| chapter 1 introduction to multivariate spline functions 1.1 basic frame of multivariate spline functions. 1.2 generalized truncated power function and general representation of multivariate spline functions 1.3 interpolation by multivariate spline functions 1.4 weighted spline and splines with different smoothness 1.5 introduction to multivariate rational splines 1.6 n-dimensional spline functions chapter 2 multivariate spline spaces 2.1 multivariate spline spaces on cross-cut partitions 2.2 spline spaces on rectangular and simple cross-cut partitions 2.3 spline spaces on type-1 triangulations 2.4 spline spaces on type-2 triangulations 2.5 spline spaces on some non-uniform triangulations 2.6 spline spaces with boundary conditions on uniform type-1 and type-2 triangulations 2.7 spline spaces with boundary conditions on non-uniform type-2 triangulations 2.8 dimension of spline space skμ(δ) on triangulations 2.9 decomposition method for studying multivariate splines 2.9.1 examples chapter 3 other methods for studying multivariate spline functions 3.1 b-spline method .3.2 b-net method 3.3 the integral methods to construct bivariate splines chapter 4 higher-dimensional spline spaces 4.1 interpolation-conforming method 4.2 the dimension of higher dimensional spline spaces 4.3 the dimension of higher dimensional spline spaces on a star 4.4 parameter-introducing skill for computing dimension of spline spaces 4.5 spline functions defined on bivariate domain with holes and on trivariate type-2 triangulations 4.5.1 the dimension of spline spaces on domain with holes 4.5.2 the three dimensional spline spaces on type-2 partitions chapter 5 rational spline functions.. 5.1 c0 rational functions over arbitrary convex polygons 5.2 c1 rational interpolation spline functions over triangulations 5.3 c2 rational interpolation spline functions over triangulations 5.4 cu rational interpolation spline functions over triangulations 5.5 interpolation rational splines over regular quadrilateral partitions 5.5.1 c1 generalized wedge functions over quadrilateral elements 5.5.2 finding solutions of conforming equations and constructing c1 generalized wedge functions 5.5.3 c1 interpolation rational approximation operators over quadrilateral elements 5.5.4 the equivalent expression of c1 piecewise rational functions 5.5.5 the blending technique for c1 structure over quadrilateral elements chapter 6 piecewise algebraic curves and surfaces 6.1 algebraic variety 6.2 smoothing connection conditions of algebraic variety 6.3 piecewise algebraic variety 6.4 the approximations of algebraic curves and surfaces 6.4.1 the parametric approximations on conics 6.4.2 parametric approximations on conic polynomials 6.4.3 generic approximations of algebraic curves and surfaces 6.5 on piecewise algebraic curve 6.5.1 some examples 6.5.2 intersection of piecewise algebraic curves 6.5.3 local branches of piecewise algebraic curves 6.6 bezout number of piecewise algebraic curves 6.6.1 bezout's number bn(1,0; 1,0) 6.6.2 the bezout number of sm0(a) and sn0(a) chapter 7 applications of multivariate spline functions in finite element method and cagd 7.1 multivariate interpolated smooth spline functions 7.1.1 zenisek's theorem on interpolated finite element 7.1.2 hct scheme and hct type interpolations 7.1.3 powell-sabin scheme 7.1.4 the space scheme 7.1.5 fraeijs de veubeck-sander scheme 7.1.6 other refinement interpolation schemes 7.2 parametric surfaces 7.2.1 the smooth parametric surface fitting 7.2.2 tensor-product type parametric surfaces 7.2.3 several special parametric surfaces 7.2.4 parametric surface fittings 7.3 smooth surface fittings of scattered data 7.3.1 triangulation 7.3.2 some commonly used methods to evaluate partial derivatives and directional derivatives 7.3.3 the least square approximation 7.4 higher dimensional hct and ps finite elements 7.5 hierarchical basis in finite element methods 7.6 automatic mesh generations and their applications references index... |
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