References
- Kumar, V., Burns, D., Dutta, D. and Hoffmann, C., 1999, "A Framework for Object Modeling," Computer-Aided Design, Vol. 31, No. 9, pp. 541-556. https://doi.org/10.1016/S0010-4485(99)00051-2
- Watari, F., Kondo, H., Matsuo, S., Miyao, R., Yokoyama, A., Omori, M., Hirai, T., Tamura, Y., Uo, M., Ohara, N. and Kawasaki, T., 2003, "Development of Functionally Graded Implant and Dental Post for Bio-Medical Application," Materials Science Forum, Vol. 423-425, pp. 321-326. https://doi.org/10.4028/www.scientific.net/MSF.423-425.321
- Shackelford, J. F., 1999, Bioceramics: Applications of Ceramic and Glass Materials in Medicine, Trans Tech Publications.
- Pise, U. V., Bhatt, A. D., Srivastava, R. K. and Warkhedkar, R. M., 2009, "A B-Spline Based Heterogeneous Modeling and Analysis of Proximal Femur with Graded Element," Journal of Biomechanics, Vol. 42, No. 12, pp. 1981-1988. https://doi.org/10.1016/j.jbiomech.2009.05.019
- Warkhedkar, R. M. and Bhatt, A. D., 2009, "Material-Solid Modeling of Human Body: A Heterogeneous B-Spline Based Approach," Computer-Aided Design, Vol. 41, No. 8, pp. 586-597. https://doi.org/10.1016/j.cad.2008.10.016
- Kou, X. Y. and Tan, S. T., 2007, "Heterogeneous Object Modeling: A Review," Computer-Aided Design, Vol. 39, No. 4, pp. 284-301. https://doi.org/10.1016/j.cad.2006.12.007
- Chandru, V., Manohar, S. and Prakash, C. E., 1995, "Voxel-Based Modeling for Layered Manufacturing," IEEE Computer Graphics and Applications, Vol. 15, No. 6, pp. 42-47. https://doi.org/10.1109/38.469516
- Cho, J. R. and Ha, D. Y., 2002, "Optimal Tailoring of 2D Volume-Fraction Distributions for Heat-Resisting Functionally Graded Materials using FDM," Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 29-30, pp. 3195-3211. https://doi.org/10.1016/S0045-7825(02)00256-6
- Jackson, T. R., 2000, Analysis of Functionally Graded Material Object Representation Methods, Ph.D. thesis, Massachusetts Institute of Technology.
- Shin, K.-H. and Dutta, D., 2001, "Constructive Representation of Heterogeneous Objects," Journal of Computing and Information Science in Engineering, Vol. 1, No. 3, pp. 205-217. https://doi.org/10.1115/1.1403448
- Shin, K.-H., 2011, "Modeling of Time-Variant Heterogeneous Objects in Micro-System Packages," Journal of Mechanical Science and Technology, Vol. 25, No. 5, pp. 1119-1128. https://doi.org/10.1007/s12206-011-0227-0
- Adzhiev, V., Kartasheva, E., Kunii, T., Pasko, A. and Schmitt, B., 2003, "Hybrid Cellular-functional Modeling of Heterogeneous Objects," Journal of Computing and Information Sciences in Engineering, Vol. 2, No. 4, pp. 312-322.
- Biswas, A., Shapiro, V. and Tsukanov, I., 2004, "Heterogeneous Material Modeling with Distance Field," Computer Aided Geometric Design, Vol. 21, No. 3, pp. 215-242. https://doi.org/10.1016/j.cagd.2003.08.002
- Siu, Y. K. and Tan, S. T., 2002, "Source-Based Heterogeneous Solid Modeling," Computer Aided Geometric Design, Vol. 34, No. 1, pp. 41-55. https://doi.org/10.1016/S0010-4485(01)00046-X
- Samanta, K. and Koc, B., 2005, "Feature-Based Design and Material Blending for Freeform Heterogeneous Object Modeling," Computer Aided Geometric Design, Vol. 37, No. 3, pp. 287-305. https://doi.org/10.1016/j.cad.2004.03.005
- Yang, P. and Qian, X., 2007, "A B-Spline-Based Approach to Heterogeneous Objects Design and Analysis," Computer-Aided Design, Vol. 39, No. 2, pp. 95-111. https://doi.org/10.1016/j.cad.2006.10.005
- Huang, J., Fadel, M. G., Blouin, V. Y. and Grujicic, M., 2002, "Bi-Objective Optimization Design of Functionally Gradient Materials," Materials and Design, Vol. 23, No. 7, pp. 657-666. https://doi.org/10.1016/S0261-3069(02)00048-1
- Piegl, L. and Tiller, W., 1997, The NURBS Book, Springer-Verlag, New York.
- Park, H., 2001, "An Approximate Lofting Approach for B-Spline Surface Fitting to Functional Surfaces," International Journal of Advanced Manufacturing Technology, Vol. 18, No. 7, pp 474-482. https://doi.org/10.1007/s0017010180474
- Park, H., 2003, "Lofted B-Spline Surface Interpolation by Linearly Constrained Energy Minimization," Computer-Aided Design, Vol. 35, No. 14, pp. 1261-1268. https://doi.org/10.1016/S0010-4485(03)00040-X
- Park, S., 2009, "A Rational B-Spline Hypervolume for Multidimensional Multivariate Modeling," Journal of Mechanical Science and Technology, Vol. 23, No. 7, pp. 1967-1981. https://doi.org/10.1007/s12206-009-0513-2
- Martin, T., Cohen, E. and Kirby, R. M., 2009, "Volumetric Parameterization and Trivariate B-Spline Fitting Using Harmonic Functions," Computer-Aided Geometric Design, Vol. 26, No. 6, pp. 648-664. https://doi.org/10.1016/j.cagd.2008.09.008
- Unser, M., Aldroubi, A. and Eden, M., 1991, "Fast B-Spline Transforms for Continuous Image Representation and Interpolation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 3, pp. 277-285. https://doi.org/10.1109/34.75515
- Thevenaz, P., Blu, T. and Unser, M., "Interpolation Revisited," IEEE Transactions on Medical Imaging, Vol. 19, No. 7, pp. 739-758. https://doi.org/10.1109/42.875199
- Rho, J. Y., Hobatho, M. C. and Ashman, R. B., 1995, "Relations of Mechanical Properties to Density and CT Numbers in Human Bone," Medical Engineering and Physics, Vo. 17, No. 5, pp. 347-355. https://doi.org/10.1016/1350-4533(95)97314-F
- Wirtz, D. C., Schiffers, N., Pandorf, T., Radermacher, K., Weichert, D. and Forst, R., 2000, "Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of the Proximal Femur," Journal of Biomechanics, Vol. 33, No. 10, 1325-1330. https://doi.org/10.1016/S0021-9290(00)00069-5
- Visible Korean Homepage, http://vkh3.kisti.re.kr/.