Sane

For part of my Graphical User Interface, I require the ability to draw custom circles. What I need to know is, given an X position of the outside curve of a circle, what equation determines the two Y values?

Please pardon my inexperience in high school math, as I'll need to know the complete equation if possible.

Thankyou in advance.


Edit, I made a circle and these are the co-ordinates for the bottom right curve, where x=0 and y=0 at the bottom most point.


But I can't exactly find a simple function out of that, at least by my limited methods of solving for quadratics, etc...

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data

Sane

Oh, that's probably because my X and Y start on the axis of the bottom of the circle, not the radius. As well as I used a very small circle, so the data will not be completely accurate.

Thanks for the answer.

Edit: Okay, so how do I exclude X? To get the equation where I just input X to solve for Y?

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data

EverLearning

If I understand your question, you are looking for equation of a circle, it's:
x^2 + y^2 = r^2 in most common form (0,0) being the center, r -radius.
Solving for y will give you +- value, since f(x) = x^2, f(x) >= 0 for all x.
If the center is shifted from the origin:
(x-a)^2 + (y-b)^2 = r^2
where a and b are (x,y) coordinates of the center of the circle, respectively.

ps: sorry there, firefox acting out on me

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got math? yumm...

"All men by nature desire to know" -Aristotle, Metaphysics

Sane

But I still need an equation where I can just input X and a radius and get a Y? I have no idea how to exclude that equation or use it to my benefits.

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data

EverLearning

It's called "solving" for y:

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

of course, you don't say what is given in the problem so I assume a, b, r are known.

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got math? yumm...

"All men by nature desire to know" -Aristotle, Metaphysics

Sane

I know, I don't know how to solve for stuff. Hehehe.

I'm grade 9, and inexperienced in certain areas of higher level math.

Thanks a lot bud.

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data

EverLearning

Welcome.
Yeah, you have not seen higher level math yet
An important fact which is ignored a lot of times is that, from purely mathematical standpoint, equation for the circle is not a function, since (in simple terms) it produces 2 values ( + and - ) of y for single x.

__________________
got math? yumm...

"All men by nature desire to know" -Aristotle, Metaphysics

Sane

Well actually I have seen higher level math. I've been taking Calculus and Grade 13 Probability for the past year. However my education has been purely general, so my coverage is very limited.

With your equation, oddly enough from a set of x values, keeping a, b, and r consistent doesn't change the y value. I'm sure there is nothing wrong with my program. But it's very strange...

I'd show you the program and output, but it's on my laptop.

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data

EverLearning

*chuckle-chuckle* nevermind *chuckle* solving for unknown variables is 7th grade algebra, but that's besides the point...

No it does not make sense, because x is changing, you cannot get the same value unless it's an equation of a horizontal line, which it is not. I don't know the language you are using or whatever, but I know in C <math.h> it does not account for negative values, i.e. it is always single absolute value. In addition it depends on the data types you are using, int truncates decimals and if you take x(i) very close to each other, y will not appear to change.

copy-paste maybe? or at least input-output? if you are interested enough, that is. And perhaps describe precisely what is given, seemingly unrelated information may happen to be useful.

__________________
got math? yumm...

"All men by nature desire to know" -Aristotle, Metaphysics

Sane

I didn't think solving that kind of equation was grade 7. I guess I assumed it would be the same kind of solving of ax^2 + bx + c = 0, to, x = -b+-((b^2-4ac)^0.5/2a). Because I know for a fact that isn't grade 7. Well I just need to prove to myself that my first impression on the equation was false:

(x-a)^2 + (y-b)^2 = r^2
(x-a)(x-a) + (y-b)(y-b) = r^2
x^2 + (x)(-a) + (-a)(x) + a^2 + y^2 + (y)(-b) + (-b)(y) + b^2 = r^2
x^2 + y^2 + a^2 + b^2 + (x)(-a)^2 + (y)(-b)^2 = r^2
...err

I don't know what kind of freaky math they taught you in grade 7, but damn it must be working...! o_o We won't learn this until grade 11.

Anyways. Yes, even when I change X, it doesn't consider it in the equation for some reason. I just get like 3.003450100000^e032 or something. I'm using Python.

And how am I supposed to copy paste it if I did it on my wireless laptop? .....................

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Waterloo's Canadian Computing Competition (CCC) - Stage 2 Problems, Solutions, and Test Data