On Approximation of Human Corneal Surface with Superellipsoids

Ţălu, Mihai; Ţălu, Ștefan; Ţălu, Ştefan; Shah, Rajiv

doi:10.1007/978-3-642-22586-4_53

Cited by 3 publications

(8 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Surface roughness consists of fine irregularities which result from the inherent action of the production process . To characterize surface roughness, two main approaches, based on different mathematical procedures, are generally used: statistical (the classical descriptive approach) and fractal description (the modern approach) .…”

Section: Introductionmentioning

confidence: 99%

“…Fractal theory, proposed by Benoît Mandelbrot (1983), has provided a more appropriate and convenient approach to the study of complex and heterogeneous geometrical structures than traditional Euclidean geometry. Fractal theory is suited to the description of objects which have an integer dimensionality and which are ideal, man‐made, or regular .…”

Section: Introductionmentioning

confidence: 99%

“…A fractal object is a mathematical set with a high degree of geometrical complexity, mainly characterized by four properties: (a) irregularity of the shape; (b) self‐similarity of the structure; (c) noninteger dimension; (d) complexity .…”

Section: Introductionmentioning

confidence: 99%

“…) gives the fractal dimension D BC , which is described with the following Eq . :

D_{BC} = \lim_{r \to 0} \frac{log (N (r))}{log (1 / r)}

where N ( r ) represents the number of nonempty boxes of size r needed to cover the fractal structure.…”

Section: Introductionmentioning

confidence: 99%

“…Multifractal theory generalizes and extends fractal theory from the geometry of sets as such to geometric properties of measure. The multifractal measures (or multifractals) are related to the study of the distribution of different physical quantities in fractal or nonfractal structures .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multifractal characterization of unworn hydrogel contact lens surfaces

Ţălu

Stach

2013

Polym Eng Sci

View full text Add to dashboard Cite

Purpose: The aim of this work was to estimate the multifractal spectra of 3D surface roughness for unworn hydrogel contact lenses (CL), obtained with atomic force microscopy (AFM) analysis. Materials and methods: Contact lenses made from vifilcon A (Focus® Monthly Toric Visitint® model, CIBA Vision Corp.) were investigated. CL surface roughness was studied by AFM in tapping‐mode™, in an aqueous environment, on square areas ranging from 1 to 4 μm2. A detailed methodology for CL surface multifractal characterization, which may be applied for AFM data, was presented. Results: The CL surface roughness revealed multifractal geometry at various magnifications. The generalized dimension Dq and the singularity spectrum f(α) provided quantitative values that characterize the local scale properties of CL surface geometry at nanometer scale. Conclusions: Multifractal analysis provides different yet complementary information to that offered by traditional surface statistical parameters. POLYM. ENG. SCI., 54:1066–1080, 2014. © 2013 Society of Plastics Engineers

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…) gives the fractal dimension D BC , which is described with the following Eq . :

D_{BC} = \lim_{r \to 0} \frac{log (N (r))}{log (1 / r)}

where N ( r ) represents the number of nonempty boxes of size r needed to cover the fractal structure.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multifractal characterization of unworn hydrogel contact lens surfaces

Ţălu

Stach

2013

Polym Eng Sci

View full text Add to dashboard Cite

show abstract

Proximity query based on second order cone programming using convex superquadrics: a static collision detection algorithm for narrow-phase

Chen

Feng

et al. 2015

Assembly Automation

View full text Add to dashboard Cite

Purpose – This paper aims to find an objects representation scheme with high precision and to compute the objects’ separation distance effectively in final analysis. Proximity queries have been used widely in robot trajectory planning, automatic assembly planning, virtual surgery and many other applications. The core of proximity query is the precise computation of (minimum) separation distance in narrow phase, and specific object representation scheme corresponds to different methods of separation distance computation. Design/methodology/approach – In this paper, a second-order cone programming (SOCP)-based (minimum) separation distance computation algorithm was proposed. It treats convex superquadrics, descriptive primitives of complex object as the study objects. The separation distance between two convex superquadrics was written as a general nonlinear programming (NLP) problem with superquadric constraints and then transformed into an SOCP problem with the method of conic formulation of superquadric constraints. Finally, a primal-dual interior point method embedded in MOSEK was used for solving the SOCP problem. Findings – The proposed algorithm achieved exact separation distance computation between convex superquadrics, with a relative error of 10-6. It is particularly suitable for proximity queries in narrow phase of static collision detection algorithms. Further, the proposed algorithm achieved continuous collision detection between rectilinear translation superquadrics. Originality/value – The proposed algorithm in narrow phase of static collision detection algorithms makes objects’ separation distance effectively computed. Proximity queries are easy and more accurate to perform in this way.

show abstract

Turkey and the Palestinian Question: The Shift of Roles in Foreign Policy

Ertosun

2016

Digest Mid East Studies

View full text Add to dashboard Cite

For Turkey, which was seeking a leading role in the Middle East, the Palestinian Question became a priority in its foreign policy during the late 1990s. In this article, it is argued that the role Turkey primarily espoused in the resolution of the Palestinian Question in the period 2000–2009 has mainly been that of a communicator. Nonetheless, in times of crises between Palestine and Israel, Ankara lost its neutrality and credibility to some extent, as it shifted to the role of guardian of Palestinians and proponent of Palestine, thereby undermining its communicator role. Finally, this dilemma in Turkish foreign policy in the Palestinian Question was the fundamental impediment to Turkey's sustainable and constructive contribution to the settlement of the problem in the examined period.

show abstract

On Approximation of Human Corneal Surface with Superellipsoids

Cited by 3 publications

References 0 publications

Multifractal characterization of unworn hydrogel contact lens surfaces

Multifractal characterization of unworn hydrogel contact lens surfaces

Proximity query based on second order cone programming using convex superquadrics: a static collision detection algorithm for narrow-phase

Turkey and the Palestinian Question: The Shift of Roles in Foreign Policy

Contact Info

Product

Resources

About