Overview of the repository

All the code is written in src, with analytic_integrals.rs, green_integrals, quadratic_surface_approximation.rs having the main integral evaluation functions for near singular K, G, and singular K respectively. These files also have the algorithm for finding the bounds of integration. Code for the specific integrals $I_0, I_x, I_y, \ldots$ are in src/integrals.rs. Some examples for calculating the integral over the triangles are in src/lib/test_functions.rs, which is also the code used to generate the data in the paper.

Using the Rust code in other languages

Steps to Create the Rust Function Callable from MATLAB

1. Set Up the Rust Project

All functions that are to be called must be written in lib.rs in the following format:

#[no_mangle] // Prevent name mangling
pub extern "C" fn function_name(a: f64, b: f64) -> f64 {
  a + b
}

The #[no_mangle] attribute allows the function name to be called from C. The extern "C" specifies taht this function uses the C calling convention, making it compatible with C/C++.

2. Update Cargo.toml

Append the Cargo.toml file with

[lib]
crate-type = ["cdylib"]

This makes Rust build a dynamic library, which will be used by the C wrapper.

3. Build the shared library

Run

cargo build --release

and copy the .dll file (or .so, .dylib if not using windows) into a path that can be found by C/C++.

4. Create the C Wrapper for MEX

Create a new file mex_wrapper.c:

#include "mex.h"

// Declare the Rust function signature
extern double function_name(double a, double b);

// The MEX function interface
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
    if (nrhs != 2) {
        mexErrMsgIdAndTxt("rust_mex:add_two_numbers", "Two input arguments required.");
    }

    // Extract inputs from MATLAB
    double a = mxGetScalar(prhs[0]);
    double b = mxGetScalar(prhs[1]);

    // Call the Rust function
    double result = function_name(a, b);

    // Return the result to MATLAB
    plhs[0] = mxCreateDoubleScalar(result);
}

If it doesn't work, maybe you need to also include

// Load the DLL
    HMODULE hLib = LoadLibrary("my_rust_lib.dll");
    if (hLib == NULL) {
        mexErrMsgIdAndTxt("MATLAB:sum_elements:loadLibrary", "Failed to load the DLL.");
    }

This allows C to find the .dll file.

5. Compile the MEX Function

Open MATLAB and run the following command, specifying the paths to the Rust shared library and the C wrapper:

mex -I/path/to/rust/include -L/path/to/rust/target/release -lrust_mex mex_wrapper.c

Replace /path/to/rust/ with the actual path to your Rust project directory. -I specifies the include path for any headers. -L specifies the path to the compiled Rust shared library. -l tells the compiler to link with the rust_mex library.

Conclusion

All functions written in the lib.rs can be called by MATLAB.