Using the geometric features of surfaces, we proposed an algorithm to construct line-shaped feature point clouds for the reverse design of a blade surface. Blade surfaces in the gas turbines field require high accuracy and have complex shapes. By quickly recognizing the border of the scattered point clouds of blades, the back-project method was used to extract the ruled generatrix vector. By solving the multi-objective optimization problem of border point clouds, the annealing algorithm was applied to match border point clouds nonrigidly. Equally divided points were constructed based on the point clouds registration results to get inerratic-orderly line-shaped feature point clouds that are beneficial for generating high quality blade surfaces quickly. The proposed algorithm is very effective for dealing with the point clouds of single-value ruled blades. It is also theoretically significant and may be applied for reconstructing the surface of point clouds of single-value ruled blade surfaces. Experiments verify the feasibility of the proposed algorithm.

References

1.
Julien
,
C. J.
,
Gérard
,
P.
, and
Emmanuel
,
D.
,
2009
, “
New Approach to 5-Axis Flank Milling of Free-Form Surfaces: Computation of Adapted Tool Shape
,”
Comput.-Aided Des.
,
41
(
12
), pp.
918
929
.10.1016/j.cad.2009.06.009
2.
Xu
,
H. X.
, and
Wang
,
G. J.
,
2009
, “
Approximating Rational Triangular Bézier Surfaces by Polynomial Triangular Bézier Surfaces
,”
J. Comput. Appl. Math.
,
228
(
1
), pp.
287
295
.10.1016/j.cam.2008.09.030
3.
Min-jae
,
O.
,
Kittichai
,
S.
, and
Sung Ha
,
P.
,
2012
, “
Constructing Bézier Surfaces Over a Boundary Curve Network With T-Junctions
,”
Comput.-Aided Des.
,
44
(
7
), pp.
671
686
.10.1016/j.cad.2012.02.008
4.
Lin
,
K.
,
Huang
,
C.
,
Lai
,
J.
,
Tsai
,
Y.
, and
Ueng
,
W.
,
2012
, “
Automatic Reconstruction of B-Spline Surfaces With Constrained Boundaries
,”
Comput. Indus. Eng.
,
62
(
1
), pp.
226
244
.10.1016/j.cie.2011.09.010
5.
Simon
,
F.
,
2009
, “
Fitting Curves and Surfaces to Point Clouds in the Presence of Obstacles
,”
Comput. Aided Geom. Des.
,
26
(
2
), pp.
192
202
.10.1016/j.cagd.2008.04.003
6.
Xie
,
W. C.
,
Zou
,
X. F.
,
Yang
,
J. D.
, and
Yang
,
J. B.
,
2012
, “
Iteration and Optimization Scheme for the Reconstruction of 3D Surfaces Based on Non-Uniform Rational B-Splines
,”
Comput.-Aided Des.
,
44
(
11
), pp.
1127
1140
.10.1016/j.cad.2012.05.004
7.
Akemi
,
G.
, and
Andrés
,
I.
,
2012
, “
Particle Swarm Optimization for Non-Uniform Rational B-Spline Surface Reconstruction From Clouds of 3D Data Points
,”
Inf. Sci.
,
192
(
0
), pp.
174
192
.10.1016/j.ins.2010.11.007
8.
Carminelli
,
A.
, and
Catania
,
G.
,
2008
, “
Curve and Surface Fitting by Means of Rational B-Spline Functions
,”
ASME International Mechanical Engineering Congress and Exposition
,
American Society of Mechanical Engineers
,
Boston, MA
, Oct. 31–Nov. 6, pp.
95
100
.
9.
Hofer
,
M.
,
Odehnal
,
B.
,
Pottmann
,
H.
,
Steiner
,
T.
, and
Wallner
,
J.
,
2005
, “
3D Shape Recognition and Reconstruction Based on Line Element Geometry
,”
Tenth IEEE International Conference on Computer Vision
, 2005, ICCV 2005, IEEE, pp.
1532
1538
.
10.
Pottmann
,
H.
,
Hofer
,
M.
,
Odehnal
,
B.
, and
Wallner
,
J.
,
2004
,
Line Geometry for 3D Shape Understanding and Reconstruction
,
Springer
, Berlin/Heidelberg.
11.
Matt
,
O.
,
Ramsay
,
D.
,
Zhang
,
H.
, and
Alla
,
S.
,
2011
, “
Point Set Silhouettes via Local Reconstruction
,”
Comput. Graphics
,
35
(
3
), pp.
500
509
.10.1016/j.cag.2011.03.034
12.
Erik
,
B.
,
Henk
,
A. D.
,
Jonas
,
T.
, and
Wubs
,
W. F.
,
2010
, “
The Application of Jacobian-Free Newton–Krylov Methods to Reduce the Spin-Up Time of Ocean General Circulation Models
,”
J. Comput. Phy.
,
229
(
21
), pp.
8167
8179
.10.1016/j.jcp.2010.07.015
13.
Berenguer
,
L.
,
Dufaud
,
T.
, and
Tromeur-Dervout
,
D.
,
2013
, “
Aitken's Acceleration of the Schwarz Process Using Singular Value Decomposition for Heterogeneous 3D Groundwater Flow Problems
,”
Comput. Fluids
,
80
, pp.
320
326
.10.1016/j.compfluid.2012.01.026
14.
Gao
,
H. S.
,
Han
,
Y. Z.
,
Zhang
,
J.
, and
Yue
,
Z. F.
,
2008
, “
Aerodynamic Optimization Based on Approximation Method for Turbine Blade
,”
Multidiscip. Model. Mater. Struct.
,
4
(
4
), pp.
385
392
.10.1163/157361108785963055
15.
Arno
,
K.
,
Jesper
,
A.
,
Babak
,
A. A.
,
Ashburner
,
J.
,
Ardekani
,
B. A.
,
Ashburner
,
J.
,
Avants
,
B.
,
Chiang
,
M.-C.
,
Christensen
,
G. E.
,
Collins
,
D. L.
,
Gee
,
J.
,
Hellier
,
P.
,
Song
,
J. H.
,
Jenkinson
,
M.
,
Lepage
,
C.
, Rueckert, D.
Thompson
,
P.
,
Vercauteren
,
T.
,
Woods
,
R. P.
,
Mann
,
J. J.
, and
Parsey
,
R. V.
,
2009
, “
Evaluation of 14 Nonlinear Deformation Algorithms Applied to Human Brain MRI Registration
,”
Neuroimage
,
46
(
3
), pp.
786
802
10.1016/j.neuroimage.2008.12.037
16.
Chui
,
H. L.
, and
Rangarajan
,
A.
,
2003
, “
A New Point Matching Algorithm for Non-Rigid Registration
,”
Comput. Vision Image Understanding
,
89
(
2–3
), pp.
114
141
.10.1016/S1077-3142(03)00009-2
17.
Qiu
,
Z. Y.
,
Tang
,
H. Y.
, and
Tian
,
D. S.
,
2009
, “
Non-Rigid Medical Image Registration Based on the Thin-Plate Spline Algorithm
,”
WRI World Congress on Computer Science and Information Engineering
, pp.
522
527
.
18.
Wu
,
H. C.
,
2009
, “
The Karush–Kuhn–Tucker Optimality Conditions in MultiObjective Programming Problems With Interval-Valued Objective Functions
,”
Eur. J. Oper. Res.
,
196
(
1
), pp.
49
60
.10.1016/j.ejor.2008.03.012
19.
Xie
,
Q.
, and
Xie
,
X. Y.
,
2011
, “
Point Cloud Data Reduction Methods of Octree-Based Coding and Neighborhood Search
,”
International Conference on Electronic and Mechanical Engineering and Information Technology (EMEIT)
, IEEE, pp.
3800
3803
.
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