This work is dedicated to the computation of Euler Beta-function B-spline (BFBS) finite elements (FE) on triangulations, and to comparative visualization of their graphs. BFBS are a particular type of generalized expo-rational B-splines (GERBS)  and provide a piecewise polynomial modification of the true expo-rational B-splines (ERBS) . The organization of the exposition is, as follows. First, we derive new formulae for triangular BFBS FE having
smoothness at the vertices
∈ ℕ. Second, we provide visualization of their graphs. Third, we compare the interpolatory and fitting properties of the new triangular BFBS FE of different polynomial degrees on two model surfaces used as a benchmark manifold.