递归的应用：最简单分形图形实现资源-CSDN下载

共29个文件

h：7个

cpp：6个

ico：2个

数据库应用

4星 · 超过85%的资源需积分: 50 22 浏览量 2002-12-25 00:00:00 上传评论 1 收藏 49KB RAR 举报

在编程世界中，递归是一种强大的工具，它允许函数或方法调用自身来解决复杂问题。递归在很多领域都有广泛的应用，特别是在算法设计、数据结构以及计算机图形学中。本示例通过创建一个最简单的分形图形来阐述递归的概念和实现方式。分形，简单来说，是一种自相似的几何形状，即无论放大多少倍，局部细节都与整体保持相似性。在分形图形的绘制中，递归是核心思想，因为每个小部分都可以用相同的方式生成，这就形成了自相似性。在C/C++中，我们可以定义一个函数，该函数负责绘制一个基本的分形图形元素，然后通过递归调用自身来创建更复杂的结构。例如，我们可以考虑著名的Sierpinski三角形。这个分形由三个等边三角形组成，它们的顶点共享，形成一个更大的等边三角形的中心。通过不断重复这一过程，我们可以在每一层添加更小的三角形，最终形成一个精细的分形图案。以下是一个简单的Sierpinski三角形的递归实现： ```cpp #include <iostream> using namespace std; // 定义绘图函数，参数为当前三角形的顶点坐标 void drawTriangle(int x1, int y1, int x2, int y2, int x3, int y3) { // 在这里可以实现实际的绘图操作，例如打印星号表示点 cout << "Drawing triangle with vertices: (" << x1 << "," << y1 << "), "; cout << "(" << x2 << "," << y2 << "), (" << x3 << "," << y3 << ")" << endl; } // 递归函数，用于创建Sierpinski三角形 void sierpinskiTriangle(int x1, int y1, int x2, int y2, int x3, int y3, int level) { if (level == 0) { // 基本情况，不再继续分割 drawTriangle(x1, y1, x2, y2, x3, y3); return; } // 计算中间点的坐标 int xm = (x1 + x2) / 2, ym = (y1 + y2) / 2; int xn = (x2 + x3) / 2, yn = (y2 + y3) / 2; int xm2 = (x1 + x3) / 2, ym2 = (y1 + y3) / 2; // 递归调用，绘制三个子三角形 sierpinskiTriangle(x1, y1, xm, ym, xm2, ym2, level - 1); sierpinskiTriangle(xm, ym, x2, y2, xn, yn, level - 1); sierpinskiTriangle(xm2, ym2, xn, yn, x3, y3, level - 1); } int main() { // 初始化初始三角形的顶点 int x1 = 0, y1 = 0; int x2 = 5, y2 = 0; int x3 = 2.5, y3 = sqrt(3.0) / 2; // 正等边三角形的顶点坐标 // 开始绘制分形，设置递归深度 int depth = 5; sierpinskiTriangle(x1, y1, x2, y2, x3, y3, depth); return 0; } ``` 在上述代码中，`drawTriangle()`函数负责绘制单个三角形，而`sierpinskiTriangle()`是递归函数，它根据当前三角形的顶点和递归层次来决定是否继续细分。当递归到指定深度（即基本情况）时，不再细分，而是直接绘制三角形。虽然这里的标签是"数据库应用"，但分形和递归的概念并不局限于某个特定的领域。实际上，递归的思想在数据库查询优化、数据结构（如树和图）的遍历、算法（如快速排序和二分查找）等方面都有所体现。然而，由于提供的标签与示例内容不符，我们没有深入讨论数据库相关的知识点。递归是一种强大的编程技术，它使我们能够解决复杂问题，如创建自相似的分形图形。通过理解和掌握递归，程序员可以设计出更加优雅和高效的解决方案。在学习C/C++或其他编程语言时，理解并熟练运用递归是至关重要的技能。

资源推荐

资源详情

资源评论

收起资源包目录

ksqx.rar （29个子文件）

ksqx

KSQX

KSQX.h 1KB

KSQXView.h 2KB

resource.h 638B

KSQX.dsw 533B

KSQX.APS 45KB

Debug

KSQX.ncb 57KB

codechina.txt 2KB

KSQX.plg 2KB

KSQXDoc.cpp 2KB

KSQXClass.h 772B

KSQXView.cpp 3KB

KSQXDoc.h 1KB

KSQX.rc 12KB

ReadMe.txt 4KB

KSQX.exe 44KB

res

KSQX.ico 1KB

Toolbar.bmp 1KB

KSQXDoc.ico 1KB

KSQX.rc2 396B

KSQXClass.cpp 2KB

MainFrm.h 2KB

KSQX.clw 3KB

StdAfx.cpp 206B

KSQX.dsp 5KB

MainFrm.cpp 2KB

KSQX.opt 54KB

StdAfx.h 1KB

代码中国源代码下载.htm 972B

KSQX.cpp 4KB

======================================================================== MICROSOFT FOUNDATION CLASS LIBRARY : KSQX ======================================================================== AppWizard has created this KSQX application for you. This application not only demonstrates the basics of using the Microsoft Foundation classes but is also a starting point for writing your application. This file contains a summary of what you will find in each of the files that make up your KSQX application. KSQX.dsp This file (the project file) contains information at the project level and is used to build a single project or subproject. Other users can share the project (.dsp) file, but they should export the makefiles locally. KSQX.h This is the main header file for the application. It includes other project specific headers (including Resource.h) and declares the CKSQXApp application class. KSQX.cpp This is the main application source file that contains the application class CKSQXApp. KSQX.rc This is a listing of all of the Microsoft Windows resources that the program uses. It includes the icons, bitmaps, and cursors that are stored in the RES subdirectory. This file can be directly edited in Microsoft Visual C++. KSQX.clw This file contains information used by ClassWizard to edit existing classes or add new classes. ClassWizard also uses this file to store information needed to create and edit message maps and dialog data maps and to create prototype member functions. res\KSQX.ico This is an icon file, which is used as the application's icon. This icon is included by the main resource file KSQX.rc. res\KSQX.rc2 This file contains resources that are not edited by Microsoft Visual C++. You should place all resources not editable by the resource editor in this file. ///////////////////////////////////////////////////////////////////////////// For the main frame window: MainFrm.h, MainFrm.cpp These files contain the frame class CMainFrame, which is derived from CFrameWnd and controls all SDI frame features. res\Toolbar.bmp This bitmap file is used to create tiled images for the toolbar. The initial toolbar and status bar are constructed in the CMainFrame class. Edit this toolbar bitmap using the resource editor, and update the IDR_MAINFRAME TOOLBAR array in KSQX.rc to add toolbar buttons. ///////////////////////////////////////////////////////////////////////////// AppWizard creates one document type and one view: KSQXDoc.h, KSQXDoc.cpp - the document These files contain your CKSQXDoc class. Edit these files to add your special document data and to implement file saving and loading (via CKSQXDoc::Serialize). KSQXView.h, KSQXView.cpp - the view of the document These files contain your CKSQXView class. CKSQXView objects are used to view CKSQXDoc objects. ///////////////////////////////////////////////////////////////////////////// Other standard files: StdAfx.h, StdAfx.cpp These files are used to build a precompiled header (PCH) file named KSQX.pch and a precompiled types file named StdAfx.obj. Resource.h This is the standard header file, which defines new resource IDs. Microsoft Visual C++ reads and updates this file. ///////////////////////////////////////////////////////////////////////////// Other notes: AppWizard uses "TODO:" to indicate parts of the source code you should add to or customize. If your application uses MFC in a shared DLL, and your application is in a language other than the operating system's current language, you will need to copy the corresponding localized resources MFC42XXX.DLL from the Microsoft Visual C++ CD-ROM onto the system or system32 directory, and rename it to be MFCLOC.DLL. ("XXX" stands for the language abbreviation. For example, MFC42DEU.DLL contains resources translated to German.) If you don't do this, some of the UI elements of your application will remain in the language of the operating system. /////////////////////////////////////////////////////////////////////////////

评论收藏

内容反馈