Single valuedness, parameterization, and approximating 3D surfaces using B-splines

1993 ◽  
Author(s):  
Saravajit S. Sinha ◽  
Pradeep Seneviratne
Keyword(s):  
B Splines ◽  
3D Surfaces

Iteration and optimization scheme for the reconstruction of 3D surfaces based on non-uniform rational B-splines

2012 ◽  
Vol 44 (11) ◽  
pp. 1127-1140 ◽  
Author(s):  
Wei-Cheng Xie ◽  
Xiu-Fen Zou ◽  
Jian-Dong Yang ◽  
Jie-Bin Yang
Keyword(s):  
Optimization Scheme ◽  
B Splines ◽  
3D Surfaces

Draping 2D Patterns Onto 3D Surfaces

2003 ◽  
Author(s):  
Ajay Joneja ◽  
Angela Tam ◽  
Fu Jing
Keyword(s):  
Mold Surface ◽  
Polygonal Approximation ◽  
Surface Representation ◽  
B Splines ◽  
3D Surface ◽  
Software Program ◽  
2D Pattern ◽  
Representation Scheme ◽  
3D Surfaces

We describe a simple new CAD operator that allows draping of given 2D patterns onto the surface of a 3D mold. The 2D pattern is any closed, connected polygon or a polygonal approximation of a shape bounded by curves. The mold is typically described in terms of any standard surface representation scheme, such as NURBS or B-Splines. The draping is achieved by mapping skeletal lines on the 2D pattern onto corresponding geodesic curves on the 3D surface. If the mold surface is developable, our method gives a draping with zero distortion. A useful application in the CAD of footwear is demonstrated as a motivation for this work. A simple software program has been implemented to test the operator, and examples are provided to demonstrate its use.

AlCu Pattern Generation on 3D StructuredWafer Using Multi Level Exposure Method on Electrodeposited Polymer Material

2003 ◽  
Vol 766 ◽  
Author(s):  
Vineet Sharma ◽  
Arief B. Suriadi ◽  
Frank Berauer ◽  
Laurie S. Mittelstadt
Keyword(s):  
Line Width ◽  
Metal Film ◽  
Focal Depth ◽  
Cost Effective ◽  
Pattern Generation ◽  
Promising Technique ◽  
Critical Dimensions ◽  
Exposure Method ◽  
Multi Level ◽  
3D Surfaces

AbstractNormal photolithography tools have focal depth limitations and are unable to meet the expectations of high resolution photolithography on highly topographic structures. This paper shows a cost effective and promising technique of combining two different approaches to achieve critical dimensions of traces on slope pattern continuity on highly topographic structures. Electrophoretically deposited photoresist is used on 3-D structured wafers. This photoresist coating technique is fairly known in the MEMS industries to achieve uniform and conformal photoresist films on 3D surfaces. Multi step exposures are used to expose electrophoretically deposited photoresist. AlCu (Cu-0.5%), 0.47-0.53 μm thick metal film is deposited on 3D structured silicon substrate to plate photoresist. By combining these two novel methods, metal (AlCu) traces of 75 μm line width and 150 μm pitch (from top flat to down the slope) have been demonstrated on isotropically etched 350 μm deep trenches with 5-10% line width loss.

2D periodic structures patterned on 3D surfaces by interference lithography for SERS

2018 ◽  
Vol 461 ◽  
pp. 171-174 ◽  
Author(s):  
Ivana Lettrichova ◽  
Agata Laurencikova ◽  
Dusan Pudis ◽  
Jozef Novak ◽  
Matej Goraus ◽  
...  
Keyword(s):  
Periodic Structures ◽  
Interference Lithography ◽  
3D Surfaces

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines

scholarly journals 3D-surface MALDI mass spectrometry imaging for visualising plant defensive cardiac glycosides in Asclepias curassavica

2021 ◽  
Vol 413 (8) ◽  
pp. 2125-2134
Author(s):  
Domenic Dreisbach ◽  
Georg Petschenka ◽  
Bernhard Spengler ◽  
Dhaka R. Bhandari
Keyword(s):  
Mass Spectrometry ◽  
Mass Spectrometry Imaging ◽  
Cardiac Glycosides ◽  
Molecular Mechanisms ◽  
Plant Science ◽  
Primary Metabolism ◽  
Native Plant ◽  
Asclepias Curassavica ◽  
3D Surface ◽  
3D Surfaces

AbstractMass spectrometry–based imaging (MSI) has emerged as a promising method for spatial metabolomics in plant science. Several ionisation techniques have shown great potential for the spatially resolved analysis of metabolites in plant tissue. However, limitations in technology and methodology limited the molecular information for irregular 3D surfaces with resolutions on the micrometre scale. Here, we used atmospheric-pressure 3D-surface matrix-assisted laser desorption/ionisation mass spectrometry imaging (3D-surface MALDI MSI) to investigate plant chemical defence at the topographic molecular level for the model system Asclepias curassavica. Upon mechanical damage (simulating herbivore attacks) of native A. curassavica leaves, the surface of the leaves varies up to 700 μm, and cardiac glycosides (cardenolides) and other defence metabolites were exclusively detected in damaged leaf tissue but not in different regions of the same leaf. Our results indicated an increased latex flow rate towards the point of damage leading to an accumulation of defence substances in the affected area. While the concentration of cardiac glycosides showed no differences between 10 and 300 min after wounding, cardiac glycosides decreased after 24 h. The employed autofocusing AP-SMALDI MSI system provides a significant technological advancement for the visualisation of individual molecule species on irregular 3D surfaces such as native plant leaves. Our study demonstrates the enormous potential of this method in the field of plant science including primary metabolism and molecular mechanisms of plant responses to abiotic and biotic stress and symbiotic relationships. Graphical abstract

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

2021 ◽  
Vol 381 ◽  
pp. 113779
Author(s):  
Wenbin Hou ◽  
Kai Jiang ◽  
Xuefeng Zhu ◽  
Yuanxing Shen ◽  
Ping Hu
Keyword(s):  
Isogeometric Analysis ◽  
B Splines ◽  
Discontinuous Problems
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