标题：冯玉瑜
人物简介
多年来一直从事本科生和研究生教学，主讲多门本科生课程，一直担任研究生的学位课程，如样条函数、（多变量）函数逼近论、计算代数几何，以及计算机辅助几何设计的教学工作。从1983年开始培养硕士生，1993年开始培养博士生，至今已培养毕业11名博士生，20多名硕士生。
从上世纪七十年代后期开始，从事三次样条、Bézier曲线等应用研究，1979－81年在美国Wisconsin大学数学研究中心，跟随de Boor教授系统地学习了样条函数和函数逼近论的基本理论，并完成了多篇研究论文。81年回国后，从事计算机辅助设计和图形学，以及数值逼近等方向的研究，并从上世纪八十年代开始，一直承担中科院、教育部（教委）和自然科学基金委的研究课题。
二十多年来已在国内外学术刊物上发表论文70多篇，其中20多篇论文发表在SIAM，CAGD, Graphical Models, JAT, CAT, BIT, JCAM等国际著名刊物上，早期主要从事曲面的保型和逼近、三角域上B－B曲面、样条函数等方面的研究，取得了一系列令国内外同行所关注的成果。近几年来，在代数曲面造型，把分片代数曲面应用于构造过渡曲面及补洞等方面做了具有国际水平的研究成果。曾获中科院自然科学贰等奖。最近在动态隐式曲线、曲面重构的理论和应用方面做了一些初步的工作。
工作简历
1 学习、工作简历

著作及论文
[1]钢闸门板、梁组合结构的有限元方法（与石钟慈合作），科大学报，Vol.6 (1976), 18-40.
[2]全正矩阵逆阵的p范数的一个性质，科大学报，Vol.10 (1980), 145-146.
[3]On the generalized Euler-Frobenius polynomials (with J. Kozak), J. of Approximation Theory, Vol.32 (1981), 327-338 (SCI)
[4]L-bound of L2-projections onto splines on a geometric mesh (with J. Kozak), J. of Approximation Theory, Vol.25 (1982), 64-76. (SCI)
[5]一类分片正交多项式快速变换的注记（与齐东旭合作），科大学报专辑(1983), 10-15.
[6]On the Haar and Walsh systems on a triangle (with D. X. Qi), J. of Computational Mathematics, Vol.1(1993), 223-232 (SCI)
[7]奇阶的Euler-Frobenius多项式最接近于?1的零点的估计，科大学报，Vol.13(1983), 288-292.
[8]Walsh-Fourier投影的极小性质（与奚梅成合作），第五届逼近论会议文集(1983), 189-193.
[9]Error bound for Bernstein-Bézier triangular approximation (with G. Z. Chang), J. of Computational Mathematics, Vol. 1(1983), No.4, 335-340. (SCI)
[10]有界变差函数的U富氏级数在不连续点的发散性（与奚梅成合作），科大学报数学专辑 (1983), 1-7.
[11]On the convergence of Fourier-U-series (with D. X. Qi), J. of USTC (Math. Issue) (1983), 7-17.
[12]计算几何与Bernstein多项式（与常庚哲合作），应用数学与计算数学，No.3(1984), 1-10.
[13]A sequence of piecewise orthogonal polynomials (with D. X. Qi), SIAM J. of Mathematical Analysis, Vol.15 (1984), No.4, 834-844. (SCI)
[14]在几何剖分平均节点上的样条插值，数学研究与评论，Vol.4(1984), No.2, 37-42.
[15]关于正交完备系U（与齐东旭合作），吉林大学学报（自然科学版），1984, No.2, 21-32.
[16]样条函数变差减缩算子迭代极限的简单证明（与常庚哲合作），系统科学与数学，Vol.4 (1984), 165-172
[17]An improved condition for the convexity of Bernstein-Bézier surfaces over triangles (with G. Z. Chang), Computer Aided Geometric Design, Vol.1 (1984), 279-283. (SCI)
[18]矩形域上Bernstein多项式的迭代极限（与常庚哲合作），工程数学，Vol.1, No.2 (1984), 137-141. 
[19]A new proof of the convexity of the Bernstein polynomials over triangles (with G. Z. Chang), The Chinese Annual of Mathematics, Vol.6 (1985), Series B, 141-146. (SCI)
[20]Limit of iterates for Bernstein polynomials defined on higher dimensional domains (with G. Z. Chang), A Monthly Journal of Science, Vol.31 (1986), 157-160 (SCI)
[21]矩形域上Bernstein多项式的逼近阶（与常庚哲合作），湖南数学年刊，Vol.5 (1985), 23-31.
[22]一类广义的显式样条插值格式，高校计算数学，Vol.8 (1986), 327-333.
[23]Rates of convergence of Bézier net over triangles, Computer Aided Geometric Design, Vol.4 (1987), 245-249. (SCI)
[24]Formula of degree elevation for B-splines and its applications (with J. W. Zhou), The Proceedings of the Fourth Chinese Approximation Theory Conference, 1987, 86-87.
[25]An approach to the interpolation of nonuniformly paced data (with J. Kozak), J. of Comput. and Math., 23 (1988), 169-178. (SCI)
[26]Farin定理的一个简单证明，湖南数学年刊，Vol.8, No.1-2 (1988), 60-63.
[27]A pair of compatible variations for Bernstein triangular polynomials (with G. Z. Chang), Approximation Theory and its Applications, Vol.5, No.1 (1989), 1-10. (SCI)
[28]Lipschitz constants for the Bernstein polynomials over a triangle, J. of Mathematical Research and Exposition, Vol.10, No.1 (1990), 105-108. (SCI)
[29]Gn-1-Functional splines for interpolation and approximation of surfaces and solids (with J. Hoschek, E. Hartmann and J. Li), International Series in Numerical Mathematics, 1990, Birkhauser Verlag Basel, 1-14.
[30]The convexity of families of adjoint patches for a Bézier triangular surfaces (with J. Kozak), Journal of Comp. Math., Vol.9, No.4 (1991), 301-304. (SCI)
[31]Asymptotic expantion formula for Bernstein polynomials defined on a simplex (with J. Kozak), Constru. Approx. Theory Vol.8 (1992), 49-59. (SCI)
[32]Limit of iterate for Bernstein polynomials defined over triangles (with F. L. Chen), Applied Math., A Journal of Chinese Univ., Vol.8, Ser.B (1993), 45-53.
[33]On the convexity for functional splines (with E. Hartmann), Computer Aided Geometric Design, 10 (1993), 127-142. (SCI)
[34]Positivity and convexity conditions for Bernstein-Bézier polynomials over rectangles (with Youdong Ding), J. of China Univ. of Sci. and Tech., Vol.23 (1993), 391-397.
[35]Criteria for copositive matrices of order four (with P. Li), Linear Algebra and its Application, 194(1993), 109-124. (SCI)
[36]Invariance of weak convex conditions of B-net with respect to subdivision (with F. L. Chen, H. L. Zhou), Computer Aided Geometric Design, 11 (1994), 97-107. (SCI)
[37]On convexity and Schoenberg’s variation diminishing splines (with J. Kozak), J. of China Univ. of Sci. and Tech., Vol.24 (1994), 129-134.
[38]Cutting corners preserves lipschitz continuity (with J. Kozak), Applied Math., A Journal of Chinese Univ., 9 (1994), 31-34.
[39]On the convexity of Bézier surfaces defined on a rectangular (with F. L. Chen), Compu. Math., J. of Chinese Uni., (special issue of Comp. Geome.), 1995, 7-13.
[40]On G2 continuous interpolatory composite quadratic Bézier curve (with J. Kozak), J. of Compu. And Applied Math., 72 (1996), 141-159. (SCI)
[41]The theorems on the B-B polynomials defined on a simplex in blossoming form (with J. Kozak), J. of Compu. Math., Vol.14, No.1 (1996), 64-70. (SCI)
[42]On the dimension of the C1 spline space for the Morgan-Scott triangulation from the blossoming approach (with J. Kozak and M. Zhang), Proceedings of the International Workshop, Advanced Topics in Multivaraite Approximation, edited by F. Foutanella, K. Jeffer, P. J. Lanrent, World Scientific, 1996, 71-86. (ISTP)
[43]On G2 continuous cubic spline interpolation, BIT, Vol.37, No.2 (1996), 312-332. (SCI)
[44]Tracing a planar algebraic curve (with F. L. Chen and J. Kozak), Applied Math., A Journal of Chinese Unv., 12B (1997), 15-24. 
[45]On spline interpolation of space data (with J. Kozak), International Conference on Mathematical Methods for Curves and Surfaces, Lille Hammer Norway, Jul 3-8, 1997. (ISTP)
[46]研究二元样条空间维数的blossoming方法（与陈之兵等合作），高校应用数学学报，几何设计专辑，13A(1998), 64-78.
[47]Morgan-Scott剖分上样条空间 的维数（与邓建松等合作），高校应用数学学报”几何设计专辑，13A(1998), 91-98.
[48]一种平面保凸插值构造光滑曲线的方法（与邓建松合作），高校应用数学学报”几何设计专辑，13A(1998), 1-8。
[49]Morgan-Scott剖分上样条空间 的维数（?与邓建松等合作），中国科大学报，1998, Vol. 21, No. 9, 855-859.
[50]关于自然样条空间的维数（与陈效群等合作），中国科大学报，1998, Vol.28, No.4, 377-383.
[51]多项式模上的全次数除法及其在CAGD中的应用(I)（与邓建松等合作），中国科大学报, Vol. 30, No.3, 263 – 269, 2000. 
[52]多项式模上的全次数除法及其在CAGD中的应用(II)（与邓建松等合作），中国科大学报, Vol. 30, No.4, 379 – 386, 2000.
[53]Blending pipe surfaces with G2 piecewise algebraic surfaces (with C. S. Chen etal.), 8th Proc. of Pacific Graphics, 2000, HongKong, China, 175 – 183. (ISTP)
[54]A note on the dimension of the bivariate spline space over the Morgan--Scott triangulation (with J. S. Deng etal), SIAM J. Numer. Anal., Vol.37, No.3(2000), 1021 – 1028. (SCI)
[55]The blossom approach to the dimension of the bivariate spline space, J. of Comp. Math., Vol.18, No.2, 2000, 183-198. (SCI)
[56]On the convexity of algebraic curves and surfaces (with X. Tang etal.), CAD/Graphics 2001, The 7th International Conference on Computer Aided Design and Computer Graphics, August, 2001, 40-48. (ISTP)
[57]Blending quadric surfaces with piecewise algebraic surfaces (with C. S. Chen etal.), Graphical Models 63, 212-227 (2001). (SCI)
[58]双曲面片的高精度多项式逼近（与曾芳玲等合作），计算机辅助设计与计算机图形学学报，Vol.14, No.10, 2002, 953-958. (EI)
[59]构造代数曲面的Gr?bner基方法（与娄文平等合作），计算机学报，Vol.25, No.6 (2002), 599-606. (EI)
[60]Subdivision for generating quadrics (with G. F. Wei etal.), Comp. Science, 2002, Vol.29, No.11(special issue), 33-35. (EI)
[61]High accurate approximation of the ellipsoid surface patch by bicubic Bézier polynomial (with F. L. Zeng etal.), The Second International Conference on Image and Graphics, Anhui, Hefei, 2002, 1032-1040. (ISTP)
[62]Perfect approximation of ellipsoid by polynomials (with F. L. Zeng etal), J. of Chinese software, 13 (2002), 526-531. (EI)
[63]One-sided approximation of polynomial under L1 norm (with J. S. Deng etal), J. of Comp. and Appl. Math., 144(2002), 161-174. (SCI)
[64]二次曲线的多项式逼近（与曾芳玲等合作），计算机辅助设计和计算机图形学学报，Vol.15, No.5, 2003, 547-551. (EI)
[65]The solution of difference equations and its applications in CAGD (with W. H. Tong etal), CAD/Graphics, 2003. (ISTP)
[66]Some notes on the best one-sided approximation of polynomials under L1 norm (with J. S. Deng etal.), CAD/Graphics, 2003. (ISTP)
[67]Polynomial interpolant approximation with geometric continuity is much better than Hermite interpolation (with F. L. Zeng etal.), J. of USTC, vol.23, No.2, 2003, 127-133.
[68]Yuyu Feng, Falai Chen, Jiansong Deng, Changsong Chen, Xing Tang, Constructing piecewise algebraic blending surfaces, in Geometric Computing, Lecture Notes Series on Computing, Vol.11, ed. Falai Chen and Dongming Wang, World Scientific, 34--64, 2004.
承担项目
基金 “曲面造型的代数几何方法”
1998.1 — 2000.12 国家自然科学基金 “计算几何中曲面设计的代数几何方法”
1999.1 — 2001.12 博士点基金 “曲面造型的代数几何方法和物理模型方法”
1995.1 — 1997.12 国家自然科学基金 “计算机辅助几何设计中代数曲面的研究”
1996.9 — 1998.12 中科院特别支持费 “CAGD中代数曲面的研究”
1995.1 — 1997.12 博士点基金 “计算几何中代数曲面的研究”
1993.9 — 1996.8 中科院特别支持费 “CAGD中曲面的表示和逼近”
1992.1 — 1994.12 国家自然科学基金 “计算几何中曲面设计的方法和理论”
1991.1 — 1993.12 中科院特别支持费 “CAGD中Bernstein-Bézier方法”
1988.1 — 1990.12 国家自然科学基金 “计算机辅助几何设计中曲面的表示和逼近”
1985 — 1987 高校基金准字2号 “计算机辅助几何设计中的B-B方法”
1983 — 1984 (83) 858号科学院科学基金 “计算几何与样条函数”