Developments in bivariate spline interpolation

[1]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[2]  Larry L. Schumaker,et al.  Macro-elements and stable local bases for splines on Clough-Tocher triangulations , 2001, Numerische Mathematik.

[3]  Frank Zeilfelder,et al.  Bivariate spline interpolation with optimal approximation order , 2001 .

[4]  Günther Nürnberger,et al.  Interpolation by C 1 splines of degree q ≥4 on triangulations , 2000 .

[5]  Larry L. Schumaker,et al.  Locally linearly independent bases for bivariate polynomial spline spaces , 2000, Adv. Comput. Math..

[6]  Oleg Davydov,et al.  Interpolation by bivariate linear splines , 2000 .

[7]  Frank Zeilfelder,et al.  Interpolation by spline spaces on classes of triangulations , 2000 .

[8]  Tomas Sauer,et al.  Polynomial interpolation in several variables , 2000, Adv. Comput. Math..

[9]  Larry L. Schumaker,et al.  Nonexistence of Star-Supported Spline Bases , 1999, SIAM J. Math. Anal..

[10]  Frank Zeilfelder,et al.  Cubic Spline Interpolation on Nested Polygon Triangulations , 2000 .

[11]  Larry L. Schumaker,et al.  Stable Local Nodal Bases for C1 Bivariate Polynomial Splines , 2000 .

[12]  Optimal Interpolating Spaces Preserving Shape , 1999 .

[13]  Carla Manni,et al.  A local shape-preserving interpolation scheme for scattered data , 1999, Comput. Aided Geom. Des..

[14]  Paul Sablonnière,et al.  Subharmonicity and convexity properties of Bernstein polynomials and Bézier nets on triangles , 1999, Comput. Aided Geom. Des..

[15]  D. Hong,et al.  Some smoothness conditions and conformality conditions for bivariate quartic and quintic splines , 1999 .

[16]  Martin D. Buhmann,et al.  New Developments in Approximation Theory , 1999 .

[17]  Oleg Davydov,et al.  On almost interpolation and locally linearly independent bases , 1999 .

[18]  Frank Zeilfelder,et al.  Interpolation by Splines on Triangulations , 1999 .

[19]  Larry L. Schumaker,et al.  On the Approximation Power of Splines on Triangulated Quadrangulations , 1998 .

[20]  Larry L. Schumaker,et al.  On the approximation power of bivariate splines , 1998, Adv. Comput. Math..

[21]  Günther Nürnberger,et al.  Error analysis in interpolation by bivariate C1-splines , 1998 .

[22]  O. Davydov.  Locally linearly independent basis for C 1 bivariate splines of degree q ≥ 5 , 1998 .

[23]  Frank Zeilfelder,et al.  Approximation order of bivariate spline interpolation for arbitrary smoothness , 1998 .

[24]  G. Nürnberger,et al.  On bivariate spline spaces , 1998 .

[25]  Frank Zeilfelder,et al.  Spline interpolation on convex quadrangulations , 1998 .

[26]  G. Nürnberger,et al.  Lagrange interpolation by splines on triangulations , 1998 .

[27]  Frank Zeilfelder,et al.  Interpolation by cubic splines on triangulations , 1998 .

[28]  Oleg Davydov.  On Almost Interpolation , 1997 .

[29]  Charles K. Chui,et al.  Swapping Edges of Arbitrary Triangulations to Achieve the Optimal Order of Approximation , 1997 .

[30]  L. Schumaker,et al.  Scattered Data Interpolation Using C 2 Supersplines of Degree Six , 1997 .

[31]  Marion Walther,et al.  Gridded Data Interpolation with Restrictions on the First Order Derivatives , 1997 .

[32]  Oleg Davydov,et al.  Locally Linearly Independent Systems and Almost Interpolation , 1997 .

[33]  Günther Nürnberger,et al.  Multivariate Approximation and Splines , 1997 .

[34]  On Almost Interpolation by Multivariate Splines , 1997 .

[35]  Frank Zeilfelder,et al.  Interpolation by Bivariate Splines on Crosscut Partitions , 1997 .

[36]  Hans Strauss,et al.  A condition of Schoenberg-Whitney type for multivariate spline interpolation , 1996, Adv. Comput. Math..

[37]  Paul Sablonnière,et al.  Cr-finite elements of Powell-Sabin type on the three direction mesh , 1996, Adv. Comput. Math..

[38]  Günther Nürnberger,et al.  Approximation Order of Bivariate Spline Interpolation , 1996 .

[39]  Ming-Jun Lai,et al.  On C 2 quintic spline functions over triangulations of Powell-Sabin's type , 1996 .

[40]  Peter Alfeld.  Upper and lower bounds on the dimension of multivariate spline spaces , 1996 .

[41]  Ming-Jun Lai,et al.  Scattered data interpolation and approximation using bivariate C1 piecewise cubic polynomials , 1996, Comput. Aided Geom. Des..

[42]  Charles K. Chui,et al.  Construction of local C1 quartic spline elements for optimal-order approximation , 1996, Math. Comput..

[43]  M. Sommer,et al.  Interpolation by uni- and multivariate generalized splines , 1995 .

[44]  Don Hong,et al.  Stability of optimal-order approximation by bivariate splines over arbitrary triangulations , 1995 .

[45]  Günther Nürnberger,et al.  Bivariate spline interpolation at grid points , 1995 .

[46]  M. Laghchim-Lahlou,et al.  Quadrilateral finite elements of FVS type and class $C^\rho$ , 1995 .

[47]  Th.J. Ripmeester.  Upper bounds on the dimension of bivariate spline spaces and duality in the plane , 1995 .

[48]  Tommy R. Jensen,et al.  Graph Coloring Problems , 1994 .

[49]  Larry L. Schumaker,et al.  Wavelets, Images, and Surface Fitting , 1994 .

[50]  Paul Sablonniére,et al.  Hermite and Lagrange interpolation by quadratic splines on non-uniform criss-cross triangulations , 1994 .

[51]  F. Jeeawock-Zedek.  Operator norm and error bounds for interpolating quadratic splines on a non-uniform type-2 triangulation of a rectangular domain , 1994 .

[52]  Ming-Jun Lai,et al.  Approximation order from bivariate C1-cubics on a four-directional mesh is full , 1994, Comput. Aided Geom. Des..

[53]  P. Sablonnière,et al.  Triangular finite elements of HCT type and classCρ , 1994, Adv. Comput. Math..

[54]  J. M. Peña,et al.  A Marsden Type Identity for Periodic Trigonometric Splines , 1993 .

[55]  G. Nürnberger.  Approximation by univariate and bivariate splines , 1993 .

[56]  C. D. Boor,et al.  Box splines , 1993 .

[57]  C. D. Boor,et al.  A sharp upper bound on the approximation order of smooth bivariate PP functions , 1993 .

[58]  Hans-Peter Seidel,et al.  An introduction to polar forms , 1993, IEEE Computer Graphics and Applications.

[59]  Tianjun Wang,et al.  A C2-quintic spline interpolation scheme on triangulation , 1992, Comput. Aided Geom. Des..

[60]  Larry L. Schumaker,et al.  On dimension and existence of local bases for multivariate spline spaces , 1992 .

[61]  Carla Manni,et al.  On the dimension of bivariate spline spaces on generalized quasi-cross-cut partitions , 1992 .

[62]  Paul Dierckx,et al.  Algorithms for surface fitting using Powell-Sabin splines , 1992 .

[63]  F. Zedek.  Interpolation de Lagrange par des splines quadratiques sur un quadrilatère de $\mathbb {R}^2$ , 1992 .

[64]  Günther Nürnberger,et al.  Lagrange and hermite interpolation by bivariate splines , 1992 .

[65]  F. Jeeawock-Zedek.  Interpolation scheme by C1 cubic splines on a non uniform type-2 triangulation of a rectangular domain , 1992 .

[66]  Larry L. Schumaker,et al.  Super spline spaces of smoothnessr and degreed≥3r+2 , 1991 .

[67]  Xiquan Shi,et al.  The singularity of Morgan-Scott triangulation , 1991, Comput. Aided Geom. Des..

[68]  Allan Pinkus,et al.  Progress in Approximation Theory , 1991 .

[69]  Hong Dong,et al.  Spaces of bivariate spline functions over triangulation , 1991 .

[70]  L. Billera,et al.  The dimenstion and bases of divergence-free splines; a homological approach , 1991 .

[71]  Carla Manni,et al.  On the dimension of bivariate spline spaces over rectilinear partitions , 1991 .

[72]  Tony DeRose,et al.  A Tutorial Introduction to Blossoming , 1991 .

[73]  Charles K. Chui,et al.  On bivariate super vertex splines , 1990 .

[74]  Larry L. Schumaker,et al.  On the dimension of bivariate spline spaces of smoothnessr and degreed=3r+1 , 1990 .

[75]  W. Dahmen,et al.  Scattered data interpolation by bivariate C1-piecewise quadratic functions , 1990 .

[76]  Pia R. Pfluger,et al.  Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree , 1990, Comput. Aided Geom. Des..

[77]  Dwight Diener,et al.  Instability in the dimension of spaces of bivariate piecewise polynomials of degree 2 r and smoothness order r , 1990 .

[78]  Wolfgang Dahmen,et al.  Convexity and Bernstein polynomials on k -simploids , 1990 .

[79]  R. Jia.  Lower Bounds on the Dimension of Spaces of Bivariate Splines , 1990 .

[80]  Jacques Periaux,et al.  Proceedings of the Fifth International Symposium on Numerical Methods in Engineering , 1989 .

[81]  Larry L. Schumaker,et al.  On super splines and finite elements , 1989 .

[82]  M. Laghchim-Lahlou,et al.  Composite quadrilateral finite elements of class C r , 1989 .

[83]  G. Nürnberger.  Approximation by Spline Functions , 1989 .

[84]  Larry L. Schumaker,et al.  Dual bases for spline spaces on cells , 1988, Comput. Aided Geom. Des..

[85]  Klaus Höllig,et al.  Approximation power of smooth bivariate PP functions , 1988 .

[86]  R. Jia.  LOCAL APPROXIMATION ORDER OF BOX SPLINES , 1988 .

[87]  L. Billera.  Homology of smooth splines: generic triangulations and a conjecture of Strang , 1988 .

[88]  Larry L. Schumaker,et al.  The dimension of bivariate spline spaces of smoothnessr for degreed≥4r+1 , 1987 .

[89]  Thomas A. Grandine,et al.  An iterative method for computing multivariate C1 piecewise polynomial interpolants , 1987, Comput. Aided Geom. Des..

[90]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[91]  Paul Sablonnière,et al.  Error Bounds for Hermite Interpolation by Quadratic Splines on an α-Triangulation , 1987 .

[92]  Bruce R. Piper,et al.  An explicit basis for C 1 quartic by various bivariate splines , 1987 .

[93]  Larry L. Schumaker,et al.  Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree d 4r + 1 , 1987, Comput. Aided Geom. Des..

[94]  R. Meyling,et al.  Approximation by cubic C 1 -splines on arbitrary triangulations , 1987 .

[95]  Charles K. Chui,et al.  On multivariate Vertex splines and Applications , 1987, Topics in Multivariate Approximation.

[96]  C. D. Boor,et al.  B-Form Basics. , 1986 .

[97]  Gerald Farin,et al.  Triangular Bernstein-Bézier patches , 1986, Comput. Aided Geom. Des..

[98]  Tracy Whelan,et al.  A representation of a C2 interpolant over triangles , 1986, Comput. Aided Geom. Des..

[99]  Rong-Qing Jia,et al.  Approximation order from certain spaces of smooth bivariate splines on a three-direction mesh , 1986 .

[100]  Paul Sablonnière,et al.  Bernstein-Bézier methods for the construction of bivariate spline approximants , 1985, Comput. Aided Geom. Des..

[101]  Gerald E. Farin,et al.  A modified Clough-Tocher interpolant , 1985, Comput. Aided Geom. Des..

[102]  Paul Sablonnière,et al.  Composite finite elements of class Ck , 1985 .

[103]  R. Beatson,et al.  Monotonicity Preserving Surface Interpolation , 1985 .

[104]  Lothar Bamberger,et al.  Interpolation in Bivariate Spline Spaces , 1985 .

[105]  P. R. Pfluger,et al.  On the Dimension of the Spline Space S 2 1 (Δ) in Special Cases , 1985 .

[106]  Peter Alfeld,et al.  A bivariate C2 Clough-Tocher scheme , 1984, Comput. Aided Geom. Des..

[107]  Peter Alfeld,et al.  A trivariate clough-tocher scheme for tetrahedral data , 1984, Comput. Aided Geom. Des..

[108]  Ren-Hong Wang,et al.  Spaces of bivariate cubic and quartic splines on type-1 triangulations , 1984 .

[109]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[110]  C. Chui,et al.  Approximation Theory IV , 1984 .

[111]  Larry L. Schumaker,et al.  Bounds on the dimension of spaces of multivariate piecewise polynomials , 1984 .

[112]  Charles K. Chui,et al.  On smooth multivariate spline functions , 1983 .

[113]  Ren-Hong Wang,et al.  Multivariate spline spaces , 1983 .

[114]  Klaus Höllig,et al.  Approximation order from bivariate ¹-cubics: a counterexample , 1983 .

[115]  Rong-Qing Jia,et al.  Approximation by Smooth Bivariate Splines on a Three-Direction Mesh. , 1983 .

[116]  G. Alexits.  Approximation theory , 1983 .

[117]  C. Micchelli,et al.  Recent Progress in multivariate splines , 1983 .

[118]  W. Schempp,et al.  Multivariate Approximation Theory IV , 1989 .

[119]  G. Farin,et al.  C1 quintic interpolation over triangles: Two explicit representations , 1981 .

[120]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[121]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[122]  Robin Sibson,et al.  A Seamed Quadratic Element for Contouring , 1981, Comput. J..

[123]  Gerhard Heindl,et al.  Interpolation and Approximation by Piecewise Quadratic C1 — Functions of Two Variables , 1979 .

[124]  Graeme Fairweather.  An investigation of Romberg quadrature , 1978, TOMS.

[125]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[126]  Philippe G. Ciarlet,et al.  Interpolation error estimates for the reduced Hsieh-Clough-Tocher triangle , 1978 .

[127]  Malcolm A. Sabin,et al.  Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[128]  P. Percell.  On Cubic and Quartic Clough–Tocher Finite Elements , 1976 .

[129]  L. R. Scott,et al.  A nodal basis for ¹ piecewise polynomials of degree ≥5 , 1975 .

[130]  P. M. Prenter.  Splines and variational methods , 1975 .

[131]  P. G. Ciarlet,et al.  Sur l'élément de Clough et Tocher , 1974 .

[132]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[133]  G. Strang.  Piecewise polynomials and the finite element method , 1973 .

[134]  P. G. Ciarlet,et al.  General lagrange and hermite interpolation in Rn with applications to finite element methods , 1972 .

[135]  A. Ženíšek.  Interpolation polynomials on the triangle , 1970 .

[136]  D. W. Scharpf,et al.  The TUBA Family of Plate Elements for the Matrix Displacement Method , 1968, The Aeronautical Journal (1968).

[137]  E. H. Mansfield.  The Bending and Stretching of Plates , 1963 .

[138]  E. Wagner.  International Series of Numerical Mathematics , 1963 .