메뉴 건너뛰기




Volumn 23, Issue 5, 2006, Pages 419-438

Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices

Author keywords

Ck continuity; Characteristic map; Extraordinary vertices; Matrix valued surface subdivision; Matrix valued templates; Surface shape control

Indexed keywords

COMPUTATIONAL GEOMETRY; FUNCTIONS; MATRIX ALGEBRA; OPTIMIZATION; PARAMETER ESTIMATION; VECTORS;

EID: 33747113064     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2006.02.001     Document Type: Article
Times cited : (10)

References (43)
  • 1
    • 0023999814 scopus 로고
    • Conditions for tangent plane continuity of recursively generated B-splines
    • Ball A.A., and Storry J.T. Conditions for tangent plane continuity of recursively generated B-splines. ACM Trans. Graphics 7 (1988) 83-102
    • (1988) ACM Trans. Graphics , vol.7 , pp. 83-102
    • Ball, A.A.1    Storry, J.T.2
  • 2
    • 0018035441 scopus 로고
    • Recursively generated B-splines surfaces on arbitrary topological meshes
    • Catmull E., and Clark J. Recursively generated B-splines surfaces on arbitrary topological meshes. Computer-Aided Design 10 (1978) 350-355
    • (1978) Computer-Aided Design , vol.10 , pp. 350-355
    • Catmull, E.1    Clark, J.2
  • 3
  • 4
    • 2342629332 scopus 로고    scopus 로고
    • Convergence of multivariate non-stationary vector subdivision schemes
    • Charina M., and Conti C. Convergence of multivariate non-stationary vector subdivision schemes. Appl. Numer. Anal. 49 (2004) 43-354
    • (2004) Appl. Numer. Anal. , vol.49 , pp. 43-354
    • Charina, M.1    Conti, C.2
  • 5
    • 0003352571 scopus 로고
    • Multivariate Splines
    • SIAM Publ., Philadelphia
    • Chui C.K. Multivariate Splines. NSF-CBMS Series vol. 54 (1988), SIAM Publ., Philadelphia
    • (1988) NSF-CBMS Series , vol.54
    • Chui, C.K.1
  • 6
    • 0346849805 scopus 로고    scopus 로고
    • Surface subdivision schemes generated by refinable bivariate spline function vectors
    • Chui C.K., and Jiang Q.T. Surface subdivision schemes generated by refinable bivariate spline function vectors. Appl. Comput. Harmonic Anal. 15 (2003) 147-162
    • (2003) Appl. Comput. Harmonic Anal. , vol.15 , pp. 147-162
    • Chui, C.K.1    Jiang, Q.T.2
  • 7
    • 21644487458 scopus 로고    scopus 로고
    • 2-splines for multi-level data representation and surface display
    • 2-splines for multi-level data representation and surface display. Math Comput. 74 (2005) 1369-1390
    • (2005) Math Comput. , vol.74 , pp. 1369-1390
    • Chui, C.K.1    Jiang, Q.T.2
  • 8
    • 0033239768 scopus 로고    scopus 로고
    • Regularity of multivariate refinable functions
    • Cohen A., Gröchenig K., and Villemoes L.F. Regularity of multivariate refinable functions. Constr. Approx. 15 (1999) 241-255
    • (1999) Constr. Approx. , vol.15 , pp. 241-255
    • Cohen, A.1    Gröchenig, K.2    Villemoes, L.F.3
  • 9
    • 0018040207 scopus 로고
    • Analysis of the behaviour of recursive division surfaces near extraordinary points
    • Doo D.W.H., and Sabin M.A. Analysis of the behaviour of recursive division surfaces near extraordinary points. Computer-Aided Design 10 (1978) 356-360
    • (1978) Computer-Aided Design , vol.10 , pp. 356-360
    • Doo, D.W.H.1    Sabin, M.A.2
  • 10
    • 84976724020 scopus 로고
    • A butterfly subdivision scheme for surface interpolation with tension control
    • Dyn N., Levin D., and Gregory J.A. A butterfly subdivision scheme for surface interpolation with tension control. ACM Trans. Graphics 2 (1990) 160-169
    • (1990) ACM Trans. Graphics , vol.2 , pp. 160-169
    • Dyn, N.1    Levin, D.2    Gregory, J.A.3
  • 11
    • 0033548979 scopus 로고    scopus 로고
    • Edge and vertex insertion for a class of subdivision surfaces
    • Habib A., and Warren J. Edge and vertex insertion for a class of subdivision surfaces. Computer Aided Geometric Design 16 (1999) 223-247
    • (1999) Computer Aided Geometric Design , vol.16 , pp. 223-247
    • Habib, A.1    Warren, J.2
  • 12
    • 0036003389 scopus 로고    scopus 로고
    • Quincunx fundamental refinable functions and quincunx biorthogonal wavelets
    • Han B., and Jia R.Q. Quincunx fundamental refinable functions and quincunx biorthogonal wavelets. Math Comput. 71 (2002) 165-196
    • (2002) Math Comput. , vol.71 , pp. 165-196
    • Han, B.1    Jia, R.Q.2
  • 13
    • 5644297306 scopus 로고    scopus 로고
    • Multivariate refinable Hermite interpolants
    • Han B., Yu T., and Piper B. Multivariate refinable Hermite interpolants. Math. Comput. 73 (2004) 1913-1935
    • (2004) Math. Comput. , vol.73 , pp. 1913-1935
    • Han, B.1    Yu, T.2    Piper, B.3
  • 15
    • 22844456721 scopus 로고    scopus 로고
    • Characterization of smoothness of multivariate refinable functions in Sobolev spaces
    • Jia R.Q. Characterization of smoothness of multivariate refinable functions in Sobolev spaces. Trans. Amer. Math. Soc. 351 (1999) 4089-4112
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 4089-4112
    • Jia, R.Q.1
  • 16
    • 0346878763 scopus 로고    scopus 로고
    • Approximation power of refinable vectors of functions
    • Wavelet Analysis and Applications, Amer. Math. Soc., Providence, RI
    • Jia R.Q., and Jiang Q.T. Approximation power of refinable vectors of functions. Wavelet Analysis and Applications. AMS/IP Stud. Adv. Math. vol. 25 (2002), Amer. Math. Soc., Providence, RI 155-178
    • (2002) AMS/IP Stud. Adv. Math. , vol.25 , pp. 155-178
    • Jia, R.Q.1    Jiang, Q.T.2
  • 17
    • 0142200354 scopus 로고    scopus 로고
    • Spectral analysis of transition operators and its applications to smoothness analysis of wavelets
    • Jia R.Q., and Jiang Q.T. Spectral analysis of transition operators and its applications to smoothness analysis of wavelets. SIAM J. Matrix Anal. Appl. 24 (2003) 1071-1109
    • (2003) SIAM J. Matrix Anal. Appl. , vol.24 , pp. 1071-1109
    • Jia, R.Q.1    Jiang, Q.T.2
  • 18
    • 0032384592 scopus 로고    scopus 로고
    • Vector subdivision schemes and multiple wavelets
    • Jia R.Q., Riemenschneider S.D., and Zhou D.X. Vector subdivision schemes and multiple wavelets. Math. Comp. 67 (1998) 1533-1563
    • (1998) Math. Comp. , vol.67 , pp. 1533-1563
    • Jia, R.Q.1    Riemenschneider, S.D.2    Zhou, D.X.3
  • 19
    • 0001730758 scopus 로고    scopus 로고
    • Multivariate matrix refinable functions with arbitrary matrix dilation
    • Jiang Q.T. Multivariate matrix refinable functions with arbitrary matrix dilation. Trans. Amer. Math. Soc. 351 (1999) 2407-2438
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 2407-2438
    • Jiang, Q.T.1
  • 20
    • 0038547747 scopus 로고    scopus 로고
    • Triangular sqrt(3)-subdivision schemes: the regular case
    • Jiang Q.T., and Oswald P. Triangular sqrt(3)-subdivision schemes: the regular case. J. Comput. Appl. Math. 156 (2003) 47-75
    • (2003) J. Comput. Appl. Math. , vol.156 , pp. 47-75
    • Jiang, Q.T.1    Oswald, P.2
  • 21
    • 0037971977 scopus 로고    scopus 로고
    • sqrt(3)-subdivision schemes: maximal sum rule orders
    • Jiang Q.T., Oswald P., and Riemenschneider S.D. sqrt(3)-subdivision schemes: maximal sum rule orders. Constr. Approx. 19 (2003) 437-463
    • (2003) Constr. Approx. , vol.19 , pp. 437-463
    • Jiang, Q.T.1    Oswald, P.2    Riemenschneider, S.D.3
  • 22
    • 0034446865 scopus 로고    scopus 로고
    • Kobbelt, L., 2000. sqrt(3)-subdivision. In: SIGGRAPH Computer Graphics Proceedings, pp. 103-112
  • 23
  • 24
    • 2942731465 scopus 로고    scopus 로고
    • sqrt(2) subdivision for quadrilateral meshes
    • Li G.Q., Ma W.Y., and Bao H.J. sqrt(2) subdivision for quadrilateral meshes. Visual Computer 20 (2004) 180-189
    • (2004) Visual Computer , vol.20 , pp. 180-189
    • Li, G.Q.1    Ma, W.Y.2    Bao, H.J.3
  • 25
    • 33747093921 scopus 로고    scopus 로고
    • Loop, C., 1987. Smooth subdivision surfaces based on triangles. Master's thesis, University of Utah, Department of Mathematics, Salt Lake City
  • 26
    • 0032281718 scopus 로고    scopus 로고
    • On vector subdivision
    • Micchelli C.A., and Sauer T. On vector subdivision. Math. Z. 229 (1998) 621-674
    • (1998) Math. Z. , vol.229 , pp. 621-674
    • Micchelli, C.A.1    Sauer, T.2
  • 27
    • 24644465107 scopus 로고    scopus 로고
    • Designing composite triangular subdivision schemes
    • Oswald P. Designing composite triangular subdivision schemes. Computer Aided Geometric Design 22 (2005) 659-679
    • (2005) Computer Aided Geometric Design , vol.22 , pp. 659-679
    • Oswald, P.1
  • 28
    • 0038485753 scopus 로고    scopus 로고
    • Composite primal/dual sqrt(3)-subdivision schemes
    • Oswald P., and Schröder P. Composite primal/dual sqrt(3)-subdivision schemes. Computer Aided Geometric Design 20 (2003) 135-164
    • (2003) Computer Aided Geometric Design , vol.20 , pp. 135-164
    • Oswald, P.1    Schröder, P.2
  • 29
    • 0031245869 scopus 로고    scopus 로고
    • The simplest subdivision scheme for smoothing polyhedra
    • Peters J., and Reif U. The simplest subdivision scheme for smoothing polyhedra. ACM Trans. Graphics 16 (1997) 34-73
    • (1997) ACM Trans. Graphics , vol.16 , pp. 34-73
    • Peters, J.1    Reif, U.2
  • 30
    • 0347594463 scopus 로고    scopus 로고
    • Analysis of algorithms generalizing B-spline subdivision
    • Peters J., and Reif U. Analysis of algorithms generalizing B-spline subdivision. SIAM J. Numer. Anal. 35 (1998) 728-748
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 728-748
    • Peters, J.1    Reif, U.2
  • 32
    • 0003413039 scopus 로고    scopus 로고
    • Preprint 04/98, Fakultät für Informatik, Universität Karlsuhe, Germany, available at
    • k-subdivision surfaces at extraordinary points. Preprint 04/98, Fakultät für Informatik, Universität Karlsuhe, Germany, available at (1998). http://i33www.ira.uka.de
    • (1998) k-subdivision surfaces at extraordinary points
    • Prautzsch, H.1
  • 33
    • 0001880616 scopus 로고    scopus 로고
    • 2-subdivision algorithm
    • Geometric Modelling. Farin G., Bieri H., Brunnet G., and DeRose T. (Eds), Springer Verlag, New York
    • 2-subdivision algorithm. In: Farin G., Bieri H., Brunnet G., and DeRose T. (Eds). Geometric Modelling. Computing Suppl vol. 13 (1998), Springer Verlag, New York 217-224
    • (1998) Computing Suppl , vol.13 , pp. 217-224
    • Prautzsch, H.1    Umlauf, G.2
  • 35
    • 0029271013 scopus 로고
    • A unified approach to subdivision algorithms near extraordinary vertices
    • Reif U. A unified approach to subdivision algorithms near extraordinary vertices. Computer Aided Geometric Design 21 (1995) 153-174
    • (1995) Computer Aided Geometric Design , vol.21 , pp. 153-174
    • Reif, U.1
  • 36
    • 0032342028 scopus 로고    scopus 로고
    • TURBS-topologically unrestricted rational B-splines
    • Reif U. TURBS-topologically unrestricted rational B-splines. Constr. Approx. 14 (1998) 57-77
    • (1998) Constr. Approx. , vol.14 , pp. 57-77
    • Reif, U.1
  • 37
    • 33747141621 scopus 로고    scopus 로고
    • Schweitzer, J.E., 1996. Analysis and application of subdivision surfaces. PhD thesis, University of Washington, Dept. of Computer Science and Engineering, Seattle
  • 38
    • 0032338133 scopus 로고    scopus 로고
    • Refinable function vectors
    • Shen Z.W. Refinable function vectors. SIAM J. Math. Anal. 29 (1998) 235-250
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 235-250
    • Shen, Z.W.1
  • 39
    • 0034364817 scopus 로고    scopus 로고
    • Analyzing the characteristic map of triangular subdivision schemes
    • Umlauf G. Analyzing the characteristic map of triangular subdivision schemes. Constr. Approx. 16 (2000) 145-155
    • (2000) Constr. Approx. , vol.16 , pp. 145-155
    • Umlauf, G.1
  • 42
    • 0000931011 scopus 로고    scopus 로고
    • 1-continuity of subdivision surfaces
    • 1-continuity of subdivision surfaces. SIAM J. Numer. Anal. 37 (2000) 1677-1708
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 1677-1708
    • Zorin, D.1
  • 43
    • 0034343560 scopus 로고    scopus 로고
    • Smoothness of subdivision on irregular meshes
    • Zorin D. Smoothness of subdivision on irregular meshes. Constr. Approx. 16 (2000) 359-397
    • (2000) Constr. Approx. , vol.16 , pp. 359-397
    • Zorin, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.