Drawing circles in OpenGL

[anneranch]

This is a math problem, not OpenGL problem , but I cannot find a solution.
My task is to draw series of circles - actually polar coordinates.

I start with these basic equations / parameters
radius = 1 / (R + 1);
center = R / (R + 1);
where R goes from 0.1 to 1.0 ( normalized coordinates )

This draws 10 circles of normalized coordinates of diameters of 1 to 0.5 - each circle with different diameter and center , and
passing thru coordinates of x = 1 and y = 0.

I can "scale up " by factor of 0.5 and build higher value / scale polar coordinates grid. No problem.

My task is to "downscale" and build another set of polar coordinates for R from 0.01 to 0.1 of "basic" parameters.

If there a way to set / modify the "basic" equations to accomplish that?

 

[LCKurtz]

What you want isn't entirely clear to me, but, here goes. First, notice that

[MATH]\frac R {R+1} = \frac {(R+1) - 1}{R+1} = 1 - \frac {1}{R+1}[/MATH]
so you are centering the circle at [MATH]1 - \frac {1}{R+1}[/MATH] with a radius of [MATH]\frac 1 {R+1}[/MATH].

To make it even simpler to understand, let's let [MATH]\lambda = \frac 1 {R+1}[/MATH] so you have circles of radius [MATH]\lambda[/MATH] centered at [MATH]x= 1-\lambda[/MATH]. You can make the circles as large or small as you like choosing [MATH]0 < \lambda <\infty[/MATH] with the corresponding values of [MATH]R[/MATH]. You can center them on the other side by centering at [MATH]1+\lambda[/MATH].

Not sure whether I've answered your question or not.

 

[anneranch]

I do not get your logic.
The variable is R applied to equations , them determining both diameter and center.
How does replacing the 1/R+1 with another variable / symbol improves the math?
And just the math, never mind " the solution " ? Just asking.

 

[LCKurtz]

I do not get your logic.
The variable is R applied to equations , them determining both diameter and center.

What are you talking about above? What equations? What does it have to do with polar coordinates? We aren't mind readers here.

How does replacing the 1/(R+1) with another variable / symbol improves the math?

It makes it clear to me that the circles pass though [MATH](1,0)[/MATH], which your original description: "circles of radius [MATH]\frac 1 {R+1}[/MATH] with centers of [MATH]\frac R {R+1}[/MATH]" doesn't make clear.

And just the math, never mind " the solution " ? Just asking.

The solution to what? State your problem clearly and maybe we can help you.

 

[anneranch]

NOW DIFFICULT IT IS TO JUST ANSWER?

"How does replacing the 1/R+1 with another variable / symbol improves the math?"

Let me help you , just fill in the blanks:
"Replacing 1/R+1 with another variable / symbol improves the math because .......


If you do not understand the question, spare me of your commentaries.
I will not get bent out of shape likes you if you do not have an answer, but YOUR rhetoric / EDITORIALS are INSULTING AND UNNECESSARY .
If you do not understand the question, spare me of your commentaries.

PLEASE STOP.

 

[tkhunny]

1) If you wish to abuse those who wish to help you, you should probably consider paying for it - a lot - unlikely to be enough, whatever it is.

2) If you wish to learn how to solve your task, you should answer the questions presented and release your arrogance.

3) So far, the only things on this thread that are "insulting and unnecessary" are comments from you.

4) If your problem is ill-defined, one would expect questions on the definitions, rather than feeling that the cowering masses will respond to your demands without delay.

5) You have specified a parameter, R, with multiple values. Okay.

6) From R, you have calculated a radius for each value of R. Okay.

7) From R, you have calculated a number that you are calling the "Center". Unfortunately, a Center requires two pieces. You'll have to get the other piece from somewhere. Is this value you have specified an x-coordinate, a y-coordinate, a distance from the Origin, or a positive angle in the normal sense of polar coordinates? It appears to be the third options. Okay, so centers are on the positive x-axis. You could have stated that clearly.

8) You have specified that each circle must pass through (x,y) = (1,0). This is odd, because you stated that you are in polar coordinates. Please clarify your intent.

9) You started out okay with 1/(R+1). Did your misplaced consternation cause you to forget the order of operations as you went on raging? Please be more careful.

10) It is not clear at all what you mean by "scale up" or "scale down". Rather than shouting it more loudly, hoping it will magically make sense because of the majesty of your voice, why not try explaining it and offering examples or definitions?

11) You may wish to consider the first response more carefully, rather than your offhanded dismissal.

12) So far, you have not exhibited behavior mandated by the site participation rules. Please consider this one of the two warnings you will receive. Please read and heed the rules and see if we can learn something.

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