static class BezierSurface
    {
        private const int n = 3;// размерность массива  
        private const int m = 4;// mBezierSurface (3 на 4)
        private static Point3D[,] mBezierSurface = new Point3D[n, m]{//Второго порядка
		// можно сделать 9, ставь m = 3 и подбирай координаты.
                { new Point3D(0, 0, 0), new Point3D(0, 0, 0.5), new Point3D(0, 0.5, 0), new Point3D(0, 0.5, 0.5) }, 
                { new Point3D(1, 0, 0), new Point3D(1, 0, 1), new Point3D(1, 1, 0), new Point3D(1, 1, 1) }, 
                { new Point3D(1, 0, 0), new Point3D(1, 0, 1), new Point3D(1, 1, 0), new Point3D(1, 2, 3) },
        };


public class BSplineSurface
    {
        private double size;
        private const int m = 4;// ненужный аппендикс, в топку его
        private Point3D start = new Point3D(400, 220, 0);
        private double psi;// огорчаешь: углы обзора 
        private double phi;// на поверхность
        public BSplineSurface(double size, double psi, double phi)//конструктор класса
        {
            this.size = size;
            this.psi = psi;
            this.phi = phi;
        }
        Point3D[][] mBSplineSurface = new Point3D[][] {
                new Point3D[] { new Point3D(0, 0, 0), new Point3D(0, 0, 0.5), new Point3D(0, 0.5, 0), new Point3D(0, 0.5, 0.5) }, 
                new Point3D[] { new Point3D(0.5, 0, 0), new Point3D(0.5, 0, 0.5), new Point3D(0.5, 0.5, 0), new Point3D(0.5, 0.5, 0.5) }, 
                new Point3D[] { new Point3D(2, 0, 0), new Point3D(2, 0, 2), new Point3D(2, 2, 0), new Point3D(2, 2, 2) }
        };
        private PointF Project(Point3D p)// метод проецирования трехмерной точки на двумерную плоскость
        {
            Point3D a1 = new Point3D(Math.Cos(phi), Math.Sin(phi), 0);
            Point3D a2 = new Point3D(-1 * Math.Sin(phi) * Math.Sin(psi), Math.Cos(phi) * Math.Sin(psi), Math.Cos(psi));
            double x = p.X - start.X;//?
            double y = p.Y - start.Y;
            double z = p.Z - start.Z;
            return new PointF((float)(a1.scalyar(new Point3D(x, y, z)) * size), (float)(a2.scalyar(new Point3D(x, y, z)) * size));

        }
        public void Show(Graphics g, Pen pen)
        {
            List<Point3D> polygon = new List<Point3D>();// Лист для точек на сетке
            for (double u = 0; u <= 1.0; u += 0.01)
            {
                for (double v = 0; v <= 1.0; v += 0.01)
                {
                    var pList = new List<Point3D>();// Лист, в котором лежат точки сплайна.
                    for (int i = 0; i < mBSplineSurface.Length; i++)
                    {
                        for (int j = 0; j < mBSplineSurface.Length - 2; j++)
                        {
                            pList.Add(new Point3D((float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].X + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].X + 0.5f * v * v * mBSplineSurface[i][j + 2].X),
                                (float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].Y + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].Y + 0.5f * v * v * mBSplineSurface[i][j + 2].Y),
                                (float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].Z + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].Z + 0.5f * v * v * mBSplineSurface[i][j + 2].Z)));
                        }
                    }
                    for (int j = 0; j < pList.Count - 2; j++)
                    {
                        polygon.Add(new Point3D((float)(0.5f * (1f - u) * (1f - u) * pList[j].X + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].X + 0.5f * u * u * pList[j + 2].X),
                            (float)(0.5f * (1f - u) * (1f - u) * pList[j].Y + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].Y + 0.5f * u * u * pList[j + 2].Y),
                            (float)(0.5f * (1f - u) * (1f - u) * pList[j].Z + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].Z + 0.5f * u * u * pList[j + 2].Z)));
                        polygon.Last().X = (float)(polygon.Last().X  + start.X);
                        polygon.Last().Y = (float)(polygon.Last().Y  + start.Y);
                        polygon.Last().Z = (float)(polygon.Last().Z  + start.Z);
                    }
                }
                var sub = polygon.Select(x => Project(x)).ToList();// создаем новый лист, в него кладем двухмерные точки.
				// .Select(x => Project(x)) эта штука берет каждую точку из листа polygon и прогоняет в методе Project
                for (int i = 0; i < sub.Count - 1; i++)
                {
                    if (g.ClipBounds.Contains(sub[i]) && g.ClipBounds.Contains(sub[i + 1]))
                    {
                        g.DrawLine(pen, sub[i], sub[i + 1]);
                    }
                }
                polygon.Clear();
            }
            for (double v = 0; v <= 1.0; v += 0.01)
            {
                for (double u = 0; u <= 1.0; u += 0.01)
                {
                    var pList = new List<Point3D>();
                    for (int i = 0; i < mBSplineSurface.Length; i++)
                    {
                        for (int j = 0; j < mBSplineSurface.Length - 2; j++)
                        {
                            pList.Add(new Point3D((float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].X + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].X + 0.5f * v * v * mBSplineSurface[i][j + 2].X),
                                (float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].Y + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].Y + 0.5f * v * v * mBSplineSurface[i][j + 2].Y),
                                (float)(0.5f * (1f - v) * (1f - v) * mBSplineSurface[i][j].Z + (0.75f - (v - 0.5f) * (v - 0.5f)) * mBSplineSurface[i][j + 1].Z + 0.5f * v * v * mBSplineSurface[i][j + 2].Z)));
                        }
                    }
                    for (int j = 0; j < pList.Count - 2; j++)
                    {
                        polygon.Add(new Point3D((float)(0.5f * (1f - u) * (1f - u) * pList[j].X + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].X + 0.5f * u * u * pList[j + 2].X),
                            (float)(0.5f * (1f - u) * (1f - u) * pList[j].Y + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].Y + 0.5f * u * u * pList[j + 2].Y),
                            (float)(0.5f * (1f - u) * (1f - u) * pList[j].Z + (0.75f - (u - 0.5f) * (u - 0.5f)) * pList[j + 1].Z + 0.5f * u * u * pList[j + 2].Z)));
                        polygon.Last().X = (float)(polygon.Last().X  + start.X);
                        polygon.Last().Y = (float)(polygon.Last().Y  + start.Y);
                        polygon.Last().Z = (float)(polygon.Last().Z  + start.Z);
                    }
                }
                var sub = polygon.Select(x => Project(x)).ToList();// то же самое, что было выше
                for (int i = 0; i < sub.Count - 1; i++)
                {
                    if (g.ClipBounds.Contains(sub[i]) && g.ClipBounds.Contains(sub[i + 1]))
                    {
                        g.DrawLine(pen, sub[i], sub[i + 1]);
                    }
                }
                polygon.Clear();
            }
        }
    }
}

    class DrawSurface
    {
        private Graphics e;
        private double a, b, c, d, phi, psi, Sx, Sy;// a,b,c,d - прямоугольник, ограничивающий поверхность. phi/psi - угол обзора, Sx, Sy - масштаб
        private int Picture_CODE, BEGINX, BEGINY;//Picture_CODE - номер поверхность для отрисовки, BEGINX, BEGINY - точка, с которой будем рисовать
        public DrawSurface(Graphics e, double a1, double b1, double c1, double d1, double phi, double psi, double Sx, double Sy, int Picture_CODE, int BEGINX, int BEGINY)
        {
            this.e = e;
            a = a1;
            b = b1;
            c = c1;
            d = d1;
            this.phi = phi;
            this.psi = psi;
            this.Picture_CODE = Picture_CODE;
            this.Sx = Sx;
            this.Sy = Sy;
            this.BEGINX = BEGINX;
            this.BEGINY = BEGINY;
        }
        public void Draw()
        {
            List<Point3D> list = new List<Point3D>();
            Point3D p = new Point3D();
            Point3D a1 = new Point3D(Math.Cos(phi), Math.Sin(phi), 0);
            Point3D a2 = new Point3D(-1 * Math.Sin(phi) * Math.Sin(psi), Math.Cos(phi) * Math.Sin(psi), Math.Cos(psi));
            double u, v, du, dv, Nu = 20, Nv = 20;//u, v - точки на сетке, du,dv - шаг, Nu, Nv - разбиение
            du = Math.Abs((b - a) / Nu);
            dv = Math.Abs((d - c) / Nv);
            Point temp = new Point(0, 0);
            Point3D beg = new Point3D(0, 0, 0), cur = new Point3D(0, 0, 0);// точки на сетке
            int u0, v0, v1, u1;// спроецированные точки
            for (u = a; u <= b; u += du) // рисование по горизонтали
            {
                v = c;
                beg = Function(u, v, Picture_CODE);
                u0 = ((int)(Sx * scalyar(beg, a1)));
                v0 = ((int)(Sy * scalyar(beg, a2)));
                temp.X = BEGINX + u0;
                temp.Y = BEGINY + v0;
                for (v = c + dv; v <= d; v += dv)// рисование по горизонтали
                {
                    cur = Function(u, v, Picture_CODE);
                    u1 = ((int)(Sx * scalyar(cur, a1)));
                    v1 = ((int)(Sy * scalyar(cur, a2)));
                    e.DrawLine(new Pen(Color.Black), BEGINX + u1, BEGINY + v1, temp.X, temp.Y);
                    temp.X = BEGINX + u1;
                    temp.Y = BEGINY + v1;
                }
            }
            for (v = c; v <= d; v += dv)//// рисование по вертикали
            {
                u = a;
                beg = Function(u, v, Picture_CODE);
                u0 = ((int)(Sx * scalyar(beg, a1)));
                v0 = ((int)(Sy * scalyar(beg, a2)));
                temp.X = BEGINX + u0;
                temp.Y = BEGINY + v0;
                for (u = a + du; u <= b; u += du)
                {
                    cur = Function(u, v, Picture_CODE);
                    u1 = ((int)(Sx * scalyar(cur, a1)));
                    v1 = ((int)(Sy * scalyar(cur, a2)));
                    e.DrawLine(new Pen(Color.Black), BEGINX + u1, BEGINY + v1, temp.X, temp.Y);
                    temp.X = BEGINX + u1;
                    temp.Y = BEGINY + v1;
                }
            }
        }
        private double scalyar(Point3D a, Point3D b)
        {
            return a.X * b.X + a.Y * b.Y + a.Z * b.Z;
        }
        public Point3D Function(double u, double v, int code)//Функция, которая возвращает значение для построения поверхности
        { // u, v положение на сетке(точка), code - номер фигуры, которую хочешь вывести. Дашь 0 - будешь поверхность Безье
            switch (code)
            {
                case 0:
                    return BezierSurface.drawBezierSurface(u, v);
                case 1:
                    return new Point3D(5 * Math.Cos(u) * Math.Atan(v), 5 * Math.Sin(u) * Math.Tanh(v), 5 * Math.Tanh(u * v));
                case 2:
                    return new Point3D((5 + Math.Cos(u)) * Math.Cos(v), (5 + Math.Cos(u)) * Math.Sin(v), 5 * Math.Sin(u));
                default:
                    return new Point3D(0, 0, 0);
            }
        }
    }
}