form1.h

采用拉格朗日和泰勒展开的方法对SinX进行数值的函数拟合。本代码用VC++ .net进行显示

				 this->groupBox2->Controls->Add(this->label8);
				 this->groupBox2->Controls->Add(this->hScrollBar_yscale);
				 this->groupBox2->Controls->Add(this->label7);
				 this->groupBox2->Controls->Add(this->hScrollBar_xscale);
				 this->groupBox2->Controls->Add(this->label6);
				 this->groupBox2->Controls->Add(this->label5);
				 this->groupBox2->Controls->Add(this->txtCTY);
				 this->groupBox2->Controls->Add(this->label4);
				 this->groupBox2->Controls->Add(this->label3);
				 this->groupBox2->Controls->Add(this->txtCTX);
				 this->groupBox2->Location = System::Drawing::Point(784, 292);
				 this->groupBox2->Name = L"groupBox2";
				 this->groupBox2->Size = System::Drawing::Size(140, 233);
				 this->groupBox2->TabIndex = 6;
				 this->groupBox2->TabStop = false;
				 this->groupBox2->Text = L"坐标系";
				 // 
				 // listBox_nGrid
				 // 
				 this->listBox_nGrid->FormattingEnabled = true;
				 this->listBox_nGrid->ItemHeight = 12;
				 this->listBox_nGrid->Items->AddRange(gcnew cli::array< System::Object^  >(3) {L"4", L"8", L"16"});
				 this->listBox_nGrid->Location = System::Drawing::Point(14, 117);
				 this->listBox_nGrid->Name = L"listBox_nGrid";
				 this->listBox_nGrid->Size = System::Drawing::Size(111, 16);
				 this->listBox_nGrid->TabIndex = 16;
				 this->listBox_nGrid->SelectedIndexChanged += gcnew System::EventHandler(this, &Form1::listBox_nGrid_SelectedIndexChanged);
				 // 
				 // label8
				 // 
				 this->label8->AutoSize = true;
				 this->label8->Location = System::Drawing::Point(12, 178);
				 this->label8->Name = L"label8";
				 this->label8->Size = System::Drawing::Size(41, 12);
				 this->label8->TabIndex = 15;
				 this->label8->Text = L"yscale";
				 // 
				 // hScrollBar_yscale
				 // 
				 this->hScrollBar_yscale->Location = System::Drawing::Point(14, 194);
				 this->hScrollBar_yscale->Maximum = 800;
				 this->hScrollBar_yscale->Minimum = 200;
				 this->hScrollBar_yscale->Name = L"hScrollBar_yscale";
				 this->hScrollBar_yscale->Size = System::Drawing::Size(111, 20);
				 this->hScrollBar_yscale->TabIndex = 14;
				 this->hScrollBar_yscale->Value = 200;
				 this->hScrollBar_yscale->ValueChanged += gcnew System::EventHandler(this, &Form1::btnStart_Click);
				 // 
				 // label7
				 // 
				 this->label7->AutoSize = true;
				 this->label7->Location = System::Drawing::Point(12, 140);
				 this->label7->Name = L"label7";
				 this->label7->Size = System::Drawing::Size(41, 12);
				 this->label7->TabIndex = 13;
				 this->label7->Text = L"xscale";
				 // 
				 // hScrollBar_xscale
				 // 
				 this->hScrollBar_xscale->Location = System::Drawing::Point(14, 156);
				 this->hScrollBar_xscale->Maximum = 400;
				 this->hScrollBar_xscale->Minimum = 100;
				 this->hScrollBar_xscale->Name = L"hScrollBar_xscale";
				 this->hScrollBar_xscale->Size = System::Drawing::Size(111, 20);
				 this->hScrollBar_xscale->TabIndex = 12;
				 this->hScrollBar_xscale->Value = 100;
				 this->hScrollBar_xscale->ValueChanged += gcnew System::EventHandler(this, &Form1::btnStart_Click);
				 // 
				 // label6
				 // 
				 this->label6->AutoSize = true;
				 this->label6->Location = System::Drawing::Point(12, 102);
				 this->label6->Name = L"label6";
				 this->label6->Size = System::Drawing::Size(53, 12);
				 this->label6->TabIndex = 11;
				 this->label6->Text = L"网格数量";
				 // 
				 // label5
				 // 
				 this->label5->AutoSize = true;
				 this->label5->Location = System::Drawing::Point(15, 109);
				 this->label5->Name = L"label5";
				 this->label5->Size = System::Drawing::Size(0, 12);
				 this->label5->TabIndex = 9;
				 // 
				 // txtCTY
				 // 
				 this->txtCTY->Enabled = false;
				 this->txtCTY->Location = System::Drawing::Point(14, 78);
				 this->txtCTY->Name = L"txtCTY";
				 this->txtCTY->Size = System::Drawing::Size(111, 21);
				 this->txtCTY->TabIndex = 7;
				 // 
				 // label4
				 // 
				 this->label4->AutoSize = true;
				 this->label4->Enabled = false;
				 this->label4->Location = System::Drawing::Point(12, 63);
				 this->label4->Name = L"label4";
				 this->label4->Size = System::Drawing::Size(83, 12);
				 this->label4->TabIndex = 6;
				 this->label4->Text = L"中心点横坐标Y";
				 // 
				 // label3
				 // 
				 this->label3->AutoSize = true;
				 this->label3->Enabled = false;
				 this->label3->Location = System::Drawing::Point(6, 24);
				 this->label3->Name = L"label3";
				 this->label3->Size = System::Drawing::Size(83, 12);
				 this->label3->TabIndex = 5;
				 this->label3->Text = L"中心点横坐标X";
				 // 
				 // txtCTX
				 // 
				 this->txtCTX->Enabled = false;
				 this->txtCTX->Location = System::Drawing::Point(14, 39);
				 this->txtCTX->Name = L"txtCTX";
				 this->txtCTX->Size = System::Drawing::Size(111, 21);
				 this->txtCTX->TabIndex = 0;
				 // 
				 // Form1
				 // 
				 this->AutoScaleDimensions = System::Drawing::SizeF(6, 12);
				 this->AutoScaleMode = System::Windows::Forms::AutoScaleMode::Font;
				 this->ClientSize = System::Drawing::Size(936, 598);
				 this->Controls->Add(this->groupBox2);
				 this->Controls->Add(this->tabControl1);
				 this->Controls->Add(this->groupBox1);
				 this->FormBorderStyle = System::Windows::Forms::FormBorderStyle::FixedSingle;
				 this->Name = L"Form1";
				 this->StartPosition = System::Windows::Forms::FormStartPosition::CenterScreen;
				 this->Text = L"数值作业：逼近";
				 this->Load += gcnew System::EventHandler(this, &Form1::Form1_Load);
				 this->groupBox1->ResumeLayout(false);
				 this->groupBox1->PerformLayout();
				 (cli::safe_cast<System::ComponentModel::ISupportInitialize^  >(this->numericUpDown_Input))->EndInit();
				 (cli::safe_cast<System::ComponentModel::ISupportInitialize^  >(this->pictureBox1))->EndInit();
				 this->tabControl1->ResumeLayout(false);
				 this->tabPage_FunctionShow->ResumeLayout(false);
				 this->tabPage_ErrorShow->ResumeLayout(false);
				 (cli::safe_cast<System::ComponentModel::ISupportInitialize^  >(this->pictureBox2))->EndInit();
				 this->groupBox2->ResumeLayout(false);
				 this->groupBox2->PerformLayout();
				 this->ResumeLayout(false);

			 }
#pragma endregion
	private: System::Void ctor() {
				 this->InitializeComponent();

			 }
	private: System::Void Form1_Load(System::Object^  sender, System::EventArgs^  e) {
				 pictureBox1->BackColor = Color::White;
				 pictureBox2->BackColor = Color::White;
				 // 
				 //Connect the Paint event of the PictureBox to the event handler method.
				 pictureBox1->Paint += gcnew System::Windows::Forms::PaintEventHandler( this, &Form1::pictureBox1_Paint );
				 this->listBox_nGrid->SetSelected(0,true);
				 this->listBox_Method->SetSelected(0,true);


			 }
	private:System::Void pictureBox1_Paint( Object^ /*sender*/, System::Windows::Forms::PaintEventArgs^ e )
			{
				// Create a local version of the graphics object for the PictureBox.

			}

	private: System::Void btnStart_Click(System::Object^  sender, System::EventArgs^  e) {
				 if(numericUpDown_Input->Text==""){
					 MessageBox::Show( "您必须输入误差或者", "Name Entry Error",
						 MessageBoxButtons::OK, MessageBoxIcon::Exclamation );
				 }
				 else
				 {

					 Method mthd=Taylor;
					 if(this->listBox_Method->Text=="Taylor")mthd=Taylor;
					 else if(this->listBox_Method->Text=="Lagrange")mthd=Lagrange;
					 if(!radioByError->Checked)
					 {
						 int nOrder=Convert::ToInt32(numericUpDown_Input->Text);
						 DrawSome(mthd,nOrder,Convert::ToInt32(listBox_nGrid->Text),3000);
						 lblOrder->Text="阶数n为:"+numericUpDown_Input->Text;
					 }
					 else
					 {
						 int nOrder=3;
						 while(DrawSome(mthd,nOrder,Convert::ToInt32(listBox_nGrid->Text),3000)>Math::Pow(10,-Convert::ToDouble(numericUpDown_Input->Text)))
						 {
							 nOrder++;
							 
						 }
						 lblOrder->Text="阶数n为:"+Convert::ToString(nOrder);

					 }


				 }
			 }
	private: System::Void radioByError_CheckedChanged(System::Object^  sender, System::EventArgs^  e) {
				 groupBox1->Text="方式：以误差限计算";
				 lblInput->Text="误差限:10^-n";
			 }
	private: System::Void radioByOrder_CheckedChanged(System::Object^  sender, System::EventArgs^  e) {
				 groupBox1->Text="方式：以阶数计算";
				 lblInput->Text="阶数n";
			 }
	private: double DrawSome(Method mthd,int nOrder,int nGrid,int nPoint)
			 {

				 Bitmap ^ myBitmap = gcnew Bitmap(pictureBox1->Right,pictureBox1->Bottom);
				 Graphics ^ g = Graphics::FromImage(myBitmap);
				 pictureBox1->Image=myBitmap;
				 cvsFun=gcnew Canvus(pictureBox1->Width,pictureBox1->Height,Point(0,pictureBox1->Height/2),hScrollBar_xscale->Value,hScrollBar_yscale->Value);
				 //int nGrid=Convert::ToInt32(comboBox_nGrid->Text);


				 {//坐标系
					 g->DrawLine(System::Drawing::Pens::Black,0,pictureBox1->Bottom/2,pictureBox1->Right,pictureBox1->Bottom/2);
					 g->DrawLine(System::Drawing::Pens::Black,0,0,0,pictureBox1->Bottom);
					 for(double j=0;j<nGrid;j++)
					 {
						 double h = (j/ nGrid )*pictureBox1->Height;
						 g->DrawLine(System::Drawing::Pens::Black,0,h,pictureBox1->Right,h);
						 g->DrawString( String::Format("{0:E2}",cvsFun->Ytoy(h))/*Convert::ToString(cvsFun->Ytoy(h))*/,
							 gcnew System::Drawing::Font( "Arial",8 ), System::Drawing::Brushes::Blue, Point(0,h) );

						 h=(j/ nGrid )*pictureBox1->Width;
						 g->DrawLine(System::Drawing::Pens::Black,h,0,h,pictureBox1->Width);
						 g->DrawString( String::Format("{0:E2}",cvsFun->Xtox(h)),
							 gcnew System::Drawing::Font( "Arial",8 ), System::Drawing::Brushes::Blue, Point(h,pictureBox1->Height/2) );
					 }
				 }
				 double n=nPoint;
				 GraphicPoint ^p1=GraphicPoint::From(0/n,Math::Sin(0/n),cvsFun);
				 GraphicPoint ^p2=GraphicPoint::From(1/n,Math::Sin(1/n),cvsFun);
				 for(double i=0;i<n;i++)
				 {
					 double t=i*2*Math::PI/n;
					 g->DrawLine(System::Drawing::Pens::Red,p1->X(),p1->Y(),p2->X(),p2->Y());

					 p2=p1;
					 p1=GraphicPoint::From(t,Math::Sin(t),cvsFun);
				 }


				 p1=GraphicPoint::From(0/n,AF::AF_func(0/n,mthd,nOrder),cvsFun);
				 p2=GraphicPoint::From(1/n,AF::AF_func(1/n,mthd,nOrder),cvsFun);
				 for(double i=0;i<n;i++)
				 {
					 double t=i*2*Math::PI/n;
					 if(IsInCanvus(myBitmap->Width,myBitmap->Height,p1,p2))g->DrawLine(System::Drawing::Pens::Green,p1->X(),p1->Y(),p2->X(),p2->Y());

					 p2=p1;
					 p1=GraphicPoint::From(t,AF::AF_func(t,mthd,nOrder),cvsFun);
				 }				 



				 Bitmap ^ myBitmapErr = gcnew Bitmap(pictureBox2->Right,pictureBox2->Bottom);
				 Graphics ^ ge = Graphics::FromImage(myBitmapErr);
				 pictureBox2->Image=myBitmapErr;
				 double yscale=100000000000000;
				 double most_err=0;
				 double most_err_at=0;
				 for(double i=0;i<n;i++)
				 {

					 double t=i*2*Math::PI/n;
					 double temp=Math::Abs(Math::Sin(t)-AF::AF_func(t,mthd,nOrder));
					 if(temp>most_err)
					 {
						 most_err=temp;
						 most_err_at=t;
					 }
					 yscale=pictureBox2->Height/2/most_err;
				 }
				 yscale=yscale*0.9;
				 /*ge->DrawString( String::Format("最大误差={0:E2}",most_err),
				 gcnew System::Drawing::Font( "Arial",8 ), System::Drawing::Brushes::Blue, Point(cvsErr->xtoX(most_err_at),cvsErr->ytoY(most_err)) );*/
				 this->lblDisp2->Text=String::Format("最大误差: {0:E2}",most_err);
				 cvsErr=gcnew Canvus(pictureBox2->Width,pictureBox2->Height,Point(0,pictureBox2->Height/2),hScrollBar_xscale->Value,yscale);
				 {//坐标系
					 ge->DrawLine(System::Drawing::Pens::Black,0,pictureBox2->Bottom/2,pictureBox2->Right,pictureBox2->Bottom/2);
					 ge->DrawLine(System::Drawing::Pens::Black,0,0,0,pictureBox2->Bottom);
					 for(double j=0;j<nGrid;j++)
					 {
						 double h = (j/ nGrid )*pictureBox2->Height;
						 ge->DrawLine(System::Drawing::Pens::Black,0,h,pictureBox2->Right,h);
						 ge->DrawString( String::Format("{0:E2}",cvsErr->Ytoy(h)),
							 gcnew System::Drawing::Font( "Arial",8 ), System::Drawing::Brushes::Blue, Point(0,h) );
						 h=(j/ nGrid )*pictureBox2->Width;
						 ge->DrawLine(System::Drawing::Pens::Black,h,0,h,pictureBox2->Width);
						 ge->DrawString( String::Format("{0:E2}",cvsErr->Xtox(h)),
							 gcnew System::Drawing::Font( "Arial",8 ), System::Drawing::Brushes::Blue, Point(h,pictureBox2->Height/2) );
					 }
				 }

				 p1=GraphicPoint::From(0/n,Math::Sin(0)-AF::AF_func(0,mthd,nOrder),cvsErr);
				 p2=GraphicPoint::From(1/n,Math::Sin(1/n)-AF::AF_func(1/n,mthd,nOrder),cvsErr);
				 for(double i=0;i<n;i++)
				 {
					 double t=i*2*Math::PI/n;
					 if(IsInCanvus(myBitmap->Width,myBitmap->Height,p1,p2))ge->DrawLine(System::Drawing::Pens::Blue,p1->X(),p1->Y(),p2->X(),p2->Y());
					 p2=p1;
					 p1=GraphicPoint::From(t,Math::Sin(t)-AF::AF_func(t,mthd,nOrder),cvsErr);
				 }
				 return most_err;
			 }




	private: Boolean IsInCanvus(int w,int h,GraphicPoint^ p1,GraphicPoint^ p2)
			 {
				 if(p1->X()<0 ||p1->X()> w)return false;
				 if(p1->Y()<0 ||p1->Y()> h)return false;
				 if(p2->X()<0 ||p2->X()> w)return false;
				 if(p2->Y()<0 ||p2->Y()> h)return false;
				 return true;

			 }

	private: System::Void listBox_nGrid_SelectedIndexChanged(System::Object^  sender, System::EventArgs^  e) {
			 }
	};

}