How do I calculate a point on a circle’s circumference?

Question

How can the following function be implemented in various languages?

Calculate the (x,y) point on the circumference of a circle, given input values of:

• Radius
• Angle
• Origin (optional parameter, if supported by the language)

Answer 1

Here is my implementation in C#:

    public static PointF PointOnCircle(float radius, float angleInDegrees, PointF origin)
    {
        // Convert from degrees to radians via multiplication by PI/180        
        float x = (float)(radius * Math.Cos(angleInDegrees * Math.PI / 180F)) + origin.X;
        float y = (float)(radius * Math.Sin(angleInDegrees * Math.PI / 180F)) + origin.Y;

        return new PointF(x, y);
    }

Answer 2

The parametric equation for a circle is

x = cx + r * cos(a)
y = cy + r * sin(a)

Where r is the radius, cx,cy the origin, and a the angle from 0..2PI radians or 0..360 degrees.

That's pretty easy to adapt into any language with basic trig functions.

Answer 3

Who needs trig when you have complex numbers:

#include <complex.h>
#include <math.h>

#define PI   3.14159265358979323846

typedef complex double Point;

Point point_on_circle ( double radius, double angle_in_degrees, Point centre )
{
    return centre + radius * cexp ( PI * I * ( angle_in_degrees  / 180.0 ) );
}