Evaluate a Bézier curve in Bernstein form at a point, using De Casteljau's algorithm, in the STAN language

bernstein.stan

functions {
  /**
  * Computes the value of a Bernstein polynomial of degree N at point t,
  * using De Casteljau's algorithm.
  *
  * @param t      Point in [0, 1] where the the polynomial will be evaluated.
  * @param beta   Vector of the real N + 1 coefficients of the polynomial.
  * @param N      Degree of the polynomial.
  *
  * @return Value of the polynomial at point t.
  */
  real bernstein(real t,
                 vector beta,
                 int N)
  {
    vector[N + 1] curr_beta;
    vector[N + 1] next_beta;
    for (i in 1:N + 1) {
        curr_beta[i] = beta[i];
    }
    for (j in 1:N + 1) {
      for (i in 1:N + 1 - j) {
        next_beta[i] = curr_beta[i] * (1 - t) + curr_beta[i + 1] * t;
      }
      curr_beta = next_beta;
    }
    return next_beta[1];
  }
}

De Casteljau's algorithm: https://en.m.wikipedia.org/wiki/De_Casteljau%27s_algorithm