Построение графиков на плоскости и в трёхмерном пространстве.

Пример 1:

Вычерчиваются графики функций:

Астроида:

Для астроиды b=1,3 (вычерчивается синим цветом). Масштабирование выполняется с учетом размеров компонента Image1, в котором выполняется рисование. Для заданного промежутка изменения аргумента x находится промежуток изменения функции (y).

 

Решение от преподавателя:

Файл Form1.h

 

#pragma once

 

namespace lab3 {

 

using namespace System;

using namespace System::ComponentModel;

using namespace System::Collections;

using namespace System::Windows::Forms;

using namespace System::Data;

using namespace System::Drawing;

 

///

/// Summary for Form1

///

public ref class Form1 : public System::Windows::Forms::Form

{

public:

Form1(void)

{

InitializeComponent();

//

//TODO: Add the constructor code here

//

}

 

protected:

///

/// Clean up any resources being used.

///

~Form1()

{

if (components)

{

delete components;

}

}

private: System::Windows::Forms::PictureBox^  pictureBox1;

protected: 

 

private:

///

/// Required designer variable.

///

System::ComponentModel::Container ^components;

 

#pragma region Windows Form Designer generated code

///

/// Required method for Designer support - do not modify

/// the contents of this method with the code editor.

///

void InitializeComponent(void)

{

this->pictureBox1 = (gcnew System::Windows::Forms::PictureBox());

(cli::safe_cast(this->pictureBox1))->BeginInit();

this->SuspendLayout();

// 

// pictureBox1

// 

this->pictureBox1->Location = System::Drawing::Point(12, 12);

this->pictureBox1->Name = L"pictureBox1";

this->pictureBox1->Size = System::Drawing::Size(484, 367);

this->pictureBox1->TabIndex = 0;

this->pictureBox1->TabStop = false;

this->pictureBox1->Paint += gcnew System::Windows::Forms::PaintEventHandler(this, &Form1::pictureBox1_Paint);

// 

// Form1

// 

this->AutoScaleDimensions = System::Drawing::SizeF(6, 13);

this->AutoScaleMode = System::Windows::Forms::AutoScaleMode::Font;

this->ClientSize = System::Drawing::Size(522, 391);

this->Controls->Add(this->pictureBox1);

this->FormBorderStyle = System::Windows::Forms::FormBorderStyle::FixedSingle;

this->MaximizeBox = false;

this->Name = L"Form1";

this->Text = L"Графики y=f(x)";

(cli::safe_cast(this->pictureBox1))->EndInit();

this->ResumeLayout(false);

 

}

#pragma endregion

 

private:

int l, b, h, w;

 

private: System::Void pictureBox1_Paint(System::Object^  sender, System::Windows::Forms::PaintEventArgs^ e) {

 

             h = pictureBox1->Height;            // Ширина

   w = pictureBox1->Width;             // Высота

 

   // Osi

   e->Graphics->DrawLine(Pens::Black,0,h/2,w,h/2);

    e->Graphics->DrawLine(Pens::Black,w/2,0,w/2,h);

   

   // Strelki

   

    e->Graphics->DrawLine(Pens::Black,w-25,h/2+8,w,h/2);

     e->Graphics->DrawLine(Pens::Black,w-25,h/2-8,w,h/2);

     e->Graphics->DrawLine(Pens::Black,w/2-8,25,w/2,0);

     e->Graphics->DrawLine(Pens::Black,w/2+8,25,w/2,0);

  

   

   // Podpisi

   e->Graphics->DrawString("X",this->Font,Brushes::Black,w-15,h/2-25);

   e->Graphics->DrawString("Y",this->Font,Brushes::Black,w/2-25,5);

  

   double x1, x2, y1, y2, x, y, mx, my, x0, y0, dx,dt;

   x1 = -5;    // from

   x2 = 5;     // to

 

   dx = 0.001;     // step

 

   y1 = 1/(3*(-5)*(-5)+2*(-5)+1);

   y2 = 1/(3*5*5+2*5+1);

 

   x = x1;

   while(x <= x2)

   {

     y = 1/(3*x*x+2*x+1);

     if (y < y1) y1 = y;

     if (y > y2) y2 = y;

     x+=dx;

   }

 

   my = 0.5*h/(y2-y1);           // mashtab po osi y

   mx = w/(x2-x1);                 // mashtab po osi x

 

   x = x1;

   y1=1/(3*x1*x1+2*x1+1);

   x+=dx;

   // График

 

   while(x <= x2)

   {

      y = 1/(3*x*x+2*x+1);

      e->Graphics->DrawLine(Pens::Black,(int)(x1*mx+w/2),(int)(h/2-y1*my),(int)(x*mx+w/2),(int)(h/2-y*my));

      x1=x;

      y1=y;

      x+=dx;

   }

   x1 = -1.3;    // from

   x2 = 1.3;     // to

 

   dt = 0.001;     // step

 

   y1 = -1.3;

   y2 = 1.3;

 

   my = h/(y2-y1);           // mashtab po osi y

   mx = w/(x2-x1);                 // mashtab po osi x

 

   double t = 0;

   // График

   

    x1=Math::Cos(t)*Math::Cos(t)*Math::Cos(t)*1.3;

    y1=Math::Sin(t)*Math::Sin(t)*Math::Sin(t)*1.3;

    t+=dt;

   while(t <= 2*3.14)

   {

       x=Math::Cos(t)*Math::Cos(t)*Math::Cos(t)*1.3;

       y=Math::Sin(t)*Math::Sin(t)*Math::Sin(t)*1.3;

       e->Graphics->DrawLine(Pens::Red,(int)(x1*mx+w/2),(int)(h/2-y1*my),(int)(x*mx+w/2),(int)(h/2-y*my));

       t+=dt;

       x1=x;

       y1=y;

   }

}

};

}

 

Пример 2:

Вычерчивается поверхность

 

Решение от преподавателя:

Файл реализации Form1.h

 

#pragma once

 

namespace lab3b {

 

using namespace System;

using namespace System::ComponentModel;

using namespace System::Collections;

using namespace System::Windows::Forms;

using namespace System::Data;

using namespace System::Drawing;

 

///

/// Summary for Form1

///

public ref class Form1 : public System::Windows::Forms::Form

{

public:

Form1(void)

{

InitializeComponent();

//

//TODO: Add the constructor code here

//

}

 

protected:

///

/// Clean up any resources being used.

///

~Form1()

{

if (components)

{

delete components;

}

}

private: System::Windows::Forms::PictureBox^  pictureBox1;

protected: 

 

private:

///

/// Required designer variable.

///

System::ComponentModel::Container ^components;

 

#pragma region Windows Form Designer generated code

///

/// Required method for Designer support - do not modify

/// the contents of this method with the code editor.

///

void InitializeComponent(void)

{

this->pictureBox1 = (gcnew System::Windows::Forms::PictureBox());

(cli::safe_cast(this->pictureBox1))->BeginInit();

this->SuspendLayout();

// 

// pictureBox1

// 

this->pictureBox1->Location = System::Drawing::Point(12, 12);

this->pictureBox1->Name = L"pictureBox1";

this->pictureBox1->Size = System::Drawing::Size(401, 333);

this->pictureBox1->TabIndex = 0;

this->pictureBox1->TabStop = false;

this->pictureBox1->Paint += gcnew System::Windows::Forms::PaintEventHandler(this, &Form1::pictureBox1_Paint);

// 

// Form1

// 

this->AutoScaleDimensions = System::Drawing::SizeF(6, 13);

this->AutoScaleMode = System::Windows::Forms::AutoScaleMode::Font;

this->ClientSize = System::Drawing::Size(458, 357);

this->Controls->Add(this->pictureBox1);

this->FormBorderStyle = System::Windows::Forms::FormBorderStyle::FixedSingle;

this->MaximizeBox = false;

this->Name = L"Form1";

this->Text = L"Поверхность z=f(x,y)";

(cli::safe_cast(this->pictureBox1))->EndInit();

this->ResumeLayout(false);

 

}

#pragma endregion

        

private:

static double x0=4,Y0=-0.5,z0=3,alf=4.31,bet=4.92,A=-6.5,a=-6.5;

static double Xmin=-1.5,Xmax=1.5,Ymin=-1.5,Ymax=1.5;

static int Width=200,Height=200;

static double h=0.1,h0=0.25;

static array^ ob=gcnew array (4);

 

//------------------------------------------------------------------------------

//*********** void IJ(double x, double y, double z, array^ ar) **********

private: void IJ(double x, double y, double z,array^ ar)

{

 double Xn,Yn,Zn;

 

 //Осуществляем перенос системы координат в т.(x0,Y0,z0)

 Xn=(x-x0)*Math::Cos(alf)-(y-Y0)*Math::Sin(alf);

 Yn=((x-x0)*Math::Sin(alf)+(y-Y0)*Math::Cos(alf))*Math::Cos(bet)-(z-z0)*Math::Sin(bet);

 Zn=((x-x0)*Math::Sin(alf)+(y-Y0)*Math::Cos(alf))*Math::Sin(bet)+(z-z0)*Math::Cos(bet);

 

 //Делаем проекцию на плоскость

 Xn/=Zn/A+1;

 Yn/=Zn/a+1;

 

 //Масштабируем оси x и y

 ar[0]=Width*(Xn-Xmin)/(Xmax-Xmin);

 ar[1]=Height*(Yn-Ymax)/(Ymin-Ymax);

}

//******* void IJ(double x, double y, double z, array^ ar) **********

//------------------------------------------------------------------------------

 

//------------------------------------------------------------------------------

//****** double F1(double x1,double y1) *****************************

private: double F1(double x1,double y1)

{

 return 1/((x1+y1)*(x1+y1));

}

//***** double F1(double x1,double y1) *****************************

//------------------------------------------------------------------------------

//Рисование поверхности

private: System::Void pictureBox1_Paint(System::Object^  sender, System::Windows::Forms::PaintEventArgs^ e) {

 

          int i3,j3;

 int i1,j1,i2,j2;

 array^ a1;

 array^ a2;

 a1=gcnew array (2);

 a2=gcnew array (2);

 IJ(0,0,0,a1);

 

 //Рисуем и подписываем ось x

 IJ(4,0,0,a2);

e->Graphics->DrawLine(Pens::Red,a1[0],a1[1],a2[0],a2[1]);

e->Graphics->DrawString("X",this->Font,Brushes::Red,a2[0]+3,a2[1]);

 

 //Рисуем и подписываем ось y

 IJ(0,4,0,a2);

 e->Graphics->DrawLine(Pens::Red,a1[0],a1[1],a2[0],a2[1]);

 e->Graphics->DrawString("Y",this->Font,Brushes::Red,a2[0]+3,a2[1]);

 

 //Рисуем и подписываем ось z

 IJ(0,0,4.3,a2);

 e->Graphics->DrawLine(Pens::Red,a1[0],a1[1],a2[0],a2[1]);

 e->Graphics->DrawString("Z",this->Font,Brushes::Red,a2[0]+3,a2[1]-3);

 

 

 for(j3=0;j3<25;j3++)

  {

   for(i3=0;i3<30;i3++)

    {

     IJ(h0+h*i3,h0+h*j3,F1(h0+h*i3,h0+h*j3),a1);

     ob[0].X=a1[0];

     ob[0].Y=a1[1];

     IJ(h0+h*i3,h0+h*(j3+1),F1(h0+h*i3,h0+h*(j3+1)),a1);

     ob[1].X=a1[0];

     ob[1].Y=a1[1];

     IJ(h0+h*(i3+1),h0+h*(j3+1),F1(h0+h*(i3+1),h0+h*(j3+1)),a1);

     ob[2].X=a1[0];

     ob[2].Y=a1[1];

     IJ(h0+h*(i3+1),h0+h*j3,F1(h0+h*(i3+1),h0+h*j3),a1);

     ob[3].X=a1[0];

     ob[3].Y=a1[1];

     e->Graphics->DrawPolygon(Pens::Blue,ob);

 

     

    }

  }

}

};

}