skip to main content

Ship Hull Geometry Design by Using B-Spline Curve Fitting and Lofted Surface Generation

Sheely Leony Artha Pasaribu  -  Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Indonesia
Berlian Arswendo Adietya scopus  -  Department of Naval Architecture, Diponegoro University, Indonesia
Muhammad Iqbal orcid scopus  -  Department of Naval Architecture, Diponegoro University, Indonesia
Hasanudin Hasanudin scopus  -  Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Indonesia
Wiwin Sulistyawati scopus  -  Department of Naval Architecture, Universitas Pembangunan Nasional Veteran Jakarta, Indonesia
Mohammad Sholikhan Arif orcid scopus  -  Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, United Kingdom
*Ardi Nugroho Yulianto orcid scopus  -  Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Indonesia
Received: 13 May 2026; Revised: 29 Jun 2026; Accepted: 30 Jun 2026; Available online: 30 Jun 2026; Published: 1 Jul 2026.
Open Access Copyright (c) 2026 Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:
Abstract

As one of the largest archipelago countries in the world, Indonesia requires technological capability to independently develop efficient ship design systems. Currently, the Computer-Aided Design (CAD) software used for domestic ship design is still largely dominated by foreign commercial products, which require costly subscription fees. This dependence limits the technological independence of the national shipbuilding industry. This study aims to develop a simple CAD-based program for representing ship hull geometry using a parametric mathematical approach. The program reconstructs sectional curves using mathematics formulations and generates a continuous three-dimensional hull surface through a lofting method based on equal arc-length discretization and triangular mesh representation. The research methodology includes system design, curve and surface generation, geometric visualization, and validation through comparison with results obtained from commercial CAD software. The results demonstrate that the developed system is capable of accurately reconstructing sectional curves and generating a consistent lofted hull surface suitable for representing simple ship hull forms. This work provides an initial step toward the development of domestic ship hull design tools to support preliminary geometric modeling in Indonesia’s maritime industry.

Keywords: Computer Aided Design (CAD); Design; Hydrostatic; Ship Hull

Article Metrics:

  1. Badan Pembinaan Hukum Nasional, “Indonesia Merupakan Negara Kepulauan yang Terbesar di Dunia,” Oct. 28, 2015. [Online]. Available: https://bphn.go.id/berita-utama/indonesia-merupakan-negara-kepulauan-yang-terbesar-di-dunia-3441
  2. Hasanudin, A. D. Saputra, and A. N. Yulianto, “A Study on Stability and Passenger Capacity of Traditional River and Lake Boats,” BIO Web of Conferences, vol. 157, 2025, doi: https://doi.org/10.1051/bioconf/202515703005
  3. A. N. Yulianto, R. R. Winarko, S. L. A. Pasaribu, R. F. Ahmad, B. A. Adietya, and Hasanudin, “Optimization of Inner Bilge Design to Enhance Cargo Tank Capacity in Tankers,” Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan, vol. 23, no. 1, pp. 49–63, 2026, doi: https://doi.org/10.14710/kapal.v23i1.82683
  4. L. Y. Wang and Z. J. Wang, “Reparameterization of B-spline surface and its application in ship hull form design,” Computer-Aided Design, vol. 115, pp. 102–112, 2019, doi: https://doi.org/10.1016/j.oceaneng.2023.115535
  5. A. F. Molland, T. S. Turnock, and H. D. Hudson, Ship Resistance and Propulsion: Practical Estimation of Propulsive Power. New York, NY, USA: Cambridge University Press, 2011
  6. I. E. Sutherland, “Sketchpad: A Man–Machine Graphical Communication System,” Doctoral dissertation, Massachusetts Institute of Technology, Cambridge, MA, USA, 1963
  7. D. F. Rogers, An Introduction to NURBS: With Historical Perspective. Annapolis, MD, USA: Academic Press, 2001
  8. F. Pérez, J. A. Suárez, J. A. Clemente, and A. Souto, “Geometric modelling of bulbous bows with the use of non-uniform rational B-spline surfaces,” Journal of Marine Science and Technology, vol. 12, no. 2, pp. 83–94, 2007, https://doi.org/10.1007/s00773-006-0225-6
  9. F. Pérez and J. Clemente, “Constrained design of simple ship hulls with B-spline surface,” Computer-Aided Design, vol. 43, no. 12, pp. 1829–1840, 2011, doi: https://doi.org/10.1016/j.cad.2011.07.008
  10. J. Y. Kang and B. Lee, “Mesh-based morphing method for rapid hull form generation,” Computer-Aided Design, vol. 42, no. 11, pp. 970–976, 2010, doi: https://doi.org/10.1016/j.cad.2009.07.00
  11. D. Chrismianto and D.-J. Kim, “Parametric bulbous bow design using the cubic Bezier curve and curve-plane intersection method for the minimization of ship resistance in CFD,” Journal of Marine Science and Technology, vol. 19, no. 4, pp. 479–492, 2014, doi: https://doi.org/10.1007/s00773-014-0278-x
  12. D. Chrismianto, A. F. Zakki, B. Arswendo, and D. J. Kim, “Development of Cubic Bezier Curve and Curve-Plane Intersection Method for Parametric Submarine Hull Form Design to Optimize Hull Resistance Using CFD,” Journal of Marine Science and Application, vol. 14, no. 2, pp. 132–144, 2015, doi: https://doi.org/10.1007/s11804-015-1324-8
  13. J. K. Chau and S. W. Chau, “Computer-Aided Geometric Design and Panel Generation for Hull Forms Based on Rational Cubic Bézier Curves,” Computer Aided Geometric Design, vol. 10, no. 5, pp. 431–447, 1993, doi: https://doi.org/10.1016/0167-8396(93)90030-7
  14. K. Kostas, “Ship-hull shape optimization with a T-spline based method,” Computer Methods in Applied Mechanics and Engineering, vol. 279, pp. 415–438, 2014, doi: https://doi.org/10.1016/j.cma.2014.10.030
  15. P. Charrot and J. A. Gregory, “A pentagonal surface patch for computer aided geometric design,” Computer Aided Geometric Design, vol. 1, no. 1, pp. 87–94, 1984, doi: https://doi.org/10.1016/0167-8396(84)90006-2
  16. F. Massarwi and G. Elber, “A B-spline based framework for volumetric object modeling,” Computer-Aided Design, vol. 78, pp. 36–47, 2016, doi: https://doi.org/10.1016/j.cad.2016.05.003
  17. K. Qin, Y. Li, and C. Deng, “Generalized Bézier volumes over simple convex polyhedra,” Computer Aided Geometric Design, vol. 111, p. 102338, 2024, doi: https://doi.org/10.1016/j.cagd.2024.102338
  18. D. J. Willis, J. Peraire, and J. K. White, “A Quadratic Basis Function, Quadratic Geometry, High Order Panel Method,” in Proc. 44th AIAA Aerospace Sciences Meeting, 2006, pp. 1–17, doi: https://doi.org/10.2514/6.2006-1253
  19. G.-D. Kim, C.-S. Lee, and J. Kerwin, “A B-spline based higher order panel method for analysis of steady flow around marine propellers,” Ocean Engineering, vol. 34, no. 15–16, pp. 2045–2060, 2007, doi: https://doi.org/10.1016/j.oceaneng.2007.02.013
  20. Z.-l. Gao and Z.-j. Zou, “A Three-Dimensional Desingularized High Order Panel Method Based on NURBS,” Journal of Hydrodynamics, Ser. B, vol. 20, no. 2, pp. 137–146, 2008, doi: https://doi.org/10.1016/S1001-6058(08)60039-6
  21. X. Jiang and Y. Lin, "Relevant integrals of NURBS and its application in hull line element design," Ocean Engineering, vol. 251, p. 111147, May 2022, doi: https://doi.org/10.1016/j.oceaneng.2022.111147
  22. K.-G. Zhu, G.-Y. Shi, and J. Liu, "Improved flattening algorithm for NURBS curve based on bisection feedback search algorithm and interval reformation method," Ocean Engineering, vol. 247, p. 110635, Mar. 2022, doi: https://doi.org/10.1016/j.oceaneng.2022.110635
  23. S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, 7th ed. New York, NY, USA: McGraw-Hill Education, 2015
  24. L. Piegl and W. Tiller, The NURBS Book, 2nd ed. Berlin, Germany: Springer, 1997
  25. T. H. Chien, Development of Isogeometric Finite Element Methods. Vietnam: Ton Duc Thang University, 2015
  26. V. P. Nguyen, K. P. Nguyen, and B. S. A. Nguyen, “Two- and three-dimensional isogeometric cohesive elements for composite delamination analysis,” Composites Part B: Engineering, vol. 53, pp. 390–408, 2013, doi: https://doi.org/10.1016/j.compositesb.2013.12.018
  27. M. Lutz, Learning Python, 5th ed. Sebastopol, CA, USA: O’Reilly Media, Inc., 2013

Last update:

No citation recorded.

Last update: 2026-07-25 17:47:53

No citation recorded.