  We discuss how Dokken's methods of approximate implicitization can be applied
to triangular B\'ezier surfaces in both the original and weak forms. The
matrices $\mathbf{D}$ and $\mathbf{M}$ that are fundamental to the respective
forms of approximate implicitization are shown to be constructed essentially by
repeated multiplication of polynomials and by matrix multiplication. A
numerical approach to weak approximate implicitization is also considered and
we show that symmetries within this algorithm can be exploited to reduce the
computation time of $\mathbf{M}.$ Explicit examples are presented to compare
the methods and to demonstrate properties of the approximations.
