Multivariate Spline Functions And Their Applications Book

Ch. 1	Introduction to Multivariate Spline Functions	1
1.1	Basic frame of multivariate spline functions	2
1.2	Generalized truncated power function and general representation of multivariate spline functions	10
1.3	Interpolation by multivariate spline functions	13
1.4	Weighted Spline and splines with different smoothness	18
1.5	Introduction to multivariate rational splines	21
1.6	N-Dimensional Spline Functions	22
Ch. 2	Multivariate spline spaces	27
2.1	Multivariate spline spaces on cross-cut partitions	27
2.2	Spline spaces on rectangular and simple cross-cut partitions	41
2.3	Spline spaces on type-1 triangulations	45
2.4	Spline spaces on type-2 triangulation	57
2.5	Spline spaces on some non-uniform triangulations	68
2.6	Spline spaces with boundary conditions on uniform type-1 and type-2 triangulations	76
2.7	Spline spaces with boundary conditions on non-uniform type-2 triangulations	89
2.8	Dimension of spline space S[subscript [kappa]][superscript [mu]] ([Delta]) on triangulations	92
2.9	Decomposition method for studying multivariate splines	111
Ch. 3	Other methods for studying multivariate spline functions	119
3.1	B-spline method	119
3.2	B-net method	134
3.3	The integral methods to construct bivariate splines	149
Ch. 4	Higher-dimensional spline spaces	163
4.1	Interpolation-conforming method	164
4.2	The dimension of higher dimensional spline spaces	185
4.3	The dimension of higher dimensional spline spaces on a star	198
4.4	Parameter-introducing skills for computing dimension of spline spaces	212
4.5	Spline functions defined on bivariate domain with holes and on trivariate type-2 triangulations	231
Ch. 5	Rational spline functions	247
5.1	C[superscript 0] rational functions over arbitrary convex polygons	249
5.2	C[superscript 1] rational interpolation spline functions over triangulations	254
5.3	C[superscript 2] rational interpolation spline functions over triangulations	264
5.4	C[superscript [mu]] rational interpolation spline functions over triangulations	273
5.5	Interpolation rational splines over regular quadrilateral partitions	282
Ch. 6	Piecewise algebraic curves and surfaces	301
6.1	Algebraic variety	302
6.2	Smoothing connection conditions of algebraic variety	309
6.3	Piecewise algebraic variety	318
6.4	The approximations of algebraic curves and surfaces	326
6.5	On Piecewise Algebraic Curve	353
6.6	Bezout Number of Piecewise Algebraic Curves	365
Ch. 7	Applications of multivariate spline functions in finite element method and CAGD	373
7.1	Multivariate interpolated smooth spline functions	375
7.2	Parametric surfaces	414
7.3	Smooth surface fittings of scattered data	439
7.4	Higher dimensional HCT and PS finite elements	451
7.5	Hierarchical basis in finite element methods	465
7.6	Automatic mesh generations and their applications	485
	References	495
	Index	509