Calculate coordinates of a regular polygon's vertices

Question

I am writing a program in which I need to draw polygons of an arbitrary number of sides, each one being translated by a given formula which changes dynamically. There is som

Answer 1

One possible implementation to generate a set of coordinates for regular polygon is to:

Define polygon center, radius and first vertex¹.
Rotate the vertex n-times² at an angle of: 360/n.

In this implementation I use a vector to store the generated coordinates and a recursive function to generate them:

void generateRegularPolygon(vector& v, Point& center, int sidesNumber, int radius){
    // converted to radians
    double angRads = 2 * PI / double(sidesNumber);
    // first vertex  
    Point initial(center.x, center.y - radius);
    rotateCoordinate(v, center, initial, angRads, sidesNumber);
}

where:

void rotateCoordinate(vector& v, Point& axisOfRotation, Point& initial, double angRads, int numberOfRotations){
    // base case: number of transformations < 0
    if(numberOfRotations <= 0) return;
    else{
        // apply rotation to: initial, around pivot point: axisOfRotation
        double x = cos(angRads) * (initial.x - axisOfRotation.x) - sin(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.x;
        double y = sin(angRads) * (initial.x - axisOfRotation.x) + cos(angRads) * (initial.y - axisOfRotation.y) + axisOfRotation.y;
        // store the result
        v.push_back(Point(x, y));
        rotateCoordinate(v, axisOfRotation, Point(x,y), angRads, --numberOfRotations);
    }
}

Note:

Point is a simple class to wrap the coordinate into single data structure:

class Point{
public:
    Point(): x(0), y(0){ }
    Point(int xx, int yy): x(xx), y(yy) { }
private:
    int x;
    int y; 
}; 

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^{1 in terms of (relative to) the center, radius. In my case the first vertex is translated from the centre up horizontally by the radius lenght.}

^{2 n-regular polygon has n vertices.}