def compute_triangle_circumcenters(X, ei_dot_ei, ei_dot_ej):
    """Computes the circumcenters of all given triangles.
    """
    alpha = ei_dot_ei * ei_dot_ej
    alpha_sum = alpha[0] + alpha[1] + alpha[2]
    beta = alpha / alpha_sum[None]
    a = X * beta[..., None]
    cc = a[0] + a[1] + a[2]
    return cc
