#include <bits/stdc++.h>
#include "opencv2/core.hpp"
#include "opencv2/imgproc.hpp"
#include "opencv2/video.hpp"
#include "opencv2/objdetect.hpp"
#include "opencv2/imgcodecs.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/ml.hpp"
#define inf 2333333333333333
#define N 1000010
#define p(a) putchar(a)
#define
 
 For(i,a,b) for(int i=a;i<=b;++i)
typedef unsigned char uchar;
//by war
//2020.10.4
using namespace std;
using namespace cv;
int T;
Mat image0,image1,new_image;
double w,h,eps=1e-7;

struct nose{
    double x;
    double y;
    int X;
    int Y;
}a[100];

void in(int &x){
    int y=1;char c=getchar();x=0
 
;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(int x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

double get_x(double x,double y){
    double r=sqrt(x*x+y*y);
    
 
if(r-1.0>=eps) return x;
    double theta=(1.0-r)*(1.0-r);
    return cos(theta)*x-sin(theta)*y;
}

double get_y(double x,double y){
    double r=sqrt(x*x+y*y);
    if(r-1.0>=eps) return y;
    double theta=(1.0-r)*(1.0-r);
    return sin(theta)*x+cos(theta)*y;
}

signed main(){
    image0 = imread("/Users/war/Downloads/Lisa.png");
    new_image = Mat::zeros(image0.size(), image0.type());
    w=(double)image0.cols*0.5;
    h=(double)image0.rows*0.5;
    For(i,0,image0.rows-1)
        For(j,0,image0.cols-1){
            a[0].x=(i-h)/h;a[0].y=(j-w)/w;
            a[1].x=get_x(a[0].x,a[0].y);
            a[1].y=get_y(a[0].x,a[0].y);
            a[1].x=a[1].x*h+h;
            a[1].y=a[1].y*w+w;
            For(k,0,2){
                auto t0=image0.at<Vec3b>(floor(a[1].x),floor(a[1].y))[k];
                auto t1=image0.at<Vec3b>(floor(a[1].x),ceil(a[1].y))[k];
                auto t2=image0.at<Vec3b>(ceil(a[1].x),floor(a[1].y))[k];
                auto t3=image0.at<Vec3b>(ceil(a[1].x),ceil(a[1].y))[k];
                auto t4=(1.0-(a[1].y-floor(a[1].y)))*t0+(a[1].y-floor(a[1].y))*t1;
                auto t5=(1.0-(a[1].y-floor(a[1].y)))*t2+(a[1].y-floor(a[1].y))*t3;
                auto t6=(1.0-(a[1].x-floor(a[1].x)))*t4+(a[1].x-floor(a[1].x))*t5;
                new_image.at<Vec3b>(i, j)[k] = t6;
            }
        }
    imshow("background", new_image);
    waitKey(0);
    return 0;
}