1. Ship Hull Design 赵宏艳 Email: hongyanzhao_cn@yahoo.com.cnhongyanzhao_cn@yahoo.com.cn Nov. 21, 2007

2. 张明霞，林焰，纪卓尚. 船体曲面造型研究进展. 大连理工 大学学报, 2003, 43(2): 207-212. F. Pérez, J.A. Suárez, L. Fernández. Automatic Surface Modeling of a Ship Hull, Computer-Aided Design, 2006, 38(6):584-594. F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862. References 123

4. 张明霞，林焰，纪卓尚. 船体曲面造型研究进展. 大连理工 大学学报, 2003, 43(2): 207-212. F. Pérez, J.A. Suárez, L. Fernández. Automatic Surface Modeling of a Ship Hull, Computer-Aided Design, 2006, 38(6):584-594. F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862. References 123

5. Concepts Stations Waterlines

6. 张明霞，林焰，纪卓尚. 船体曲面造型研究进展. 大连理工 大学学报, 2003, 43(2): 207-212. F. Pérez, J.A. Suárez, L. Fernández. Automatic Surface Modeling of a Ship Hull, Computer-Aided Design, 2006, 38(6):584-594. F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862. References 123

7. 船体曲面造型研究进展船体曲面造型研究进展 张明霞，林焰，纪卓尚 大连理工大学学报, 43(2): 207-212

8. 计算机辅助船舶设计的实际应用 etc. 船舶总性能的计算 船舶生产设计 船舶总布置设计 船舶适航性、 受力分析等研究 船体结构设计 计算机辅助 船舶设计

9. 船体曲面 NURBS 造型的关键技术 控制顶点确定 曲面的参数化 3D 网格的生成 确定合适的边界条件

10. Automatic Surface Modelling of a Ship Hull F. Pérez-Arribas, J.A. Suárez-Suárez, L. Fernández-Jambrina Computer-Aided Design, 38(6): 584-594

11. Author introduction Francisco L. Pérez Arribas Associate Professor in the Naval Architecture and Marine Engineering School of Madrid (ETSIN), UPM. Research interests: ship hull modeling, parametric ship design and geometric modeling Jos é Antonio Suárez PhD student at the ETSIN Research interests: parametric ship design Leonardo Fernández-Jambrina Professor of Applied Maths at the Universidad Politécnica de Madrid Research interests: computer-aided design and geometric modeling with applications to naval architecture

12. Automatic Surface Modelling of a Ship Hull Thorough procedure for automatic modeling with a fair NURBS surface InputOutput Lists of Points On stations

13. Automatic Surface Modelling of a Ship Hull  OUTLINE Choosing the list of knots Choosing a parameterization Solving the approximation problem Searching for the optimal parameterization Stations with straight pieces Fairing criterion Local fairness criterion Local fairing iteration Final comments to the fairing process Mean square approximation of stations with a cubic spline Generation of a spline surface through the stations Fairing process

14. Automatic Surface Modelling of a Ship Hull First step Second step Final step Curve approxi- mation Surface generation Surface fairing

15. Automatic Surface Modelling of a Ship Hull  OUTLINE Choosing the list of knots Choosing the list of knots Choosing a parameterization Choosing a parameterization Solving the approximation problem Solving the approximation problem Searching for the optimal parameterization Searching for the optimal parameterization Stations with straight pieces Stations with straight pieces Fairing criterion Fairing criterion Local fairness criterion Local fairness criterion Local fairing iteration Local fairing iteration Final comments to the fairing process Final comments to the fairing process Mean square approximation of stations with a cubic spline Generation of a spline surface through the stations Fairing process

16. Quasi-developable B- spline Surfaces in Ship Hull Design F. Pérez-Arribas, J.A. Suárez-Suárez Computer-Aided Design, 39(10): 853-862

17. Quasi-developable B-spline Surfaces in Ship Hull Design

18. Generate quasi- developable surfaces with B-spline surfaces InputOutput Two directrices

19. Examples 7 Generation of a B-spline surface through the rulings Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

20. Examples 7 Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Generation of a B-spline surface through the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

21. Finding a developable surface

22.  The tangent planes to the surface are also tangent to the two directrix lines.  The normal vectors at the endpoints of a ruling are parallel.  Warp angle

23. Generation of a B-spline surface through the rulings Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Working with B-spline curves and nomenclature The area of regression 123 4 Gaussian curvature of the created surfaces 56 Examples 7

24. Working with B-spline curves and nomenclature  Model the chines, centre line and sheer lines as B-splines.

25. Examples 7 Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Generation of a B-spline surface through the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

26. Searching for the rulings

27.  For every fixed value of parameter on  Step 1: compute the tangent ;  Step 2: obtain different values of parameter with step ; 2.1: compute the tangent for each ; 2.2: compute and ; 2.3: compute the warp angle ;  Step 3: detect the minimum value of the warp angle ; 2.1: turn to local search until the warp angle is below a tolerance or low enough;  Next  Lofting surface with rulings

28. Searching for the rulings

29. Examples 7 Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Generation of a B-spline surface through the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

30. The area of regression  Rulings overlap

31. The area of regression  Problem: rulings overlap  Solution: multiconic algorithm

32. Examples 7 Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Generation of a B-spline surface through the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

33. Examples 7 Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Generation of a B-spline surface through the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

34. Examples 7 Generation of a B-spline surface through the rulings Quasi-developable B-spline Surfaces in Ship Hull Design  OUTLINE Finding a developable surface Searching for the rulings Working with B-spline curves and nomenclature The area of regression Gaussian curvature of the created surfaces 123 456

35. Examples  Hard chine  One chine, sheer and centre line

36. Examples  UBC fishing vessel  Two chines, one sheer and centre line

38. Choosing the list of knots  Knots  Knots number

39. Choosing a parameterization  Centripental parametrization

40. Solving the approximation problem  Equation  Matrix system

41. Searching for the optimal parameterization  Iterative process

42. Stations with straight pieces

43. Fairing criterion  A spline surface is fairer in a neighbour- hood of the inner knot if is locally at. (Hahmann S. Shape improvement of surfaces. Comput Suppl 1998;13:135-52.)  Reducing the differences between third-order partial derivatives at.

44. Local fairness criterion  Smallest deformation of the original surface  Local smoothness measure is zero

45. Final comments to the fairing process  Longitudinal distribution of curvature  Bumps  Shape preservation