scholarly journals Monotonicity-preserving rational bi-cubic spline surface interpolation

ScienceAsia ◽  
2014 ◽  
Vol 40S (1) ◽  
pp. 22 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd Majid ◽  
Mohd Nain Hj Awang ◽  
Jamaludin Md Ali
Keyword(s):  
Cubic Spline ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Monotonicity Preserving

A Smooth Contact Algorithm Using Cubic Spline Surface Interpolation for Rigid and Flexible Bodies

2013 ◽  
Author(s):  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Contact Force ◽  
Cubic Spline ◽  
Surface Representation ◽  
Flexible Bodies ◽  
Contact Algorithm ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Smooth Contact ◽  
Representation Method ◽  
Detailed Search

The contact analysis of multi-flexible-body dynamics (MFBD) has been an important issue in the area of computational dynamics because the realistic dynamic analysis of many mechanical systems includes the contacts among rigid and flexible bodies. But, until now, the contact analysis in the multi-flexible-body dynamics has still remained as a big, challenging area. Especially, the most of contact algorithms have been developed based on the facetted triangles. As a result, the contact force based on the facetted surface was not accurate and smooth because the geometrical error is already included in the contact surface representation stage. This kind of error can be very important in the precise mechanism such as gear contact or cam-valve contact problems. In order to resolve this problem, this study suggests a cubic spline surface representation method and related contact algorithms. The proposed contact algorithms are using the compliant contact force model based on the Hertzian contact theory. In order to evaluate the smooth contact force, the penetration depth and contact normal directions are evaluated by using the cubic spline surface interpolation. Also, for the robust and efficient contact algorithm development, the contact algorithms are divided into four main parts which are a surface representation, a pre-search, a detailed search and a contact force generation. In the surface representation part, we propose a smooth surface representation method which can be used for smooth rigid and flexible bodies. In the pre-search, the algorithm performs collision detection and composes the expected contact pairs for the detailed search. In the detailed search, the penetration depth and contact reference frame are calculated with the cubic spline surface interpolation in order to generate the accurate and smooth contact force. Finally in the contact force generation part, we evaluate the contact force and Jacobian matrix for the implicit time integrator.

Parallel B-Spline Surface Interpolation on a Mesh-Connected Processor Array

1995 ◽  
Vol 24 (2) ◽  
pp. 224-229
Author(s):  
F.H. Cheng ◽  
G.W. Wasilkowski ◽  
J.Y. Wang ◽  
C.M. Zhang ◽  
W.P. Wang
Keyword(s):  
Processor Array ◽  
B Spline ◽  
Surface Interpolation ◽  
Spline Surface

scholarly journals A Reconstruction Algorithm for Blade Surface Based on Less Measured Points

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jia Liu ◽  
Ji Zhao ◽  
Xu Yang ◽  
Jiming Liu ◽  
Xingtian Qu ◽  
...  
Keyword(s):  
Reconstruction Algorithm ◽  
Surface Model ◽  
Machining Accuracy ◽  
Blade Surface ◽  
B Spline ◽  
Design Concepts ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Machining Allowance ◽  
Curvature Continuity

A reconstruction algorithm for blade surface from less measured points of section curves is given based on B-spline surface interpolation. The less measured points are divided into different segments by the key geometric points and throat points which are defined according to design concepts. The segmentations are performed by different fitting algorithms with consideration of curvature continuity as their boundary condition to avoid flow disturbance. Finally, a high-quality reconstruction surface model is obtained by using the B-spline curve meshes constructed by paired points. The advantage of this algorithm is the simplicity and effectivity reconstruction of blade surface to ensure the aerodynamic performance. Moreover, the obtained paired points can be regarded as measured points to measure and reconstruct the blade surface directly. Experimental results show that the reconstruction blade surface is suitable for precisely representing blade, evaluating machining accuracy, and analyzing machining allowance.

Monotonicity Preserving Surface Interpolation

1985 ◽  
Vol 22 (2) ◽  
pp. 401-411 ◽  
Author(s):  
R. K. Beatson ◽  
Z. Ziegler
Keyword(s):  
Surface Interpolation ◽  
Monotonicity Preserving

A Subassembly Simulation Method with Physical Deformation and Reconstruction of an Aircraft

2013 ◽  
Vol 420 ◽  
pp. 3-8
Author(s):  
Yong Gang Kang ◽  
Fei Yan Guo ◽  
Ting Xu ◽  
Jie Huang ◽  
Cong Ren
Keyword(s):  
Finite Element Method ◽  
Simulation Method ◽  
Assembly Process ◽  
Model Reconstruction ◽  
B Spline ◽  
Surface Interpolation ◽  
Simulation Process ◽  
Spline Surface ◽  
Thin Walled ◽  
Structural Parts

In order to include the physical deformation of the large thin-walled structure in the subassembly simulation process in aerospace, a new method based on model reconstruction was proposed. Firstly, finite element method is applied for calculating the deformation of the structural parts according to different assembly status with certain temperature and stress field. Based on the actual deformation data of the surface, some reference point was selected and the method of bicubic B-spline surface interpolation is selected to reconstruct the above surface, and to express the deformed structural parts. Based on physical deformation, a compensating method is proposed to amend assembly path in corresponding assembly process with the constructed model. Under the DELMIA virtual environment with the real, the simulation method has been put in to use on aircraft sidewall panel assembly, and the validity of the method is verified experimentally.

Spline surface interpolation for calculating 3-D ventricular strains from MRI tissue tagging

1996 ◽  
Vol 270 (1) ◽  
pp. H281-H297 ◽  
Author(s):  
M. J. Moulton ◽  
L. L. Creswell ◽  
S. W. Downing ◽  
R. L. Actis ◽  
B. A. Szabo ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Reference Image ◽  
Line Detection ◽  
Elasticity Solution ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Tissue Tagging ◽  
Measurement Analysis ◽  
Displacement Reconstruction ◽  
Rms Errors

A method is developed and validated for approximating continuous smooth distributions of finite strains in the ventricles from the deformations of magnetic resonance imaging (MRI) tissue tagging "tag lines" or "tag surfaces." Tag lines and intersections of orthogonal tag lines are determined using a semiautomated algorithm. Three-dimensional (3-D) reconstruction of the displacement field on tag surfaces is performed using two orthogonal sets of MRI images and employing spline surface interpolation. The 3-D regional ventricular wall strains are computed from an initial reference image to a deformed image in diastole or systole by defining a mapping or transformation of space between the two states. The resultant mapping is termed the measurement analysis solution and is defined by determining a set of coefficients for the approximating functions that best fit the measured tag surface displacements. Validation of the method is performed by simulating tag line or surface deformations with a finite element (FE) elasticity solution of the heart and incorporating the measured root-mean-square (rms) errors of tag line detection into the simulations. The FE-computed strains are compared with strains calculated by the proposed procedure. The average difference between two-dimensional (2-D) FE-computed strains and strains calculated by the measurement analysis was 0.022 +/- 0.009 or 14.2 +/- 3.6% of the average FE elasticity strain solution. The 3-D displacement reconstruction errors averaged 0.087 +/- 0.002 mm or 2.4 +/- 0.1% of the average FE solution, and 3-D strain fitting errors averaged 0.024 +/- 0.011 or 15.9 +/- 2.8% of the average 3-D FE elasticity solution. When the rms errors in tag line detection were included in the 2-D simulations, the agreement between FE solution and fitted solution was 24.7% for the 2-D simulations and 19.2% for the 3-D simulations. We conclude that the 3-D displacements of MRI tag lines may be reconstructed accurately; however, the strain solution magnifies the small errors in locating tag lines and reconstructing 3-D displacements.

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