public static Polyhedron CreateTetrahedron(My_Point a, My_Point b, My_Point q)
{
My_Point c = GetThirdVertexForTriangle(a, b, q);
Vector m = new Vector(a, b);
Vector n = new Vector(a, c);
double sideLen = m.Norm();
double hLen = sideLen * Math.Sqrt(6) / 3.0;
Vector h = m[n].Normalize() * hLen;
Vector r = h + ((m + n) * (1.0 / 3.0));
My_Point d = new My_Point(a.X + r.X, a.Y + r.Y, a.Z + r.Z);
Polyhedron Tetrahedron = new Polyhedron();
Tetrahedron.faces = new Face[4];
Tetrahedron.faces[0] = Face.CreateTriangle(a, b, c);
Tetrahedron.faces[1] = Face.CreateTriangle(a, b, d);
Tetrahedron.faces[2] = Face.CreateTriangle(a, c, d);
Tetrahedron.faces[3] = Face.CreateTriangle(b, c, d);
double cx = (a.X + b.X + c.X + d.X) / 4;
double cy = (a.Y + b.Y + c.Y + d.Y) / 4;
double cz = (a.Z + b.Z + c.Z + d.Z) / 4;
Tetrahedron.center = new My_Point(cx, cy, cz);
return(Tetrahedron);
}
public static Polyhedron CreateHexahedron(My_Point a, My_Point b, My_Point q)
{
My_Point[] cd = GetVertecesForSquare(a, b, q);
My_Point c = cd[0];
My_Point d = cd[1];
Vector m = new Vector(a, b);
Vector n = new Vector(a, c);
double sideLen = m.Norm();
Vector h = m[n].Normalize() * sideLen;
My_Point a1 = new My_Point(a.X + h.X, a.Y + h.Y, a.Z + h.Z);
My_Point b1 = new My_Point(b.X + h.X, b.Y + h.Y, b.Z + h.Z);
My_Point c1 = new My_Point(c.X + h.X, c.Y + h.Y, c.Z + h.Z);
My_Point d1 = new My_Point(d.X + h.X, d.Y + h.Y, d.Z + h.Z);
Polyhedron Hexahedron = new Polyhedron();
Hexahedron.faces = new Face[6];
Hexahedron.faces[0] = Face.CreateSquare(a, b, c, d);
Hexahedron.faces[1] = Face.CreateSquare(a, b, b1, a1);
Hexahedron.faces[2] = Face.CreateSquare(b, c, c1, b1);
Hexahedron.faces[3] = Face.CreateSquare(c, d, d1, c1);
Hexahedron.faces[4] = Face.CreateSquare(a, d, d1, a1);
Hexahedron.faces[5] = Face.CreateSquare(a1, b1, c1, d1);
double cx = (a.X + c1.X) / 2;
double cy = (a.Y + c1.Y) / 2;
double cz = (a.Z + c1.Z) / 2;
Hexahedron.center = new My_Point(cx, cy, cz);
return(Hexahedron);
}
public static Polyhedron CreateOktahedron(My_Point a, My_Point b, My_Point q)
{
Polyhedron Hexahedron = CreateHexahedron(new My_Point(0, 0, 0), new My_Point(1, 0, 0), new My_Point(0, 1, 0));
My_Point[] verts = new My_Point[6];
for (int i = 0; i < 6; ++i)
{
double x = (Hexahedron.faces[i].Edges[0].First.X + Hexahedron.faces[i].Edges[1].First.X + Hexahedron.faces[i].Edges[2].First.X + Hexahedron.faces[i].Edges[3].First.X) / 2;
double y = (Hexahedron.faces[i].Edges[0].First.Y + Hexahedron.faces[i].Edges[1].First.Y + Hexahedron.faces[i].Edges[2].First.Y + Hexahedron.faces[i].Edges[3].First.Y) / 2;
double z = (Hexahedron.faces[i].Edges[0].First.Z + Hexahedron.faces[i].Edges[1].First.Z + Hexahedron.faces[i].Edges[2].First.Z + Hexahedron.faces[i].Edges[3].First.Z) / 2;
verts[i] = new My_Point(x, y, z); //Каждая координата - центр тяжести грани
}
Polyhedron Oktahedron = new Polyhedron();
Oktahedron.faces = new Face[8];
Oktahedron.faces[0] = Face.CreateTriangle(verts[0], verts[1], verts[2]);
Oktahedron.faces[1] = Face.CreateTriangle(verts[0], verts[2], verts[3]);
Oktahedron.faces[2] = Face.CreateTriangle(verts[0], verts[3], verts[4]);
Oktahedron.faces[3] = Face.CreateTriangle(verts[0], verts[4], verts[1]);
Oktahedron.faces[4] = Face.CreateTriangle(verts[5], verts[1], verts[2]);
Oktahedron.faces[5] = Face.CreateTriangle(verts[5], verts[2], verts[3]);
Oktahedron.faces[6] = Face.CreateTriangle(verts[5], verts[3], verts[4]);
Oktahedron.faces[7] = Face.CreateTriangle(verts[5], verts[4], verts[1]);
Oktahedron.center = Hexahedron.center;
return(Oktahedron);
}
public static Polyhedron CreateDodecahedron()
{
Polyhedron Icosahedron = CreateIcosahedron();
My_Point[] verts = new My_Point[20];
for (int i = 0; i < 20; ++i)
{
double x = (Icosahedron.faces[i].Edges[0].First.X + Icosahedron.faces[i].Edges[1].First.X + Icosahedron.faces[i].Edges[2].First.X) / 3;
double y = (Icosahedron.faces[i].Edges[0].First.Y + Icosahedron.faces[i].Edges[1].First.Y + Icosahedron.faces[i].Edges[2].First.Y) / 3;
double z = (Icosahedron.faces[i].Edges[0].First.Z + Icosahedron.faces[i].Edges[1].First.Z + Icosahedron.faces[i].Edges[2].First.Z) / 3;
verts[i] = new My_Point(x, y, z); //Каждая координата - центр тяжести грани
}
Polyhedron Dodecahedron = new Polyhedron();
Dodecahedron.faces = new Face[12];
Dodecahedron.faces[0] = Face.CreatePentagon(verts[0], verts[2], verts[4], verts[6], verts[8]);
Dodecahedron.faces[1] = Face.CreatePentagon(verts[1], verts[3], verts[5], verts[7], verts[9]);
Dodecahedron.faces[2] = Face.CreatePentagon(verts[2], verts[0], verts[10], verts[11], verts[12]);
Dodecahedron.faces[3] = Face.CreatePentagon(verts[3], verts[1], verts[11], verts[12], verts[13]);
Dodecahedron.faces[4] = Face.CreatePentagon(verts[4], verts[2], verts[12], verts[13], verts[14]);
Dodecahedron.faces[5] = Face.CreatePentagon(verts[5], verts[3], verts[13], verts[14], verts[15]);
Dodecahedron.faces[6] = Face.CreatePentagon(verts[6], verts[4], verts[14], verts[15], verts[16]);
Dodecahedron.faces[7] = Face.CreatePentagon(verts[7], verts[5], verts[15], verts[16], verts[17]);
Dodecahedron.faces[8] = Face.CreatePentagon(verts[8], verts[6], verts[16], verts[17], verts[18]);
Dodecahedron.faces[9] = Face.CreatePentagon(verts[9], verts[7], verts[17], verts[18], verts[19]);
Dodecahedron.faces[10] = Face.CreatePentagon(verts[0], verts[8], verts[18], verts[19], verts[10]);
Dodecahedron.faces[11] = Face.CreatePentagon(verts[9], verts[1], verts[11], verts[10], verts[19]);
Dodecahedron.center = new My_Point(0, 0, 0);
return(Dodecahedron);
}
//Поворот вокруг оси
public static void Rotate(Polyhedron polyhedron, My_Point a, My_Point b, double anglPhi)
{
double m = b.X - a.X;
double n = b.Y - a.Y;
double p = b.Z - a.Z;
double s = Math.Sqrt(m * m + n * n);
double d = Math.Sqrt(m * m + n * n + p * p);
AffineMatrix m0;
if (Math.Abs(s) < 1e-6)
{
AffineMatrix m1 = AffineMatrix.TranslationMatrix(-a.X, -a.Y, -a.Z);
AffineMatrix m4 = AffineMatrix.ZaxisRotationMatrix(anglPhi);
AffineMatrix m7 = AffineMatrix.TranslationMatrix(a.X, a.Y, a.Z);
m0 = m7 * m4 * m1;
}
else
{
AffineMatrix m1 = AffineMatrix.TranslationMatrix(-a.X, -a.Y, -a.Z);
AffineMatrix m2 = AffineMatrix.ZaxisRotationMatrix(n / s, m / s);
AffineMatrix m3 = AffineMatrix.XaxisRotationMatrix(p / d, s / d);
AffineMatrix m4 = AffineMatrix.ZaxisRotationMatrix(anglPhi);
AffineMatrix m5 = AffineMatrix.XaxisRotationMatrix(p / d, -s / d);
AffineMatrix m6 = AffineMatrix.ZaxisRotationMatrix(n / s, -m / s);
AffineMatrix m7 = AffineMatrix.TranslationMatrix(a.X, a.Y, a.Z);
m0 = m7 * m6 * m5 * m4 * m3 * m2 * m1;
}
Execute(polyhedron, m0);
}
public static Face CreateTriangle(My_Point a, My_Point b, My_Point c)
{
Face Triangle = new Face();
Triangle.edges = new Edge[3];
Triangle.edges[0] = new Edge(a, b);
Triangle.edges[1] = new Edge(b, c);
Triangle.edges[2] = new Edge(c, a);
return(Triangle);
}
private static My_Point GetThirdVertexForTriangle(My_Point a, My_Point b, My_Point q)
{
Vector m = new Vector(a, b);
Vector n = new Vector(a, q);
double sideLen = m.Norm();
double hLen = sideLen * Math.Sqrt(3) / 2.0;
double coeff = (m * n) / (m * m);
Vector h = (n - (coeff * m)).Normalize() * hLen;
Vector r = (0.5 * m) + h;
return(new My_Point(a.X + r.X, a.Y + r.Y, a.Z + r.Z));
}
public static Face CreateSquare(My_Point a, My_Point b, My_Point c, My_Point d)
{
Face Square = new Face();
Square.edges = new Edge[4];
Square.edges[0] = new Edge(a, b);
Square.edges[1] = new Edge(b, c);
Square.edges[2] = new Edge(c, d);
Square.edges[3] = new Edge(d, a);
return(Square);
}
public static Face CreatePentagon(My_Point a, My_Point b, My_Point c, My_Point d, My_Point e)
{
Face Pentagon = new Face();
Pentagon.edges = new Edge[5];
Pentagon.edges[0] = new Edge(a, b);
Pentagon.edges[1] = new Edge(b, c);
Pentagon.edges[2] = new Edge(c, d);
Pentagon.edges[3] = new Edge(d, e);
Pentagon.edges[4] = new Edge(e, a);
return(Pentagon);
}
public static Polyhedron CreateIcosahedron()
{
Polyhedron Icosahedron = new Polyhedron();
My_Point[] verts = new My_Point[12];
// верх и низ
verts[0] = new My_Point(0, 0, 1);
verts[1] = new My_Point(0, 0, -1);
double h = Math.Sqrt(5) / 5; //0.447
double R = h / Math.Sin(Math.PI / 5); //0.76
// верхний круг
double angle = 0;
for (int i = 2; i < 7; ++i)
{
verts[i] = new My_Point(R * Math.Sin(angle), R * Math.Cos(angle), h);
angle += 72 * Math.PI / 180; // 180/5 = 72
}
// нижний круг
angle = 36 * Math.PI / 180;
for (int i = 7; i < 12; ++i)
{
verts[i] = new My_Point(R * Math.Sin(angle), R * Math.Cos(angle), -h);
angle += 72 * Math.PI / 180; // 180/5 = 72
}
Icosahedron.faces = new Face[20];
for (int i = 0; i < 4; ++i)
{
Icosahedron.faces[2 * i] = Face.CreateTriangle(verts[0], verts[2 + i], verts[3 + i]); //Заполнение верхней пирамиды
Icosahedron.faces[2 * i + 1] = Face.CreateTriangle(verts[1], verts[7 + i], verts[8 + i]); //Заполенение нижней пирамиды
}
Icosahedron.faces[8] = Face.CreateTriangle(verts[0], verts[2], verts[6]);
Icosahedron.faces[9] = Face.CreateTriangle(verts[1], verts[7], verts[11]);
for (int i = 0; i < 4; ++i)
{
Icosahedron.faces[10 + 2 * i] = Face.CreateTriangle(verts[2 + i], verts[3 + i], verts[7 + i]);
Icosahedron.faces[11 + 2 * i] = Face.CreateTriangle(verts[7 + i], verts[8 + i], verts[3 + i]);
}
Icosahedron.faces[18] = Face.CreateTriangle(verts[6], verts[2], verts[11]);
Icosahedron.faces[19] = Face.CreateTriangle(verts[11], verts[7], verts[2]);
Icosahedron.center = new My_Point(0, 0, 0);
return(Icosahedron);
}
//Действия
private void Draw()
{
if (polyhedron == null)
{
return;
}
g.Clear(Color.White);
My_Point.DrawPoint0(g, Color.LimeGreen);
Polyhedron proj = polyhedron.Clone() as Polyhedron;
AffineTransform.IsometricProjection(proj);
proj.Draw(g, Color.Black);
}
private static My_Point[] GetVertecesForSquare(My_Point a, My_Point b, My_Point q)
{
Vector m = new Vector(a, b);
Vector n = new Vector(a, q);
double sideLen = m.Norm();
double coeff = (m * n) / (m * m);
Vector h = (n - (coeff * m)).Normalize() * sideLen;
Vector r = m + h;
My_Point c = new My_Point(a.X + r.X, a.Y + r.Y, a.Z + r.Z);
My_Point d = new My_Point(a.X + h.X, a.Y + h.Y, a.Z + h.Z);
return(new My_Point[2] {
c, d
});
}
public My_Point(My_Point a)
{
x = a.x;
y = a.y;
z = a.z;
}
public Edge(My_Point a, My_Point b)
{
this.a = new My_Point(a);
this.b = new My_Point(b);
}
public Vector(My_Point a)
{
this.x = a.X;
this.y = a.Y;
this.z = a.Z;
}
public Vector(My_Point a, My_Point b)
{
this.x = b.X - a.X;
this.y = b.Y - a.Y;
this.z = b.Z - a.Z;
}
public void Copy(My_Point a)
{
x = a.x;
y = a.y;
z = a.z;
}