rotation

#include <bits/stdc++.h>
#include <graphics.h>

using namespace std;

#define what_is(x) cerr << fixed << setprecision(2) << boolalpha << #x << " = " << x << endl

const double PI = acos(-1.0);

double xmid, ymid;
class Point{
    double x, y;
public:
    Point(double _x, double _y){
        x = _x;
        y = _y;
        y *= -1;/*reflect about x axis*/
        x += xmid;
        y += ymid;
    }
    Point():Point(0, 0) {}
    void setx(double _x){
        x = _x;
        x += xmid;
    }
    void sety(double _y){
        y = _y;
        y *= -1;/*reflect about x axis*/
        y += ymid;
    }
    double getx(){return x;}
    double gety(){return y;}
    string to_string(){
        char str[1000];
        sprintf(str, "x: %.2lf y: %.2lf", 1.0*x-xmid, 1.0*y-ymid);
        return str;
    }
};

void drawAxes(Point origin){
    int col = getcolor();
    setcolor(LIGHTCYAN);
    line(origin.getx()-origin.getx(), origin.gety(), origin.getx()+origin.getx(), origin.gety());
    line(origin.getx(), origin.gety()-origin.gety(), origin.getx(), origin.gety()+origin.gety());

    outtextxy(origin.getx()+1, origin.gety()+1, "O");
    outtextxy(origin.getx() + origin.getx() - textwidth("X")-1, origin.gety()+1, "X");
    outtextxy(origin.getx() - origin.getx(), origin.gety()+1, "X'");
    outtextxy(origin.getx()+1, origin.gety() - origin.gety(), "Y");
    outtextxy(origin.getx()+1, origin.gety() + origin.gety()-textheight("Y'"), "Y'");
    setcolor(col);
}

void drawGridLines(Point origin, int intv){
    int col = getcolor();
    setcolor(DARKGRAY);
    int stx = origin.getx();
    while(stx-intv > 0)
        stx -= intv;
    int sty = origin.gety();
    while(sty-intv > 0)
        sty -= intv;
    for(int i = stx; i < getmaxx(); i+=intv)
        if(i != origin.getx())
            line(i, 0, i, getmaxy());
    for(int i = sty; i < getmaxy(); i+=intv)
        if(i != origin.gety())
            line(0, i, getmaxx(), i);

    char msg[100];
    sprintf(msg, "Side of Square = %d pixel", intv);
    outtext(msg);
    setcolor(col);
}

void checkError(){
    int ecode = graphresult();
    if(ecode != grOk) {
        printf("Graphics error: %s\n", grapherrormsg(ecode));
        printf("Press any key to exit...");
        getch();
        exit(1);
    }
}

struct Matrix
{
    int row, col;
    vector<vector<double>>ele;
    Matrix(int _row, int _col){
        row = _row;
        col = _col;
        ele.resize(row);
        for(int i = 0; i < row; i++)ele[i].resize(col);
    }
    Matrix operator*(const Matrix& m)const
    {
        if(col != m.row){
            cout << "Matrices are incompatible. Can't multiply\n";
            return Matrix(0,0);
        }
        Matrix ret(row, m.col);
        for(int r = 0; r < row; r++){
            for(int c = 0; c < m.col; c++){
                ret.ele[r][c] = 0;
                for(int k = 0; k < col; k++){
                    ret.ele[r][c] += ele[r][k]*m.ele[k][c];
                }
            }
        }
        return ret;
    }
};

double toRadian(double deg)
{
    return PI*deg/180;
}

int main()
{
    int gdriver = DETECT;
    int gmode;
    initgraph(&gdriver, &gmode, NULL);
    xmid = getmaxx()/2;
    ymid = getmaxy()/2;
    checkError();
    Point origin;
    drawAxes(origin);
    drawGridLines(origin, 20);/* to show graph grid(if needed)*/

    /*do code*/
    double pix, piy;
    cout << "Enter Pivot point: ";
    cin >> pix >> piy;
    double px, py;
    cout << "Enter Point to rotate across pivot: ";
    cin >> px >> py;

    Matrix pivot(3, 1);
    pivot.ele[0][0] = pix;
    pivot.ele[1][0] = piy;
    pivot.ele[2][0] = 1;

    Matrix point(3, 1);
    point.ele[0][0] = px;
    point.ele[1][0] = py;
    point.ele[2][0] = 1;

    //draw before translation
    setcolor(LIGHTBLUE);
    Point pi(pivot.ele[0][0], pivot.ele[1][0]);
    Point p(point.ele[0][0], point.ele[1][0]);
    outtextxy(p.getx(), p.gety(), "P");
    line(pi.getx(), pi.gety(), p.getx(), p.gety());

    cout << "Enter rotation angle in degree: ";
    double ang;
    cin >> ang;

    ang = toRadian(ang);

    Matrix rotateMat(3, 3);
    rotateMat.ele[0][0] = cos(ang);
    rotateMat.ele[0][1] = -sin(ang);
    rotateMat.ele[1][0] = sin(ang);
    rotateMat.ele[1][1] = cos(ang);
    rotateMat.ele[2][2] = 1;

    Matrix translate(3, 3);
    translate.ele[0][0] = 1;
    translate.ele[1][1] = 1;
    translate.ele[2][2] = 1;
    translate.ele[0][2] = -pix;
    translate.ele[1][2] = -piy;

    Matrix invTranslate(3, 3);
    invTranslate.ele[0][0] = 1;
    invTranslate.ele[1][1] = 1;
    invTranslate.ele[2][2] = 1;
    invTranslate.ele[0][2] = pix;
    invTranslate.ele[1][2] = piy;

    //do translation to make pivot the origin
    point = translate*point;
    //do rotation
    point = rotateMat*point;
    //do translation to make previous origin as origin
    point = invTranslate*point;

    //draw after translation
    setcolor(CYAN);
    p = Point(point.ele[0][0], point.ele[1][0]);
    outtextxy(p.getx(), p.gety(), "P'");
    line(pi.getx(), pi.gety(), p.getx(), p.gety());
    getch();

    /*end code*/

    getch();
    closegraph();
    return 0;
}