The algebraicMesh function of my package cgalMeshes takes as inputs a trivariate polynomial \(P(x,y,z)\), a number \(\ell\) and some other parameters, and it returns a mesh of the isosurface defined by \(P(x,y,z) = \ell\). The computation of this mesh is done in C++ with the help of the Rcpp package and the CGAL library.

Each term of the polynomial is represented by a number, its coefficient, and a vector of three integers, the exponents of the three variables. So there is no difficulty to pass this polynomial from R to C++ with Rcpp.

I was wondering how one could pass the body of an arbitrary function \(f(x,y,z)\) from R to C++, and not only a polynomial, to compute a mesh of an isosurface \(f(x,y,z) = \ell\). I mean a simple function, whose body is given by an elementary mathematical expression. I know it is possible to pass a R function with Rcpp, as explained in the quick reference guide, but the evaluation of this function is not efficient enough for this situation.

Then I googled, and I discovered the C++ library Function Parser, written by Juha Nieminen and Joel Yliluoma. I gave it a try today; it works fine and it is easy to use.

Here is how to use it with Rcpp. First, download the zip file given in the above link. Unzip it and then, in the src folder of your package, put the files fparser.cc, fparser.hh, fpconfig.hh, fpoptimizer.cc, and the folder extrasrc. Now you’re ready to use Function Parser. Here is simple example:

// [[Rcpp::export]]
void helloWorld() {
  FunctionParser fp;
  fp.Parse("sqrt(x*x + y*y)", "x,y");
  double variables[2] = { 3.0, 4.0 };
  double result = fp.Eval(variables);
  Rcpp::Rcout << result << "\n";
}

Build the package and run helloWorld() in R. Then 5 will be printed in the console. Of course this example has no interest. Here is a more interesting one:

// [[Rcpp::export]]
double funeval(
  const std::string&        functionBody, 
  const std::string&        variableNames, 
  const Rcpp::NumericVector variableValues
) {
  FunctionParser fp;
  fp.Parse(functionBody, variableNames);
  const int nvariables = variableValues.size();
  double values[nvariables];
  for(int i = 0; i < nvariables; i++) {
    values[i] = variableValues(i);
  }
  const double result = fp.Eval(values);
  return result;
}

Build and run funeval("sqrt(x*x + y*y)", "x,y", c(3, 4)), you’ll get 5.