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Volumn 7, Issue 1, 1996, Pages 1-15

High-speed computation of spline functions and applications

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; DIGITAL FILTERS; LOW PASS FILTERS; MATHEMATICAL MODELS; POLYNOMIALS; THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 0030105906     PISSN: 08999457     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-1098(199621)7:1<1::AID-IMA1>3.0.CO;2-C     Document Type: Article
Times cited : (2)

References (58)
  • 3
    • 0002316349 scopus 로고
    • On calculating B-splines
    • Carl de Boor, "On calculating B-splines, J. Approximation Theory, 6, 50-62 (1972).
    • (1972) J. Approximation Theory , vol.6 , pp. 50-62
    • De Boor, C.1
  • 4
    • 0001523399 scopus 로고
    • The numerical evaluation of B-splines
    • M. A. Cox, "The numerical evaluation of B-splines," J. Inst. Mathematics Application, 10, 134-149 (1972).
    • (1972) J. Inst. Mathematics Application , vol.10 , pp. 134-149
    • Cox, M.A.1
  • 7
    • 0023381474 scopus 로고
    • Adaptive forward differencing for rendering curves and surfaces
    • S.-L. Lien, M. Shantz, and V. Pratt, "Adaptive forward differencing for rendering curves and surfaces", ACM Computer Graphics, 21 (1987).
    • (1987) ACM Computer Graphics , vol.21
    • Lien, S.-L.1    Shantz, M.2    Pratt, V.3
  • 8
    • 33644896303 scopus 로고
    • Rendering cubic curves and surfaces with integer adaptive forward differencing
    • S.-L. Chang, M. Shantz, and R. Rocchetti, "Rendering cubic curves and surfaces with integer adaptive forward differencing. ACM Computer Graphics, 23 (1989).
    • (1989) ACM Computer Graphics , vol.23
    • Chang, S.-L.1    Shantz, M.2    Rocchetti, R.3
  • 12
    • 3342946011 scopus 로고
    • Knot insertion using forward differences
    • P. Barry and R. Goldman, Knot insertion using forward differences," Graphics Gems, IV, 251-255 (1994).
    • (1994) Graphics Gems , vol.4 , pp. 251-255
    • Barry, P.1    Goldman, R.2
  • 13
    • 0021622286 scopus 로고
    • Efficient evaluation for splines
    • W. Böhm, "Efficient evaluation for splines," Computing, 33, 171-177 (1984).
    • (1984) Computing , vol.33 , pp. 171-177
    • Böhm, W.1
  • 14
    • 0022027481 scopus 로고
    • The insertion algorithm
    • W. Böhm. "The insertion algorithm, Computer-Aided Design, 17, 58-59 (1985).
    • (1985) Computer-Aided Design , vol.17 , pp. 58-59
    • Böhm, W.1
  • 16
    • 0019227833 scopus 로고
    • Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics
    • E. Cohen, T. Lyche, and R. Riesenfeld, "Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics," Computer Graphics and Image Processing, 14, 87-111 (1980).
    • (1980) Computer Graphics and Image Processing , vol.14 , pp. 87-111
    • Cohen, E.1    Lyche, T.2    Riesenfeld, R.3
  • 17
    • 0025258072 scopus 로고
    • Knot insertion for Beta-spline curves and surfaces
    • B. Joe, "Knot insertion for Beta-spline curves and surfaces," ACM Transactions on Graphics, 9, 41-65 (1990).
    • (1990) ACM Transactions on Graphics , vol.9 , pp. 41-65
    • Joe, B.1
  • 18
    • 0021483580 scopus 로고
    • Knot line refinement algorithms for tensor product B-spline surfaces
    • T. Lyche, E. Cohen, and K. Morken, "Knot line refinement algorithms for tensor product B-spline surfaces, Computer Aided Geometric Design, 2, 133-139 (1985).
    • (1985) Computer Aided Geometric Design , vol.2 , pp. 133-139
    • Lyche, T.1    Cohen, E.2    Morken, K.3
  • 23
    • 3342966884 scopus 로고
    • Approximation Theory, Proceedings of a Symposium held at Lancaster, July, 1969. A. Talbot, ed., Academic Press, New York
    • D. C. Handscomb, Characterization of Best Spline Approximations with Free Knots. Approximation Theory, Proceedings of a Symposium held at Lancaster, July, 1969. A. Talbot, ed., Academic Press, New York, 1970.
    • (1970) Characterization of Best Spline Approximations with Free Knots
    • Handscomb, D.C.1
  • 24
    • 0002774748 scopus 로고
    • The least-squares fitting of cubic spline surfaces to general data sets
    • J. G. Hayes and J. Holliday, "The least-squares fitting of cubic spline surfaces to general data sets," J. Inst. Maths Appl., 14, 89-105 (1974).
    • (1974) J. Inst. Maths Appl. , vol.14 , pp. 89-105
    • Hayes, J.G.1    Holliday, J.2
  • 28
    • 33747818869 scopus 로고    scopus 로고
    • Approximation to data by splines with free knots
    • D. L. B. Jupp, "Approximation to data by splines with free knots," SIAM J. Numer. Anal., 15 (1978).
    • SIAM J. Numer. Anal. , vol.15 , pp. 1978
    • Jupp, D.L.B.1
  • 29
    • 0020813567 scopus 로고
    • Knot placement for piecement polynomial approximation of curves
    • G. E. Hölzle, "Knot placement for piecement polynomial approximation of curves," Computer Aided Design, 15 (1983).
    • (1983) Computer Aided Design , vol.15
    • Hölzle, G.E.1
  • 30
    • 0009933085 scopus 로고
    • An algorithm for smoothing differentiation and integration of experimental data using spline functions
    • P. Dierckx, "An algorithm for smoothing differentiation and integration of experimental data using spline functions," J. Computational Applied Mathematics, I, 165-184 (1973).
    • (1973) J. Computational Applied Mathematics , vol.1 , pp. 165-184
    • Dierckx, P.1
  • 31
    • 0039430024 scopus 로고
    • An algorithm for surface-fitting with spline functions
    • P. Dierckx, "An algorithm for surface-fitting with spline functions," IMA J. Numerical Analysis, 1, 267-283 (1981).
    • (1981) IMA J. Numerical Analysis , vol.1 , pp. 267-283
    • Dierckx, P.1
  • 32
    • 0042257901 scopus 로고    scopus 로고
    • A fast algorithm for smoothing data on a rectangular grid while using spline functions
    • P. Dierckx, "A fast algorithm for smoothing data on a rectangular grid while using spline functions," SIAM J. Numer. Anal., 19 (1982).
    • SIAM J. Numer. Anal. , vol.19 , pp. 1982
    • Dierckx, P.1
  • 33
    • 0000652188 scopus 로고
    • Unitary triangularization of a nonsymmetric matrix
    • A. S. Householder, "Unitary triangularization of a nonsymmetric matrix," J. Ass. Comput. Mach., 5, 339-342 (1958).
    • (1958) J. Ass. Comput. Mach. , vol.5 , pp. 339-342
    • Householder, A.S.1
  • 36
    • 85033830707 scopus 로고
    • Proceeding of the 24th Asilomar Conference on Signals, Systems, Computers, Nov., Pacific Grove, CA.
    • S.-Y. Wang and L. A. Ferrari, Automatic Data Visualization Using Spline Functions. Proceeding of the 24th Asilomar Conference on Signals, Systems, Computers, Nov., 1990, Pacific Grove, CA.
    • (1990) Automatic Data Visualization Using Spline Functions
    • Wang, S.-Y.1    Ferrari, L.A.2
  • 37
    • 0000873069 scopus 로고
    • A method for the solution of certain nonlinear problems in least squares
    • K. Levenberg, "A method for the solution of certain nonlinear problems in least squares." Q. Appl. Math., 2, 164-168 (1944).
    • (1944) Q. Appl. Math. , vol.2 , pp. 164-168
    • Levenberg, K.1
  • 38
    • 0000169232 scopus 로고
    • An algorithm for least squares estimation of nonlinear parameters
    • D. W. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," J. Soc. Indust. Appl. Math., 11, 431-41 (1963).
    • (1963) J. Soc. Indust. Appl. Math. , vol.11 , pp. 431-441
    • Marquardt, D.W.1
  • 39
    • 0015039199 scopus 로고
    • Techniques for designing finite-duration impulse response digital filters
    • L. R. Rabiner, "Techniques for designing finite-duration impulse response digital filters," IEEE Trans. Commun. Technol., com-19, 188-195 (1971).
    • (1971) IEEE Trans. Commun. Technol. , vol.COM-19 , pp. 188-195
    • Rabiner, L.R.1
  • 40
    • 11544317371 scopus 로고
    • Digital filters with equiripple or minimax responses
    • H. D. Helms, "Digital filters with equiripple or minimax responses," IEEE Trans. Audio Electroacoust., AU-19, 8793 (1971).
    • (1971) IEEE Trans. Audio Electroacoust. , vol.AU-19 , pp. 8793
    • Helms, H.D.1
  • 41
    • 0005460787 scopus 로고
    • A direct search procedure for designing finite duration impulse response filters
    • B. Gold and K. L. Jordan, Jr., "A direct search procedure for designing finite duration impulse response filters," IEEE Trans. Audio Electroacoust., AU-17, 33-36 (1969).
    • (1969) IEEE Trans. Audio Electroacoust. , vol.AU-17 , pp. 33-36
    • Gold, B.1    Jordan Jr., K.L.2
  • 43
    • 0015316461 scopus 로고
    • Chebyshev approximation for nonrecursive digital filters with linear phase
    • T. W. Parks and J. H. McClellan, "Chebyshev approximation for nonrecursive digital filters with linear phase," IEEE Trans. Circuit Theory, CT-19, 189-194 (1972).
    • (1972) IEEE Trans. Circuit Theory , vol.CT-19 , pp. 189-194
    • Parks, T.W.1    McClellan, J.H.2
  • 44
    • 0015682115 scopus 로고
    • A united approach to the design of optimum FIR linear-phase digital filters
    • J. H. McClellan and T. W. Parks, "A united approach to the design of optimum FIR linear-phase digital filters," IEEE Trans. Circuit Theory, CT-20, 697-701 (1973).
    • (1973) IEEE Trans. Circuit Theory , vol.CT-20 , pp. 697-701
    • McClellan, J.H.1    Parks, T.W.2
  • 46
    • 1542743831 scopus 로고
    • General computational methods of Tchebysheff approximation
    • E. Ya. Remez, "General computational methods of Tchebysheff approximation," Kiev, USSR, Atomic Energy Transl. 4491, pp. 1-85, 1957.
    • (1957) Kiev, USSR, Atomic Energy Transl. , vol.4491 , pp. 1-85
    • Remez, E.Ya.1
  • 47
    • 0016090362 scopus 로고
    • Interpolation, extrapolation, and reduction of computation speed in digital filters
    • M. G. Bellanger, J. L. Daguet, and G. P. Lepagnol, "Interpolation, extrapolation, and reduction of computation speed in digital filters," IEEE Trans. ASSP., ASSP-22 (1974).
    • (1974) IEEE Trans. ASSP. , vol.ASSP-22
    • Bellanger, M.G.1    Daguet, J.L.2    Lepagnol, G.P.3
  • 48
    • 0016588155 scopus 로고
    • Optimum FIR digital filter implementations for decimation, interpolation, and narrow-band filtering
    • R. E. Crochiere and L. R. Rabiner, "Optimum FIR digital filter implementations for decimation, interpolation, and narrow-band filtering," IEEE Trans. ASSP., ASSP-23 (1975).
    • (1975) IEEE Trans. ASSP. , vol.ASSP-23
    • Crochiere, R.E.1    Rabiner, L.R.2
  • 49
    • 3343001133 scopus 로고
    • Thinning digital filter: A piecewise-exponential approximation approach
    • G. F. Boudreaux and T. W. Parks, "Thinning digital filter: A piecewise-exponential approximation approach," IEEE ASSP, ASSP-31, 1 (1983).
    • (1983) IEEE ASSP , vol.ASSP-31 , pp. 1
    • Boudreaux, G.F.1    Parks, T.W.2
  • 50
    • 0020750048 scopus 로고
    • A new approach to FIR digital filters with fewer multipliers and reduced sensitivity
    • J. W. Adams and A. N. Willson, 'A new approach to FIR digital filters with fewer multipliers and reduced sensitivity," IEEE Trans. Circuits Systems, CAS-30, (1983).
    • (1983) IEEE Trans. Circuits Systems , vol.CAS-30
    • Adams, J.W.1    Willson, A.N.2
  • 53
    • 0021442830 scopus 로고
    • Interpolated finite impulse response filters
    • Y. Neuvo, D. Chengyu, and S. K. Mitra, "Interpolated finite impulse response filters," IEEE Trans. ASSP., ASSP-32 (1984).
    • (1984) IEEE Trans. ASSP. , vol.ASSP-32
    • Neuvo, Y.1    Chengyu, D.2    Mitra, S.K.3
  • 54
    • 0023327784 scopus 로고
    • Design of narrow-band FIR band-pass digital filters with reduced arithmetic complexity
    • Y. Neuvo, G. Rajan, and S. K. Mitra, "Design of narrow-band FIR band-pass digital filters with reduced arithmetic complexity," IEEE Trans. Circuits Systems, CAS-34 (1987).
    • (1987) IEEE Trans. Circuits Systems , vol.CAS-34
    • Neuvo, Y.1    Rajan, G.2    Mitra, S.K.3
  • 56
    • 3342994299 scopus 로고
    • Efficient digital filters using B-spline approximations
    • L. A. Ferrari, P. V. Sankar, J. Sklansky, and S. Leeman, "Efficient digital filters using B-spline approximations," CVGIP, 29, 358-360 (1985).
    • (1985) CVGIP , vol.29 , pp. 358-360
    • Ferrari, L.A.1    Sankar, P.V.2    Sklansky, J.3    Leeman, S.4
  • 58
    • 85033820638 scopus 로고    scopus 로고
    • A new approach to FIR filter design using B-spline functions
    • submitted
    • D. Pang, L. A. Ferrari, and P. V. Sankar, "A new approach to FIR filter design using B-spline functions," submitted to IEEE Trans. ASSP.
    • IEEE Trans. ASSP
    • Pang, D.1    Ferrari, L.A.2    Sankar, P.V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.