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

[lab1]

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!

[Lindley]

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.

[0xC0000005]

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

#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;
}