(x,y)$
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