Methods for curve modeling with cubic algebraic curves based on geometric constraints are introduced in this paper. A 1-parameter family of cubic curves with four given points as well as two tangent lines at the endpoints is constructed in the first part of the paper. A 1-parameter family and 2-parameter family of cubic curve constructions are presented for interpolating two given endpoints and two given tangent lines as well as two given curvatures at the endpoints in the last part of the paper. 2001 Elsevier Science B.V. All rights reserved.