Helper function to resize and rotate contours using OpenCV

rotate_contour.py

import cv2
import numpy as np


def cart2pol(x, y):
    theta = np.arctan2(y, x)
    rho = np.hypot(x, y)
    return theta, rho


def pol2cart(theta, rho):
    x = rho * np.cos(theta)
    y = rho * np.sin(theta)
    return x, y


def rotate_contour(cnt, angle):
    M = cv2.moments(cnt)
    cx = int(M['m10']/M['m00'])
    cy = int(M['m01']/M['m00'])

    cnt_norm = cnt - [cx, cy]
    
    coordinates = cnt_norm[:, 0, :]
    xs, ys = coordinates[:, 0], coordinates[:, 1]
    thetas, rhos = cart2pol(xs, ys)
    
    thetas = np.rad2deg(thetas)
    thetas = (thetas + angle) % 360
    thetas = np.deg2rad(thetas)
    
    xs, ys = pol2cart(thetas, rhos)
    
    cnt_norm[:, 0, 0] = xs
    cnt_norm[:, 0, 1] = ys

    cnt_rotated = cnt_norm + [cx, cy]
    cnt_rotated = cnt_rotated.astype(np.int32)

    return cnt_rotated

scale_contour.py

import cv2
import numpy as np


def scale_contour(cnt, scale):
    M = cv2.moments(cnt)
    cx = int(M['m10']/M['m00'])
    cy = int(M['m01']/M['m00'])

    cnt_norm = cnt - [cx, cy]
    cnt_scaled = cnt_norm * scale
    cnt_scaled = cnt_scaled + [cx, cy]
    cnt_scaled = cnt_scaled.astype(np.int32)

    return cnt_scaled

I translate your code to C++

#include <algorithm>
#include <cmath>
#include <array>
#include <math.h>
using namespace cv;
using namespace std;
array<double,2> cart2pol(int &x,int &y){
    double theta=atan2(y,x);
    double rho=hypot(x,y);
    return array<double,2>{{theta,rho}};
}

Point pol2cart(double &theta,double  &rho)
{
    int x=ceil(rho*cos(theta));
    int y=ceil(rho*sin(theta));
    return Point(x,y);
}
  
vector<Point> rotate_contour(vector<Point> &cnt,float &angle){
Moments M=moments(cnt);
int cx= int(M.m10/M.m00);
int cy = int(M.m01/M.m00);
vector<Point>cnt_rot;
cnt_rot.reserve(cnt.size());
Point pcenter(cx,cy);
for (Point icnt : cnt)
{  
    Point tmp(icnt-pcenter);
   array<double,2> thetasRho=cart2pol(tmp.x,tmp.y);
   thetasRho[0]=thetasRho[0]+angle*M_PI/180;//no rounded to 360 (2*PI)
    cnt_rot.push_back(pol2cart(thetasRho[0],thetasRho[1])+pcenter);
}
return (cnt_rot); 
}