ship hull design

Ship Hull DesignShip Hull DesignShip Hull DesignShip Hull Design

赵宏艳Email: hongyanzhao_cn@yahoo.com.cn

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