統計方法求π的方式：如果在正方形區域內隨機產生大量的均勻分佈的點，那麼落入內切圓和正方形中的隨機點個數的比值等於它們的面積之比。該比值乘以4，即為PI值。這就是統計方法求π的過程。

  視覺化求解過程是指：把產生隨機點的過程在影象中顯示,視覺化過程用到了opencv庫，利用opencv建立一個影象，並將資料寫入到影象資料的記憶體位置。

具體要求：

1、顯示一幅邊長為R的正方形（設定為0，全黑色），利用已經給出的畫圓函式，顯示出此正方形邊長為R/2的內切圓（設定為255，白色），圓心位於正方形中心；

2、通過系統函式rand（）產生隨機數，將每一個產生的點寫入影象的陣列，利用上次實驗的函式寫入影象並在上述的正方形顯示區域內顯示出來，賦值為

（一）：顯示一幅邊長為R的正方形，（設定為0，全黑色）：

先建立一個圖片（將P設定為500）：

int width = 500;
int height = 500;
IplImage* img = cvCreateImage(cvSize(width, height), IPL_DEPTH_8U, 1);
unsigned char *img_data = (unsigned char *)(img->imageData);
int width_step = img->widthStep;//width_step在灰度影象中表示一行資料的個數 
 

動態宣告一個二維陣列，用來儲存影象灰度值。

unsigned char **array_of_img; //開闢一個最初始的地址
	array_of_img = new unsigned char *[width_step];//開闢的行數
	array_of_img[0] = new unsigned char[width_step * width_step];//開闢的總空間
	
	
	for (int i = 1; i < width_step; ++i)//將每一行的行首地址賦值
	{
		array_of_img[i] = array_of_img[i-1] + width_step;
	}
 

for (int k = 0; k < width_step; ++k)
	{
		for (int j = 0; j < width_step; ++j) 
		{
			array_of_img[k][j] = 0;
		}
	}

void WriteImageData(unsigned char *src, int rows, int cols, int width_step,unsigned char ** &dst, bool flag)
{
     //src影象資料在記憶體的首地址  rows 行，cols列，dst二維陣列,flag 是否賦值的引數
        int count =0;
	for (int i = 0; i < cols; ++i)
	{
		for (int j = 0; j < rows; ++j)
		{
			if(flag) src[count] = dst[i][j];
			else src[count] = (unsigned char)'a';
			count++;
		}
	}
	printf("%d\n", count);
        return;
} 

呼叫opencv庫的畫圓函式，並顯示影象：

cvCircle(img, cvPoint(250,250), 250, cvScalar(255), 1, 8, 0);
cvNamedWindow("Image", CV_WINDOW_AUTOSIZE);
cvShowImage("Image", img);
cvWaitKey(0);

int sumSquare = 10000;
	int sumCircle = 0;

	double PI = 0.0;
	//generate 100 point(x,y)
	for(int count = 0; count < sumSquare; ++count)
	{
		//陣列中所有非零元素的值減5 使顏色變暗
		for (int n = 0; n < width_step; ++n) 
		{
			for(int m = 0; m < width_step; ++m )
			{
				if (array_of_img[m][n] > 0) 
				{
					array_of_img[m][n] -= 5;
				}
			}
		}
		//產生一個(0,1)之間的 隨機點
		double numA = (double)(rand())/(double)(RAND_MAX);
		double numB = (double)(rand())/(double)(RAND_MAX);
		
		//將[0,1]的點 放大到 [0,500] 之間
		int Px = (int) (numA * 500);
		int Py = (int) (numB * 500);
		//標示 剛生成的點
		array_of_img[Px][Py] = 255;
		// 把陣列寫入影象中
		WriteImageData(img_data, width_step, width_step,width_step, array_of_img, true);
		//重新繪製內切圓
		cvCircle(img, cvPoint(250,250), 250, cvScalar(255), 1, 8, 0);
		
		//判斷剛生成的點 是否在 園內
		if(((numA - 0.5)*(numA - 0.5) + (numB - 0.5)*(numB - 0.5)) <= 0.25)
		{
			sumCircle++;
		}
		cvShowImage("Image", img);//顯示影象
		cvWaitKey(50); //延時50毫秒
		
		PI =(double)sumCircle / (double)count;
		PI *= 4;
		printf("%d %d\n",sumCircle,count);
		printf("The PI is : %lf\n",PI);
	}

下面是完整的程式原始碼：

#include "cv.h"
#include "highgui.h"
#include <cstdio>

//read the img data from the Memory to own array
void ReadImageData(unsigned char *src, int rows, int cols, int width_step, unsigned char ** &dst)
{
	int count = 0;
	for (int i = 0; i < cols; ++i)
	{
		for (int j = 0; j < rows; ++j)
		{
			// printf("%c\n", *((unsigned char*)dst + rows * i + j));
			// *((unsigned char*)dst + rows * i + j) = src[count];
			dst[i][j] = src[count];
			count++;
		}
	}
	printf("%d\n", count);
	return;
}
//將使用者自己陣列儲存的輸入拷貝到影象相應的記憶體位置
//write the img data ( my array) to the memory
void WriteImageData(unsigned char *src, int rows, int cols, int width_step,unsigned char ** &dst, bool flag)
{
	int count =0;
	for (int i = 0; i < cols; ++i)
	{
		for (int j = 0; j < rows; ++j)
		{
			if(flag) src[count] = dst[i][j];
			else src[count] = (unsigned char)'a';
			count++;
		}
	}
	printf("%d\n", count);

	return;
}

int main(int args,char * argv[])
{
//	double PI = 0.0;
	//設定圖片的大小
	int width = 500;
	int height = 500;
	//利用opencv建立一個 空的圖片影象
	IplImage* img = cvCreateImage(cvSize(width, height), IPL_DEPTH_8U, 1);
	unsigned char *img_data = (unsigned char *)(img->imageData);
	//獲得 一行 大小
	int width_step = img->widthStep;
	
	//動態建立 正方形的 二維陣列  邊長為width
	unsigned char **array_of_img; 
	array_of_img = new unsigned char *[width_step];
	array_of_img[0] = new unsigned char[width_step * width_step];
	
	//為每一行 分配地址
	for (int i = 1; i < width_step; ++i)
	{
		array_of_img[i] = array_of_img[i-1] + width_step;
	}
	//初始化動態 宣告的二維陣列 0，即黑色
	for (int k = 0; k < width_step; ++k)
	{
		for (int j = 0; j < width_step; ++j) 
		{
			array_of_img[k][j] = 0;
		}
	}
	//將陣列的資料寫入到記憶體相應的位置
	WriteImageData(img_data, width_step, width_step,width_step, array_of_img, true);
	//畫圓
	cvCircle(img, cvPoint(250,250), 250, cvScalar(255), 1, 8, 0);
	
	cvNamedWindow("Image", CV_WINDOW_AUTOSIZE);//建立視窗
    cvShowImage("Image", img);//顯示影象
	cvWaitKey(0); //等待按鍵，開始取樣隨機點
	
	int sumSquare = 10000;
	int sumCircle = 0;

	double PI = 0.0;
	//generate 100 point(x,y)
	for(int count = 0; count < sumSquare; ++count)
	{
		//陣列中所有非零元素的值減5 使顏色變暗
		for (int n = 0; n < width_step; ++n) 
		{
			for(int m = 0; m < width_step; ++m )
			{
				if (array_of_img[m][n] > 0) 
				{
					array_of_img[m][n] -= 5;
				}
			}
		}
		//產生一個(0,1)之間的 隨機點
		double numA = (double)(rand())/(double)(RAND_MAX);
		double numB = (double)(rand())/(double)(RAND_MAX);
		
		//將[0,1]的點 放大到 [0,500] 之間
		int Px = (int) (numA * 500);
		int Py = (int) (numB * 500);
		//標示 剛生成的點
		array_of_img[Px][Py] = 255;
		// 把陣列寫入影象中
		WriteImageData(img_data, width_step, width_step,width_step, array_of_img, true);
		//重新繪製內切圓
		cvCircle(img, cvPoint(250,250), 250, cvScalar(255), 1, 8, 0);
		
		//判斷剛生成的點 是否在 園內
		if(((numA - 0.5)*(numA - 0.5) + (numB - 0.5)*(numB - 0.5)) <= 0.25)
		{
			sumCircle++;
		}
		cvShowImage("Image", img);//顯示影象
		cvWaitKey(50); //延時50毫秒
		
		PI =(double)sumCircle / (double)count;
		PI *= 4;
		printf("%d %d\n",sumCircle,count);
		printf("The PI is : %lf\n",PI);
	}
	PI =(double)sumCircle / (double)sumSquare;
	PI *= 4;
	printf("The PI is : %lf\n",PI);
	cvDestroyWindow("Image");//銷燬視窗
    cvReleaseImage(&img); //釋放影象

	delete [] array_of_img[0];
	delete [] array_of_img;

	return 0;
}