Bases and dimensions of trivariate spline functions possessing first order geometric continuity on two-patch domains were studied in [4]. It was shown that the properties of the spline space depend strongly on the type of the gluing data that is used to specify the relation between the partial derivatives along the interface between the patches. Locally supported bases were shown to exist for trilinear geometric gluing data (that corresponds to piecewise trilinear domain parameteriza-tions) and sufficiently high degree. The present paper is devoted to the approximation properties of these spline functions. We recall the construction of the basis functions and show how to compute them efficiently. In contrast to the results in [4], which relied on exact arithmetic operations in the field of rational numbers, we evaluate the coefficients by computations with standard floating point numbers. We then perform numerical experiments with L 2-projection in order to explore the approximation power of the resulting spline functions. Despite the existence of locally supported bases, we observe a reduction of the approximation order for low degrees, and we provide a theoretical explanation for this locking.