Ship Hull DesignShip Hull DesignShip Hull DesignShip Hull Design
赵宏艳Email: [email protected]
Nov. 21, 2007
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 F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862.2007, 39(10):853-862.
References
1
2
3
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 F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862.2007, 39(10):853-862.
References
1
2
3
Concepts
Stations
Waterlines
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 F. Pérez, J.A. Suárez. Quasi-developable B-spline Surfaces in Ship Hull Design, Computer-Aided Design, Surfaces in Ship Hull Design, Computer-Aided Design, 2007, 39(10):853-862.2007, 39(10):853-862.
References
1
2
3
船体曲面造型研究进展船体曲面造型研究进展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
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
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
Automatic Surface Automatic Surface Modelling of a Ship Modelling of a Ship
HullHull
Automatic Surface Automatic Surface Modelling of a Ship Modelling of a Ship
HullHullF. Pérez-Arribas, J.A. Suárez-Suárez,
L. Fernández-JambrinaComputer-Aided Design, 38(6): 584-594
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
• José 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
Automatic Surface Modelling of a Ship Hull
Thorough procedure for
automatic modeling with a fair NURBS
surface
Input Output
Lists ofPoints
Onstations
Automatic Surface Modelling of a Ship Hull
OUTLINE
Choosing the list of knotsChoosing the list of knotsChoosing a parameterizationChoosing a parameterizationSolving the approximation problemSolving the approximation problemSearching for the optimal parameterizationSearching for the optimal parameterizationStations with straight piecesStations with straight pieces
Fairing criterionFairing criterionLocal fairness criterionLocal fairness criterionLocal fairing iterationLocal fairing iterationFinal comments to the fairing processFinal comments to the fairing process
Mean square approximation of stations with a cubic Mean square approximation of stations with a cubic splinespline
Generation of a spline surface through the stationsGeneration of a spline surface through the stations
Fairing processFairing process
Automatic Surface Modelling of a Ship Hull
First stepFirst step Second stepSecond step Final stepFinal step
Curve approxi-mation
Surface generation
Surface fairing
Automatic Surface Modelling of a Ship Hull
OUTLINE
Choosing the list of knotsChoosing a parameterizationSolving the approximation problemSearching for the optimal parameterizationStations with straight pieces
Fairing criterionLocal fairness criterionLocal fairing iterationFinal comments to the fairing process
Mean square approximation of stations with a cubic Mean square approximation of stations with a cubic splinespline
Generation of a spline surface through the stationsGeneration of a spline surface through the stations
Fairing processFairing process
Quasi-developable B-Quasi-developable B-spline Surfaces in Ship spline Surfaces in Ship
Hull DesignHull Design
Quasi-developable B-Quasi-developable B-spline Surfaces in Ship spline Surfaces in Ship
Hull DesignHull DesignF. Pérez-Arribas, J.A. Suárez-Suárez
Computer-Aided Design, 39(10): 853-862
Quasi-developable B-spline Surfaces in Ship Quasi-developable B-spline Surfaces in Ship Hull DesignHull Design
Quasi-developable B-spline Surfaces in Ship Quasi-developable B-spline Surfaces in Ship Hull DesignHull Design
Generatequasi-
developablesurfaces
with B-spline surfaces
Input Output
Two
directrices
ExamplesExamples7
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Quasi-developable B-spline Surfaces in Ship Quasi-developable B-spline Surfaces in Ship Hull DesignHull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
ExamplesExamples7
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
Finding a developable surfaceFinding a developable surface
Finding a developable surfaceFinding a developable surface
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.
1 1
2 2
n r t
n r t 1 2 n n 0
1 2 | sin( ) | n n
Warp angle
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
1
2
3
44
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
5
6
ExamplesExamples7
Working with B-spline curves and Working with B-spline curves and nomenclaturenomenclature
Model the chines, centre line and sheer lines as B-splines.
ExamplesExamples7
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
Searching for the rulingsSearching for the rulings
Searching for the rulingsSearching for the rulings
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
1u
1t1S
h2u2 ( )it 2( ( ))u i2S
1( )in 2 ( )in
1u
Searching for the rulingsSearching for the rulings
ExamplesExamples7
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
The area of regressionThe area of regression
Rulings overlap
The area of regressionThe area of regression
Problem: rulings overlap
Solution: multiconic algorithm
ExamplesExamples7
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
ExamplesExamples7
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
ExamplesExamples7
Generation of a B-spline surface through the rulingsGeneration of a B-spline surface through the rulings
Quasi-developable B-spline Surfaces in Quasi-developable B-spline Surfaces in Ship Hull DesignShip Hull Design
OUTLINE
Finding a developable surfaceFinding a developable surface
Searching for the rulingsSearching for the rulings
Working with B-spline curves and nomenclatureWorking with B-spline curves and nomenclature
The area of regressionThe area of regression
Gaussian curvature of the created surfacesGaussian curvature of the created surfaces
1
2
3
44
5
6
ExamplesExamples
Hard chine One chine, sheer and centre line
ExamplesExamples
UBC fishing vessel Two chines, one sheer and centre line
Choosing the list of knotsChoosing the list of knots
Knots
1 0 1 2
3
1 2 3
3,
4,
...,
1.m m m m
u u u u
u
u u u u m
Knots number
3 m p
Choosing a parameterization
1 | |, 1,...,i iU U k i p i i-1P P
0
23,
| | | |
mU k
1 0 p p-1P P P P
Centripental parametrization
Solving the approximation problem
Equation
3 3 3
0 0 0
3 3 3
0 0 0
( ) ( ) ( ),
( ) ( ) ( ).
p pm
k i j i j i k ij i i
p pm
k i j i j i k ij i i
N U N U X x N U
N U N U Y y N U
Matrix system
31 0
01
1 31 0
0
( )
( )
p
i i mi
pm
i m i mi
x N U X XX
C
Xx N U X X
1 0 1 m
m-1 0 m-1 m
B B B B
B B B B
Searching for the optimal parameterizationSearching for the optimal parameterization
Iterative process
Stations with straight piecesStations with straight pieces
Fairing criterionFairing 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.)
2C ( , )s u v( , )k lu v 3C
( , )k lu v( , )s u v
Reducing the differences between third-order partial derivatives at .( , )k lu v
3 3 1
3 34 3
3 3 1
3 33 4
( , ) ( , ) ( , )
( , ) ( , ) ( , )
k l
uuu k l k l k l ij iji k j l
k l
vvv k l k l k l ij iji k j l
u u u v u vu u
u u u v u vu u
S SV
S SV
2 2| ( , ) | | ( , ) |kl uuu k l vvv k lL u v u v
( , )s kl
k l I
G L
Local fairness criterionLocal fairness criterion
Smallest deformation of the original surface
1 12
3 3
min ( ) | |k l
ij ij iji k j l
F
V V V
( , ) 0; ( , ) 0.uuu k l vvv k lu v u v
Local smoothness measure is zero
Final comments to the fairing processFinal comments to the fairing process
Longitudinal distribution of curvature
BumpsShape preservation