A method based on canopy surfaces is presented for blending parametric surfaces. The blend designed using this method gives freedom to the designer in selecting i) the primitive surfaces to be blended, ii) the contact curves lying on them (in which the blend meets the primitives), iii) the endtangent directions along the contact curves (which are used to ensure tangentplane continuity), and iv) the shape of the cross-sectional curve. An important feature of this method, which is not seen in earlier methods, is the use of end tangents to ensure theC 1 continuity of iso-parametric curves across the junctions between the blend and the primitives in addition to the tangent-plane continuity.