android Dividing circle into N equal parts and know the coordinates of each dividing point

Question

I have requirement that a circle should be divided into N equal parts based on number(2,3...n. But I want the coordinates of dividing points.

I have a circle whose centre(x,y) and radius(150) are known.

Question:

Is there any formula which gives me the coordinates of dividing points as shown in figure. Can anyone please tell me the formula. I want to implement it in Java.

Circle image for refrence:

Answer 1

I have already accepted answer... the formula works perfectly. Here is the solution coded in Java. It will help other developers.

    private int x[];  // Class variable
    private int y[];  // Class variable

    private void getPoints(int x0,int y0,int r,int noOfDividingPoints)
    {

        double angle = 0;

        x = new int[noOfDividingPoints];
        y = new int[noOfDividingPoints];

        for(int i = 0 ; i < noOfDividingPoints  ;i++)
        {
            angle = i * (360/noOfDividingPoints);

            x[i] = (int) (x0 + r * Math.cos(Math.toRadians(angle)));
            y[i] = (int) (y0 + r * Math.sin(Math.toRadians(angle)));

        }

        for(int i = 0 ; i < noOfDividingPoints  ;i++)
        {
            Log.v("x",""+i+": "+x[i]);
            Log.v("y",""+i+": "+y[i]);

        }
    }

Where x0 and y0 are co ordinates of circle's centre.and r is radius.

In my case:

Input x0 = 0 , y0 = 0 and r = 150 , noOfDividingPoints = 5

output

point1: (150,0)

point2: (46,142)

point3: (-121,88)

point4: (-121,-88)

point5: (46,-142)

Answer 2

You need to convert between polar and Cartesian coordinates. The angle you need is the angle between the (imaginary) vertical line that splits the circle in half and the line that connects the center with the circle's boundary. With this formula you can calculate the X and Y offsets from the center.

In your example image the first angle is 0, and the second one is 360/n. Each next is i*(360/n) where i is the index of the current line you need to draw. Applying this will give you the X and Y offsets in a clockwise order (and you can just add them to the X and Y coordinates of the center to find the coordinates of each point)

EDIT: some kind of pseudo-code:

//x0, y0 - center's coordinates
for(i = 1 to n)
{
    angle = i * (360/n);
    point.x = x0 + r * cos(angle);
    point.y = y0 + r * sin(angle);
}