ISSN: 2995-5823
Volume 11, Number 2 (2026)
Year Launched: 2016
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Pipes Construction Using Quartic Bézier Curves

Volume 11, Issue 2, April 2026     |     PP. 32-40      |     PDF (537 K)    |     Pub. Date: September 7, 2026
DOI: 10.54647/mathematics110577    10 Downloads     38 Views  

Author(s)

Kusno, Department of Mathematics, University of Jember, East Java, Indonesia
I Made Tirta, Department of Mathematics, University of Jember, East Java, Indonesia
Kiswara Agung Santoso, Department of Mathematics, University of Jember, East Java, Indonesia

Abstract
A Pipe consists of cross-sectional and longitudinal directions that determine its volume. The objective of this paper is to obtain some formulas for modeling the cross-section and the radius length variation along the center curve of the pipe. The methods are as follows. By using real quartic Bézier functions, we define the cross-section and lengthwise-section radii of the pipe, respectively. Then, we calculate three orthonormal vectors that are the tangent vectors of the center curve and two-unit vectors that are perpendicular to the tangent vectors. After that, we evaluate the formulas to model the pipes. The research results indicate that this proposed method is useful for designing pipe cross-sections and for modifying their volume.

Keywords
pipes construction, quartic Bézier curve, radius, cross-section, lengthwise directions

Cite this paper
Kusno, I Made Tirta, Kiswara Agung Santoso, Pipes Construction Using Quartic Bézier Curves , SCIREA Journal of Mathematics. Volume 11, Issue 2, April 2026 | PP. 32-40. 10.54647/mathematics110577

References

[ 1 ] Bhatt, A.D., Goel, A., Gupta, U., & Awasthi, S. Reconstruction of branched surfaces: Experiments with disjoint b-spline surface. Comput.-Aided Des. & Appl., 12, 76–85, 2015. https://doi.org/10.1080/16864360.2014.949577
[ 2 ] Bizzarri, M., Lávička M., & Vršek, J. Canal surfaces with rational contour curves and blends by passing the obstacles. Comput. Aided Des., 64, 55–67, 2015. http://doi.org/10.1016/j.cad.2015.03.002
[ 3 ] Carmo, M. P. D. (1976). Differential geometry of curves and surface. Prentice Hall Inc Englewood Cliffs, New Jersey.
[ 4 ] Kreyzig, E. (1991). Differential geometry. Dover Publications Inc, New York.
[ 5 ] Kusno (2010). Geometri rancang bangun. Jember University Press, Indonesia.
[ 6 ] Kusno, & Cahyo, A.. Continuous connection of two adjacent pipe parts defined by line, Bézier and Hermite center curves. J. of Phys.: Conf. Ser., 1008, 2018. https://doi.org/10.1088/1742-6596/1008/1/012005
[ 7 ] Kusno. Pipes Construction Based on the Pipes' Centre Curve Shapes. Journal of Mathematics Research, 11(4), 69-76, 2019. https://doi.org/10.5539/jmr.v11n4p69
[ 8 ] Lipschultz, M. (1969). Theory and problems of differential geometry. Schaum's Outline Series, McGraw-Hill, New York.
[ 9 ] Moritani, R., Kanai, S., Date, H., Watanabe, M., Nakano, T., & Yamauchi, Y. Cylinder-based simultaneous registration and model fitting of laser-scanned point clouds for accurate as-built modeling of piping system. Comput.-Aided Des.& Appl., 15, 720-733, 2018. https://doi.org/10.1080/16864360.2018.1441239.
[ 10 ] Mortenson, M. E. (1996). Geometry modeling (2nd Ed). Wiley Computer Publishing, Jonh Wiley and Sons Inc., New York.
[ 11 ] Su, Z., Yang, X., Liu, G., Li, W., & Weiqing, W. Topology authentication for piping isometric drawings. Comput. Aided Des., 66, 33–44, 2015. https://doi.org/10.1016/j.cad.2015.04.005
[ 12 ] Zhou, P., & Qian, W.H. Constructive G1 connection of multiple freeform pipes in arbitrary poses. Comput. Aided Geom. Des., 30, 462–475, 2013. https://doi.org/10.1016/j.cagd.2013.02.006