Abstract: Tetrahedron can be formed with four sequence and non-coplanar points in space，and any points in it can be represented by barycentric coordinate system with space affine transform.Both regular algebraic patches of cubic and quadratic with three variables，which is constructed in the tetrahedron，represented in algebraic Bernstein-Bézier zero contour.The intersection set of both patches constructs a regular segment.The quadratic patches is fixed，and its parametric representation method is gained.The cubic patches reduce to three local factors through reducing Bernstein coefficients to control shape of curve，two of them are used to join segments into G2- continuity approximating curves for given sequence data in space，and the other is used to adjust shape of segment.The parametric representation of segment can be gained from quadratic patch and constrained equations with cubic patches.A G2-continuity approximate curve for a sequence points similar to cubic Bézier splines with four control points is generated.The method is quite different from popularly algebraic method by joining planar arc into a continuous curve，and the latter is also represented by barycentric coordinate system with planar affine transform.