Multivariate spline and algebraic geometry
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Multivariate weak spline function space
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
ACM SIGGRAPH 2003 Papers
Cayley-Bacharach theorem of piecewise algebraic curves
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Dimensions of spline spaces over T-meshes
Journal of Computational and Applied Mathematics
Structure and dimension of multivariate spline space of lower degree on arbitrary triangulation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Lagrange interpolation by bivariate splines on cross-cut partitions
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Multivariate spline space over cross-cut partition
Computers & Mathematics with Applications
The correspondence between multivariate spline ideals and piecewise algebraic varieties
Journal of Computational and Applied Mathematics
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The multivariate splines as piecewise polynomials have become useful tools for dealing with Computational Geometry, Computer Graphics, Computer Aided Geometrical Design and Image Processing. It is well known that the classical algebraic variety in algebraic geometry is to study geometrical properties of the common intersection of surfaces represented by multivariate polynomials. Recently the surfaces are mainly represented by multivariate piecewise polynomials (i.e. multivariate splines), so the piecewise algebraic variety defined as the common intersection of surfaces represented by multivariate splines is a new topic in algebraic geometry. Moreover, the piecewise algebraic variety will be also important in computational geometry, computer graphics, computer aided geometrical design and image processing. The purpose of this paper is to introduce some recent researches on multivariate spline, piecewise algebraic variety (curve), and their applications.