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[Kame]

Kame

Calculating a point around a circle

If I have the bottom half of a semicircle, and know the x value of a point, how would I calculate the y value so that the point rests directly on the edge of the circle?

[Atrius]

Atrius

Re: Calculating a point around a circle

Basic functions for calculating points around a circle based on angle.  (r = radius of circle)
x=r*cos(a)
y=r*sin(a)


So first well take the function for finding x, based on angle, and invert it to find the angle based on x.
x=r*cos(a)

x/r=cos(a)

arccos(x/r)=a

Now stick that into the function for finding y as the value for angle.

y=r*sin(arccos(x/r))


The x, and y values you use should assume that the center of the circle is at 0, 0.  If not subtract the centers x from your x value before calculating, and add the centers y to the result.  You'll probably also have to make the result negative first.  It's been a while since I've actually used these calculations, so I apologize in advance if I got something wrong.

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[PoliteProgrammer]

PoliteProgrammer

Re: Calculating a point around a circle

It's much simpler than Atrius suggested (although it is a perfectly correct method)

The general equation of a circle on the origin(0,0) is
x^2 + y^2 = r^2 (Pythagorean Theorem)
Where r is the radius of the circle.

If you know x and r, you can find y by rearranging:

y = sqrt(r^2 - x^2)

Simple. Oh, but since the value for y comes out positive from this formula, you need to make it negative in order to be in the bottom semicircle. This should be easy in whatever programming language you are using.

e.g.

 y = sqrt(r^2 - x^2)
 y = -y


Oh, and if you need the appropriate equations for a circle that is not centered on the origin, it's

(x - a)^2 + (y - b)^2 = r^2  As Atrius said.

Therefore y = sqrt( r^2 - (x - a)^2 ) + b

I hope that helps.