using GeometRi;

using System;

​

​

public class Program

{

    public static void Main()

    {

​

        Console.WriteLine("Mascheroni Construction of a Regular Pentagon");

        Console.WriteLine();

​

        // We will follow the notation from 

        // https://www.cut-the-knot.org/pythagoras/MascheroniPentagon.shtml

        // Read this article for detailed description of the algorithm

​

        // Start with arbitrary points A and B (in plane XY)

        Point3d A = new Point3d(0, 0, 0);

        Point3d B = new Point3d(5, 0, 0);

​

        // Draw a circle C1 with center in point A through point B

        Circle3d C1 = new Circle3d(A, A.DistanceTo(B), new Vector3d(0, 0, 1));

​

        // Draw a circle C2 with center in point B through point A

        Circle3d C2 = new Circle3d(B, A.DistanceTo(B), new Vector3d(0, 0, 1));

​

        // Intersection of C1 and C2 gives points C and D

        Segment3d segment = (Segment3d)C1.IntersectionWith(C2);

        Point3d C = segment.P1;

        Point3d D = segment.P2;

​

        // Draw a circle C3 with center in point C through point D

        Circle3d C3 = new Circle3d(C, C.DistanceTo(D), new Vector3d(0, 0, 1));

​

        // Intersection of C3 and C1 gives point E

        segment = (Segment3d)C3.IntersectionWith(C1);

        Point3d E = segment.P1;

        // if E == D, choose another point of intersection

        if (E == D)

        {

            E = segment.P2;

        }

​

        // Intersection of C3 and C2 gives point F

        segment = (Segment3d)C3.IntersectionWith(C2);

        Point3d F = segment.P1;

        // if F == D, choose another point of intersection

        if (F == D)

        {

            F = segment.P2;

        }

​

        // Draw a circle C4 with center in point A through point F

        Circle3d C4 = new Circle3d(A, A.DistanceTo(F), new Vector3d(0, 0, 1));

​

        // Draw a circle C5 with center in point B through point E

        Circle3d C5 = new Circle3d(B, B.DistanceTo(E), new Vector3d(0, 0, 1));

​

        // Intersection of C4 and C5 gives points G and H

        segment = (Segment3d)C4.IntersectionWith(C5);

        // point G is closer to point D

        Point3d G = new Point3d();

        Point3d H = new Point3d();

        if (segment.P1.DistanceTo(D) < segment.P2.DistanceTo(D))

        {

            G = segment.P1;

            H = segment.P2;

        }

        else

        {

            H = segment.P1;

            G = segment.P2;

        }

​

        // Draw a circle C6 with center in point G through point C

        Circle3d C6 = new Circle3d(G, G.DistanceTo(C), new Vector3d(0, 0, 1));

​

        // Intersection of C6 and C3 gives points I and J

        // we need to choose correct side for I and J

        segment = (Segment3d)C6.IntersectionWith(C3);

        Point3d I = new Point3d();

        Point3d J = new Point3d();

        if (segment.P1.DistanceTo(A) < segment.P1.DistanceTo(B))

        {

            I = segment.P1;

            J = segment.P2;

        }

        else

        {

            J = segment.P1;

            I = segment.P2;

        }

​

​

        // Draw a circle C7 with center in point H through point C

        Circle3d C7 = new Circle3d(H, H.DistanceTo(C), new Vector3d(0, 0, 1));

​

        // Intersection of C7 and C3 gives points K and L

        segment = (Segment3d)C7.IntersectionWith(C3);

        Point3d K = new Point3d();

        Point3d L = new Point3d();

        if (segment.P1.DistanceTo(I) < segment.P1.DistanceTo(J))

        {

            K = segment.P1;

            L = segment.P2;

        }

        else

        {

            L = segment.P1;

            K = segment.P2;

        }

​

​

        // Points DIKLJ define our pentagon

        // Let's check if interion angles are equal 108 degrees (with accuracy 1e-8)

        double angle1 = new Vector3d(D, I).AngleToDeg(new Vector3d(D, J));

        double angle2 = new Vector3d(I, D).AngleToDeg(new Vector3d(I, K));

        double angle3 = new Vector3d(K, I).AngleToDeg(new Vector3d(K, L));

        double angle4 = new Vector3d(L, K).AngleToDeg(new Vector3d(L, J));

        double angle5 = new Vector3d(J, L).AngleToDeg(new Vector3d(J, D));

​

        double tolerance = 1e-8;

        if (Math.Abs(angle1 - 108.0) < tolerance &&

             Math.Abs(angle2 - 108.0) < tolerance &&

             Math.Abs(angle3 - 108.0) < tolerance &&

             Math.Abs(angle4 - 108.0) < tolerance &&

             Math.Abs(angle5 - 108.0) < tolerance)

        {

            Console.WriteLine("Your construction is correct!");

            Console.WriteLine(D.ToString());

            Console.WriteLine(I.ToString());

            Console.WriteLine(K.ToString());

            Console.WriteLine(L.ToString());

            Console.WriteLine(J.ToString());

        }

​

​

​

        Console.ReadLine();

​

​

    }

}