RcppParallel to estimate distances between rows of two matrix in R

I am trying to use RcppParrallel to estimate distances between rows of two 3D-matrix and return a new matrix. I saw examples of Parallel Distance Matrix Calculation using parallelFor, but these calculations come from a single matrix with a fixed size.

For example, let’s say that I have two matrices amat and bmat, the nrow of these could differ between them, but the ncol will always be 3. In R these may look like:

set.seed(10); amat <- matrix(rnorm(9, 2, 0.5), ncol = 3)  
set.seed(50); bmat <- matrix(rnorm(9, 2, 0.5), ncol = 3)

Using this example, the expected output is a matrix of nrow = amat.row()*bmat.row() = 9, and 5 columns (1 the row index of amat, 2:4 the row values of bmat, and 5 the euclidean distance between rows of matrices. Something like this:

    points        X        Y        Z  distance
 [1,]      0 1.579198 1.136198 1.704544 0.7737024
 [2,]      0 2.274835 2.262075 2.180414 1.0006478
 [3,]      0 2.016499 1.861068 2.487795 1.1036122
 [4,]      1 2.274835 2.262075 2.180414 0.5282677
 [5,]      1 2.016499 1.861068 2.487795 0.7362889
 [6,]      1 1.579198 1.136198 1.704544 1.0692094
 [7,]      2 1.579198 1.136198 1.704544 1.2079720
 [8,]      2 2.274835 2.262075 2.180414 1.3836957
 [9,]      2 2.016499 1.861068 2.487795 1.5157243

This is the code that I have so far, inspired in RcppParallel examples

// [[Rcpp::depends(RcppParallel)]] 
#include <RcppParallel.h>
using namespace RcppParallel;

struct Mdistance : public Worker { //function object

  // input 3D-matrix
  const RMatrix<double> amat;
  const RMatrix<double> bmat;

  // output matrix to write to
  RMatrix<double> rmat;

  // initialize from Rcpp input and output matrixes
  Mdistance(const NumericMatrix amat, const NumericMatrix bmat, NumericMatrix rmat)
    : amat(amat), bmat(bmat), rmat(rmat) {}

  // function call operator that work for the specified range (begin/end) #Not sure of this part
  void operator()(std::size_t begin, std::size_t end) {
    for (std::size_t i = 0; i < amat.nrow(); i++) {
      for (std::size_t j = 0; j < bmat.nrow(); j++) {

        // write to output matrix
           rmat((i + (j * amat.nrow())), 0) = i + 1; //Row index of amat
           rmat((i + (j * amat.nrow())), 1) = bmat(j, 0); //Value of column 0 of bmat
           rmat((i + (j * amat.nrow())), 2) = bmat(j, 1); //Value of column 1 of bmat
           rmat((i + (j * amat.nrow())), 3) = bmat(j, 2); //Value of column 2 of bmat
           rmat((i + (j * amat.nrow())), 4) = sqrt((pow(bmat(j,0) - amat(i,0), 2.0) + pow(bmat(j, 1) - amat(i, 1), 2.0) + pow(bmat(j, 2) - amat(i, 2), 2.0))); //Euclidean distance between rows
      }
    }
  }
};

// [[Rcpp::export]]
NumericMatrix Mdistance_parallel(NumericMatrix amat, NumericMatrix bmat) {

  // allocate the matrix we will return
  NumericMatrix rmat((amat.nrow()*bmat.nrow()), 5);

  // create the worker
  Mdistance Mdistance(amat, bmat, rmat);

  // call it with parallelFor
  parallelFor(0, (amat.nrow()*bmat.nrow()), MDistance);

  return rmat;
}

Any idea of how I can put this to work using RcppParallel? Obviously, I am using parallel because the nrow of amat and bmat tend to be close to 10 million. I was using other routines based on foreach in R. However, it takes a long time (> 1 day) and don't seem to be stable.

Thanks...

EDIT

Here is my example using just Rcpp

#include <Rcpp.h>
#include <cmath>
#include <algorithm>
using namespace Rcpp;

// [[Rcpp::export]]
NumericMatrix rcpp_distance(NumericMatrix amat, NumericMatrix bmat) {

  // allocate the matrix we will return
  NumericMatrix rmat((amat.nrow()*bmat.nrow()), 5);

  for (int i = 0; i < amat.nrow(); i++) {
    for (int j = 0; j < bmat.nrow(); j++) {

      rmat((i + (j * amat.nrow())), 0) = i + 1; //Row index of amat
      rmat((i + (j * amat.nrow())), 1) = bmat(j, 0); //Value of column 0 of bmat
      rmat((i + (j * amat.nrow())), 2) = bmat(j, 1); //Value of column 1 of bmat
      rmat((i + (j * amat.nrow())), 3) = bmat(j, 2); //Value of column 2 of bmat
      rmat((i + (j * amat.nrow())), 4) = sqrt((pow(bmat(j,0) - amat(i,0), 2.0) + pow(bmat(j, 1) - amat(i, 1), 2.0) + pow(bmat(j, 2) - amat(i, 2), 2.0))); //Euclidean distance between rows
    }
  }

  return rmat;
}