how to calculate the points of a pentagon given the center?

Hello,

I have one XY Point that should be the center of a pentagon.
I want the length of each side to be 20.
This is a Cartesian Coordinate System.
I also want the tip on the pentagon to be facing South. So basically I want to draw an upside-down homeplate with the XY point the center. How can I calculate the points?


Thanks!

Think of the points are being on a circle, separated by angles of 2pi/5. You know the position of one point is straight down, which you can consider a zero angle (although more typically zero angle is the positive x axis), so you should be able to compute the angles for the other points from that. Once you have an angle and a distance you can convert those polar coordinates to Cartesian coordinates using the standard equations.

I had a few minutes and decided I needed the programming exercise, so...

Code:

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#include <iostream>
#include <vector>
#include <cmath>

using namespace std;
 
const double PI = 4 * atan(1.0);

inline double RadiansToDegrees(double radians) { return ( 360 * radians ) / ( 2 * PI ); }
inline double DegreesToRadians(double degrees) { return ( 2 * PI * degrees ) / 360; }

class Pentagon
{
        protected:
                double xCenter;
                double yCenter;
                double radiansOffset;
                double lengthSide;
                vector<double> x;
                vector<double> y;

        public:
                Pentagon()
                        : xCenter(0), yCenter(0), radiansOffset(0), lengthSide(1), x(5), y(5)
                {
                        CreatePoints();
                }

                Pentagon(double xCenter, double yCenter, double radiansOffset, double lengthSide)
                        : xCenter(xCenter), yCenter(yCenter), radiansOffset(radiansOffset), lengthSide(lengthSide), x(5), y(5)
                {
                        CreatePoints();
                }

                ~Pentagon()
                {
                }

                void CreatePoints()
                {
                        const double radius = Radius();

                        for( int i=0; i<5; ++i )
                        {
                                const double angle = radiansOffset + i * 2*PI/5;
                                x[i] = xCenter + radius * cos(angle);
                                y[i] = yCenter + radius * sin(angle);
                        }
                }

                double Radius() const { return lengthSide / ( 2.0 * sin(2*PI/10) ); }
                double GetX(int index) const { return index>=0 && index<x.size() ? x[index] : 0; }
                double GetY(int index) const { return index>=0 && index<y.size() ? y[index] : 0; }
};

int main()
{
        const double xCenter = 0;
        const double yCenter = 0;
        const double radiansOffset = DegreesToRadians(270);
        const double lengthSide = 20;

        const Pentagon p(xCenter, yCenter, radiansOffset, lengthSide);

        for( int i=0; i<5; ++i )
                cout << "[" << i << "] " << "x=" << p.GetX(i) << ", y=" << p.GetY(i) << endl;

  return 0;
}

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