1341901124-武易-计算方法

计算方法实验报告1341901124 武易计算机科学与技术实验一——插值方法一实验目的通过本次上机实习，能够进一步加深对各种插值算法的理解；学会使用用三种类型的插值函数的数学模型、基本算法，结合相应软件（如VC/VB/Delphi/Matlab/JAVA/Turbo C）编程实现数值方法的求解。

并用该软件的绘图功能来显示插值函数，使其计算结果更加直观和形象化。

二实验内容通过程序求出插值函数的表达式是比较麻烦的，常用的方法是描出插值曲线上尽量密集的有限个采样点，并用这有限个采样点的连线，即折线，近似插值曲线。

取点越密集，所得折线就越逼近理论上的插值X n中，通过插值方法计算得到的对应纵坐标存放曲线。

本实验中将所取的点的横坐标存放于动态数组[]Y n中。

于动态数组[]三源程序清单Cahzhi.cpp// cahzhi.cpp : 定义应用程序的入口点。

//#include"stdafx.h"#include"cahzhi.h"#include"resource.h"#include"defSelf.h"#include<iostream>#include<vector>usingnamespace std;#define MAX_LOADSTRING 100// 全局变量:HINSTANCE hInst; // 当前实例WCHAR szTitle[MAX_LOADSTRING]; // 标题栏文本WCHAR szWindowClass[MAX_LOADSTRING]; // 主窗口类名WCHAR errorMsg[MAX_LOADSTRING];vector<POINT> vp; //取点vector<POINT> wvp; //相应窗体点POINT oriWin; //原点// 此代码模块中包含的函数的前向声明:ATOM MyRegisterClass(HINSTANCE hInstance);BOOL InitInstance(HINSTANCE, int);LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);int APIENTRY wWinMain(_In_HINSTANCE hInstance,_In_opt_HINSTANCE hPrevInstance,_In_LPWSTR lpCmdLine,_In_int nCmdShow){UNREFERENCED_PARAMETER(hPrevInstance);UNREFERENCED_PARAMETER(lpCmdLine);// TODO: 在此放置代码。

// 初始化全局字符串LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);LoadStringW(hInstance, IDC_CAHZHI, szWindowClass, MAX_LOADSTRING);LoadStringW(hInstance, IDS_ERROR, errorMsg, MAX_LOADSTRING);MyRegisterClass(hInstance);// 执行应用程序初始化:if (!InitInstance (hInstance, nCmdShow)){return FALSE;}HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_CAHZHI)); MSG msg;// 主消息循环:while (GetMessage(&msg, nullptr, 0, 0)){if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg)){TranslateMessage(&msg);DispatchMessage(&msg);}}return (int) msg.wParam;}//// 函数: MyRegisterClass()//// 目的: 注册窗口类。

//ATOM MyRegisterClass(HINSTANCE hInstance){WNDCLASSEXW wcex;wcex.cbSize = sizeof(WNDCLASSEX);wcex.style = CS_HREDRAW | CS_VREDRAW;wcex.lpfnWndProc = WndProc;wcex.cbClsExtra = 0;wcex.cbWndExtra = 0;wcex.hInstance = hInstance;wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_CAHZHI));wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_CAHZHI);wcex.lpszClassName = szWindowClass;wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));return RegisterClassExW(&wcex);}//// 函数: InitInstance(HINSTANCE, int)//// 目的: 保存实例句柄并创建主窗口//// 注释://// 在此函数中，我们在全局变量中保存实例句柄并// 创建和显示主程序窗口。

//BOOL InitInstance(HINSTANCE hInstance, int nCmdShow){hInst = hInstance; // 将实例句柄存储在全局变量中HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);if (!hWnd){return FALSE;}ShowWindow(hWnd, nCmdShow);UpdateWindow(hWnd);return TRUE;}//// 函数: WndProc(HWND, UINT, WPARAM, LPARAM)//// 目的: 处理主窗口的消息。

//// WM_COMMAND - 处理应用程序菜单// WM_PAINT - 绘制主窗口// WM_DESTROY - 发送退出消息并返回////LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam) {staticint cxClient, cyClient;static POINT curPoint;static uint16_t choiceL=0, choiceN=0, choiceS=0;static TCHAR curCoor[10];staticint coorLen;static RECT txtRect;SetRect(&txtRect, 0, 0, 100,20);vLConverToW(vp, oriWin, wvp);static vector<POINT> vpDeal;vpDeal.clear();vpDeal = pointDeal(vp);switch (message){case WM_COMMAND:{int wmId = LOWORD(wParam);// 分析菜单选择:switch (wmId){case ID_RDPT:rnPointCt(vp, -cxClient / 2, cxClient / 2, -cyClient / 2, cyClient / 2, 5);InvalidateRect(hWnd, NULL, true);break;case ID_LARGERANGE:if (vp.size()) {choiceL = true;InvalidateRect(hWnd, NULL, false);}break;case ID_NEWTON:if (vp.size()) {choiceN = true;InvalidateRect(hWnd, NULL, false);}break;case ID_SPLINE:if (vp.size()) {choiceS = true;InvalidateRect(hWnd, NULL, false);}break;case ID_CLEAR:vp.clear();choiceL = choiceN = choiceS = false;InvalidateRect(hWnd, NULL, true);break;case IDM_ABOUT:DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);break;case IDM_EXIT:DestroyWindow(hWnd);break;default:return DefWindowProc(hWnd, message, wParam, lParam);}}break;case WM_SIZE:{cxClient = LOWORD(lParam);cyClient = HIWORD(lParam);oriWin.x = cxClient / 2;oriWin.y = cyClient / 2;}break;case WM_LBUTTONDOWN:{curPoint.x = LOWORD(lParam) - oriWin.x;curPoint.y = oriWin.y - HIWORD(lParam);vp.push_back(curPoint);InvalidateRect(hWnd, NULL, true);}break;case WM_MOUSEMOVE:{curPoint.x = LOWORD(lParam) - oriWin.x;curPoint.y = oriWin.y - HIWORD(lParam);InvalidateRect(hWnd, &txtRect, true);}break;case WM_PAINT:{PAINTSTRUCT ps;HDC hdc = BeginPaint(hWnd, &ps);// TODO: 在此处添加使用 hdc 的任何绘图代码...//创建并选中画笔和画刷HPEN hPen, hOldPen;LOGBRUSH logBrush;HBRUSH hBrush, hOldBrush;hPen = CreatePen(PS_SOLID, 1, RGB(0, 0, 0));hOldPen = (HPEN)SelectObject(hdc, hPen);logBrush.lbColor = RGB(10, 220, 10);logBrush.lbHatch = HS_CROSS;logBrush.lbStyle = BS_SOLID;hBrush = CreateBrushIndirect(&logBrush);hOldBrush = (HBRUSH)SelectObject(hdc, hBrush);//cursorcoorLen = wsprintf(curCoor, TEXT("(%d,%d)"), curPoint.x, curPoint.y);DrawText(hdc, curCoor, coorLen, &txtRect, DT_CENTER);//绘坐标//x轴MoveToEx(hdc, 0, cyClient / 2, NULL);LineTo(hdc, cxClient, cyClient / 2);LineTo(hdc, cxClient - 5, cyClient/2 - 5);MoveToEx(hdc, cxClient, cyClient / 2, NULL);LineTo(hdc, cxClient - 5, cyClient / 2 + 5);TextOut(hdc, cxClient - 10, cyClient / 2 + 5, TEXT("x"), 1);//y轴MoveToEx(hdc, cxClient / 2, cyClient, NULL);LineTo(hdc, cxClient / 2, 0);LineTo(hdc, cxClient / 2 - 5, 5);MoveToEx(hdc, cxClient / 2, 0, NULL);LineTo(hdc, cxClient / 2 + 5, 5);TextOut(hdc, cxClient / 2 + 5, 5, TEXT("y"), 1);TextOut(hdc, cxClient / 2-10, cyClient / 2+5, TEXT("O"), 1);//绘说明hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(255, 25, 25)));MoveToEx(hdc, 8 * cxClient / 10, cyClient / 10, NULL);LineTo(hdc, 9 * cxClient / 10, cyClient / 10);TextOut(hdc, 9 * cxClient / 10 + 5, cyClient / 10-6, TEXT("Largrange"), 9);DeleteObject(SelectObject(hdc, hPen));hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(25, 255, 25)));MoveToEx(hdc, 8 * cxClient / 10, cyClient / 10+20, NULL);LineTo(hdc, 9 * cxClient / 10, cyClient / 10+20);TextOut(hdc, 9 * cxClient / 10 + 5, cyClient / 10 +20- 6, TEXT("Newton"), 6);DeleteObject(SelectObject(hdc, hPen));hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(25, 25, 255)));MoveToEx(hdc, 8 * cxClient / 10, cyClient / 10 + 40, NULL);LineTo(hdc, 9 * cxClient / 10, cyClient / 10 + 40);TextOut(hdc, 9 * cxClient / 10 + 5, cyClient / 10 + 40 - 6, TEXT("Spline"), 6);DeleteObject(SelectObject(hdc, hPen));//绘随机点for (size_t i = 0; i < wvp.size(); i++){Ellipse(hdc, wvp[i].x - 3, wvp[i].y - 3, wvp[i].x + 3, wvp[i].y + 3);}//绘插值曲线if (choiceL){POINT tPoint;hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(255, 25, 25)));MoveToEx(hdc, -5, 0, NULL);for (int x = -cxClient / 2;x < cxClient / 2;x++){tPoint.x = x;tPoint.y = Largrange(vpDeal, tPoint.x);LineTo(hdc, LConvertToW(oriWin, tPoint).x, LConvertToW(oriWin, tPoint).y);}DeleteObject(SelectObject(hdc, hPen));}if (choiceN) {POINT tPoint;hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(25, 255, 25)));MoveToEx(hdc, -5, 0, NULL);for (int x = -cxClient / 2;x < cxClient / 2;x++){tPoint.x = x;tPoint.y = Newton(vpDeal, tPoint.x);LineTo(hdc, LConvertToW(oriWin, tPoint).x, LConvertToW(oriWin, tPoint).y);}DeleteObject(SelectObject(hdc, hPen));}if (choiceS) {POINT tPoint;hPen = (HPEN)SelectObject(hdc, CreatePen(PS_SOLID, 1, RGB(25, 25, 255)));for (int x = vpDeal[0].x,i = 0; x <= vpDeal[vp.size()-1].x; x++,i++){tPoint.x = x;tPoint.y = spline(10,vpDeal,-10,tPoint.x);if (i == 0)MoveToEx(hdc, LConvertToW(oriWin, tPoint).x,LConvertToW(oriWin, tPoint).y, NULL);LineTo(hdc, LConvertToW(oriWin, tPoint).x, LConvertToW(oriWin, tPoint).y);}DeleteObject(SelectObject(hdc, hPen));}DeleteObject(hPen);SelectObject(hdc, hOldPen);DeleteObject(hBrush);SelectObject(hdc, hOldBrush);EndPaint(hWnd, &ps);}break;case WM_DESTROY:PostQuitMessage(0);break;default:return DefWindowProc(hWnd, message, wParam, lParam);}return 0;}// “关于”框的消息处理程序。