Research Article
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Year 2022, , 356 - 370, 31.12.2022

Hakan Üstünel

https://doi.org/10.35377/saucis...1122506

Abstract

References

  • [1] Overhauser, A. W. (2005). Analytic definition of curves and surfaces by parabolic blending. arXiv preprint cs/0503054.
  • [2] Liu, Y., & Rizzo, F. J. (1991). Application of Overhauser C 1 Continuous Boundary Elements to “Hypersingular” BIE for 3-D Acoustic Wave Problems. In Boundary elements XIII (pp. 957-966). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3696-9_75
  • [3] Walters, H. G., & Gipson, G. S. (1994). Evaluation of overhauser splines as boundary elements in linear elastostatics. Engineering analysis with boundary elements, 14(2), 171-177. https://doi.org/10.1016/0955-7997(94)90093-0
  • [4] Durodola, J. F., & Fenner, R. T. (1996). OVERHAUSER TRIANGULAR ELEMENTS FOR THREE‐DIMENSIONAL POTENTIAL PROBLEMS USING BOUNDARY ELEMENT METHODS. International journal for numerical methods in engineering, 39(24), 4183-4198. https://doi.org/10.1002/(SICI)1097-0207(19961230)39:24%3C4183::AID-NME38%3E3.0.CO;2-9
  • [5] Brewer, J. A., & Anderson, D. C. (1977). Visual interaction with overhauser curves and surfaces. ACM SIGGRAPH Computer Graphics, 11(2), 132-137. https://doi.org/10.1145/965141.563883
  • [6] Schneider, W. (1986). A simple technique for adding tension to parabolic blending interpolation. Computers & Mathematics with Applications, 12(11), 1155-1160. https://doi.org/10.1016/0898-1221(86)90019-2
  • [7] Qian, X., Yuan, H., Zhou, M., & Zhang, B. (2014). A general 3D contact smoothing method based on radial point interpolation. Journal of Computational and Applied Mathematics, 257, 1-13.
  • [8] El‐Abbasi, N., Meguid, S. A., & Czekanski, A. (2001). On the modelling of smooth contact surfaces using cubic splines. International Journal for Numerical Methods in Engineering, 50(4), 953-967. https://doi.org/10.1002/1097-0207(20010210)50:4%3C953::AID-NME64%3E3.0.CO;2-P
  • [9] Chung, K. H., Kim, J. W., Ryu, K. W., Lee, K. T., & Lee, D. J. (2006). Sound generation and radiation from rotor tip-vortex pairing phenomenon. AIAA journal, 44(6), 1181-1187. https://doi.org/10.2514/1.22548
  • [10] De Almeida Barros, P. L., & de Mesquita Neto, E. (2000). Singular‐ended spline interpolation for two‐dimensional boundary element analysis. International Journal for Numerical Methods in Engineering, 47(5), 951-967.
  • [11] Kunz, T., & Stilman, M. (2012). Time-optimal trajectory generation for path following with bounded acceleration and velocity. Robotics: Science and Systems VIII, 1-8.
  • [12] Burgoyne, C. J., & Crisfield, M. A. (1990). Numerical integration strategy for plates and shells. International journal for numerical methods in engineering, 29(1), 105-121. https://doi.org/10.1002/nme.1620290108
  • [13] Ekşi, O., & Üstünel, H. (2020). Application of parabolic blending for the estimation of thickness distribution in thermoformed products. Journal of Elastomers & Plastics, 0095244320959801. https://doi.org/10.1177%2F0095244320959801
  • [14] Hadavinia, H., Travis, R. P., & Fenner, R. T. (2000). C1-continuous generalised parabolic blending elements in the Boundary Element Method. Mathematical and Computer Modelling, 31(8-9), 17-34. https://doi.org/10.1016/S0895-7177(00)00057-1
  • [15] Rogers DF and Adams JA. Mathematical elements for computer graphics. 2nd ed. New York: McGraw-Hill, 1989.

Software Development for the Use of Generalized Parabolic Blending in Data Prediction Processes

Year 2022, , 356 - 370, 31.12.2022

Hakan Üstünel

https://doi.org/10.35377/saucis...1122506

Abstract

Parabolic blending (PB) is one of the important topics in applied mathematics and computer graphics. The use of generalized parabolic blending (GPB) for different scenarios adds flexibility to the polynomial. Overhauser (OVR) elements is a special case in GPB (r=0.5, s=0.5). GPB can also be used in estimation. In this study, data obtained from thickness distribution of a 3mm thick high impact polystyrene product after thermoforming using a mold was used for data estimation. For this purpose, software has been developed. The software development steps and formula usages are explained. Using the developed software, polynomials for GPB and default PB (OVR) were created. The data set was compared with the y values produced by the polynomials for certain x values. At the end of the research, it was determined that the results obtained from the GPB were 0.1728 percent more accurate than the data obtained from the PB for the default values.

Keywords

Generalized parabolic blending computer graphics visualization software development thickness distribution

References

  • [1] Overhauser, A. W. (2005). Analytic definition of curves and surfaces by parabolic blending. arXiv preprint cs/0503054.
  • [2] Liu, Y., & Rizzo, F. J. (1991). Application of Overhauser C 1 Continuous Boundary Elements to “Hypersingular” BIE for 3-D Acoustic Wave Problems. In Boundary elements XIII (pp. 957-966). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3696-9_75
  • [3] Walters, H. G., & Gipson, G. S. (1994). Evaluation of overhauser splines as boundary elements in linear elastostatics. Engineering analysis with boundary elements, 14(2), 171-177. https://doi.org/10.1016/0955-7997(94)90093-0
  • [4] Durodola, J. F., & Fenner, R. T. (1996). OVERHAUSER TRIANGULAR ELEMENTS FOR THREE‐DIMENSIONAL POTENTIAL PROBLEMS USING BOUNDARY ELEMENT METHODS. International journal for numerical methods in engineering, 39(24), 4183-4198. https://doi.org/10.1002/(SICI)1097-0207(19961230)39:24%3C4183::AID-NME38%3E3.0.CO;2-9
  • [5] Brewer, J. A., & Anderson, D. C. (1977). Visual interaction with overhauser curves and surfaces. ACM SIGGRAPH Computer Graphics, 11(2), 132-137. https://doi.org/10.1145/965141.563883
  • [6] Schneider, W. (1986). A simple technique for adding tension to parabolic blending interpolation. Computers & Mathematics with Applications, 12(11), 1155-1160. https://doi.org/10.1016/0898-1221(86)90019-2
  • [7] Qian, X., Yuan, H., Zhou, M., & Zhang, B. (2014). A general 3D contact smoothing method based on radial point interpolation. Journal of Computational and Applied Mathematics, 257, 1-13.
  • [8] El‐Abbasi, N., Meguid, S. A., & Czekanski, A. (2001). On the modelling of smooth contact surfaces using cubic splines. International Journal for Numerical Methods in Engineering, 50(4), 953-967. https://doi.org/10.1002/1097-0207(20010210)50:4%3C953::AID-NME64%3E3.0.CO;2-P
  • [9] Chung, K. H., Kim, J. W., Ryu, K. W., Lee, K. T., & Lee, D. J. (2006). Sound generation and radiation from rotor tip-vortex pairing phenomenon. AIAA journal, 44(6), 1181-1187. https://doi.org/10.2514/1.22548
  • [10] De Almeida Barros, P. L., & de Mesquita Neto, E. (2000). Singular‐ended spline interpolation for two‐dimensional boundary element analysis. International Journal for Numerical Methods in Engineering, 47(5), 951-967.
  • [11] Kunz, T., & Stilman, M. (2012). Time-optimal trajectory generation for path following with bounded acceleration and velocity. Robotics: Science and Systems VIII, 1-8.
  • [12] Burgoyne, C. J., & Crisfield, M. A. (1990). Numerical integration strategy for plates and shells. International journal for numerical methods in engineering, 29(1), 105-121. https://doi.org/10.1002/nme.1620290108
  • [13] Ekşi, O., & Üstünel, H. (2020). Application of parabolic blending for the estimation of thickness distribution in thermoformed products. Journal of Elastomers & Plastics, 0095244320959801. https://doi.org/10.1177%2F0095244320959801
  • [14] Hadavinia, H., Travis, R. P., & Fenner, R. T. (2000). C1-continuous generalised parabolic blending elements in the Boundary Element Method. Mathematical and Computer Modelling, 31(8-9), 17-34. https://doi.org/10.1016/S0895-7177(00)00057-1
  • [15] Rogers DF and Adams JA. Mathematical elements for computer graphics. 2nd ed. New York: McGraw-Hill, 1989.
There are 15 citations in total.

Details

Primary Language English
Subjects Software Engineering, Software Testing, Verification and Validation, Software Engineering (Other)
Journal Section Articles
Authors

Hakan Üstünel 0000-0001-9903-593X

Publication Date December 31, 2022
Submission Date May 27, 2022
Acceptance Date November 18, 2022
Published in Issue Year 2022

Cite

IEEE H. Üstünel, “Software Development for the Use of Generalized Parabolic Blending in Data Prediction Processes”, SAUCIS, vol. 5, no. 3, pp. 356–370, 2022, doi: 10.35377/saucis...1122506.

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