plot points on circle between 2 points.
Author
Hi guys, I have some code that plots points on a circle:
for (float theta = 0; theta <= 2 * PI; theta += PI / (rRadius * rAccuracy))
{
float x = rRadius * cos(theta);
float y = rRadius * sin(theta);
}
How would I instead plot points between 2 points on circle?
ie I have 2 points on a circle, how do I plot points between these points?
I figure I need to convert these points to theta values (Do you know how to do this) and then use the loop from theta1 to theta2.
thanks!
EDIT: i wrote something wrong, better take a look here.
http://www.teacherschoice.com.au/Maths_Library/Coordinates/polar_-_rectangular_conversion.htm
http://www.teacherschoice.com.au/Maths_Library/Coordinates/polar_-_rectangular_conversion.htm
If you look at your (kneeride's) code snippet posted in the OP, you'll see a conversion from the angle theta to a point (x,y) like so:
x := R * cos( theta )
y := R * sin( theta )
What you want to do is the inverse function, namely convert from a point to an angle. Unfortunately you have a sine _and_ a cosine of the unknown variable theta; but there is a correspondence
tan( theta ) = sin( theta ) / cos( theta )
that can be used to isolate theta.
Since this computation is to be used w/ caution due to its division by zero possibility and its periodicity, your programming API typically offers a function atan2(y,x) that considers these aspects as well.
x := R * cos( theta )
y := R * sin( theta )
What you want to do is the inverse function, namely convert from a point to an angle. Unfortunately you have a sine _and_ a cosine of the unknown variable theta; but there is a correspondence
tan( theta ) = sin( theta ) / cos( theta )
that can be used to isolate theta.
Since this computation is to be used w/ caution due to its division by zero possibility and its periodicity, your programming API typically offers a function atan2(y,x) that considers these aspects as well.
Author
Does this look like I'm on the right track? I found some code deep in my library. it looks similar to what I need. (I however have no idea why y is before x in the parameters)
double x(double y, double x){ if (x > 0) { return atan2(y,x); } else if (x > 0) { return G_PI + atan2(y,x); } else // x == 0 { if (y >= 0) { return G_PI / 2; } else { return -(G_PI / 2); } }}
The atan2 function already does all neccessary case distinctions for you (okay, I don't really know the standard at this point, but AFAIK it does).
However, atan2 returns a value between -pi and +pi, and perhaps you would be more happy w/ values between 0 and 2pi. Then a downstream add-on
would be appropriate.
Besides that there is a typo in your snippet w/ distincting x<0.
However, atan2 returns a value between -pi and +pi, and perhaps you would be more happy w/ values between 0 and 2pi. Then a downstream add-on
if(theta<0) { theta += TWO_PI; }would be appropriate.
Besides that there is a typo in your snippet w/ distincting x<0.
You could also just add PI to all results, and get a range of 0 to 2PI. This changes where 0 radians is (opposite direction) though.
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