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How to draw anti-aliased circle in OpenGL?

My math teacher won't let us draw the unit circle on our tests anymore!?

  • He said that we can't look at a unit circle on our test, because that means we don't really know it, and we need to know everything by memory at the snap of a finger, that it will make us understand everything better. But I don't know how to think of the values if I don't have the circle in front of me. Will not drawing the circle really help us at all? It just seems impossible and like a burden and an excuse for our teacher to make us suffer.

  • Answer:

    I find memorizing is not a good idea in math. Now I don't mean you shouldn't ever memorize anything. Certain things yes. Many things I think you should practice enough that its drilled into your memory. If you need to draw a unit circle I think you should be allowed to draw a unit circle...

Elise at Yahoo! Answers Visit the source

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You can always just draw it on your test, but other than that, you just have to memorize it. Mostly, all you have to do is memorize the first quadrant, since the number are the same throughout the rest of the quadrant. Remember, on the unit circle, the x-axis is cosine, and the y is sine. Tangent is x/y. In my opinion, drawing the circle does help, it makes it easier to see where the degrees and coordinates go, but I don't think it's necessary.

Lilli

maths* just tell her you love him then kill him

DobbySalone

If you can draw the circle from memory, I don't see why he can't let you draw it.

crazydave

hey, I know it sounds really complicated, but it's actually really simple to remember the unit circle values. that's because your value is going to be either 30, 45, or 60 degrees--even if the value you are given isn't actually one of those.so all you really need to remember are the x/y values for those three numbers! say on the test he wants you to figure out the ordered pair (cos and sin) for 135 degrees. all you have to do is think of which of the four points on the graph (90, 180, 270, or 360 degrees) is this number closest to? 135 degrees is closest to 180 degrees. Then, figure out the positive difference from its closest point. 180-135=45, so you're looking at a 45 degree difference, hence a 45 degree angle. now, just think of what x and y values 45 degrees possesses. an easy way to remember is to think of 30, 45, 60 counting upward. their x values count consecutively down under square signs from 3 to 1, all of them over 2. so √3/2, √2/2, and √1/2 (which is the same as 1/2), respectively. Now that you have the x value (cos), the y value is just the opposite one, but of course for 45 degrees, both the x and y values are identical. so your ordered pair is (-√2/2, √2/2) keeping in mind where 135 degrees is on the graph (in quadrant 2) so the x value must be negative. that is pretty much the only tricky part. hope that helps and now you shouldn't have to memorize everything! :-)

<<white_roses>>

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