Necessary and sufficient conditions under which the de Boor algorithm can be applied to evaluate points on a T-spline surface of bidegree (3, 3) are investigated. These de Boor-suitable (DS) T-splines are compared to the standard analysis-suitable (AS) T-splines. An algorithm is also developed to search in a T-mesh for the appropriate control points and blend them using the de Boor algorithm to compute the corresponding point on the T-spline surface.