Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Box splines
Approximation order from bivariate C1-cubics on a four-directional mesh is full
Computer Aided Geometric Design
Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials
Computer Aided Geometric Design
On the Approximation Power of Splines on Triangulated Quadrangulations
SIAM Journal on Numerical Analysis
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
An explicit local basis for C1 cubic spline spaces over a triangulated quadrangulation
Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
Multivariate spline space over cross-cut partition
Computers & Mathematics with Applications
Computers & Mathematics with Applications
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In this paper, we mainly generalize the results in [H.W. Liu, D. Hong, D.Q. Cao, Bivariate C^1 cubic spline space over a nonuniform type-2 triangulation and its subspaces with boundary conditions, Comput. Math. Appl. 49 (2005), 1853-1865] from the type-2 triangulation to the so-called FVS triangulation (a triangulated quadrangulation). We study the bivariate C^1 cubic spline spaces S"3^1^,^0(@?@?) and S"3^1^,^1(@?@?) with homogeneous boundary conditions over an FVS triangulation @?@?. The dimensions are obtained and the locally supported bases are constructed for these spline spaces. Furthermore, we also study the explicit Bezier ordinates of the interpolation basis splines on a representative triangulated quadrilateral. The results of this paper can be applied in many fields such as the finite element method for partial differential equation, computer aided geometric design, numerical approximation, and so on.