Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Dipolar depletion effect on the differential capacitance of carbon based materials

The remarkably low experimental values of the capacitance data of carbon based materials in contact with water solvent needs to be explained from a microscopic theory in order to optimize the efficiency of these materials. We show that this experimental result can be explained by the dielectric screening deficiency of the electrostatic potential, which in turn results from the interfacial solvent depletion effect driven by image dipole interactions. We show this by deriving from the microscopic system Hamiltonian a non-mean-field dipolar Poisson-Boltzmann equation. This can account for the interaction of solvent molecules with their electrostatic image resulting from the dielectric discontinuity between the solvent medium and the substrate. The predictions of the extended dipolar Poisson-Boltzmann equation for the differential capacitance are compared with experimental data and good agreement is found without any fitting parameters

A variational model for data fitting on manifolds by minimizing the acceleration of a B\'ezier curve

We derive a variational model to fit a composite B\'ezier curve to a set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closed-form, numerically stable and efficient algorithm to compute the gradient of a B\'ezier curve on manifolds with respect to its control points, expressed as a concatenation of so-called adjoint Jacobi fields. Several examples illustrate the capabilites and validity of this approach both for interpolation and approximation. The examples also illustrate that the approach outperforms previous works tackling this problem

Extracting 3D parametric curves from 2D images of Helical objects

Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively

Neuromeasure: A software package for quantification of cortical motor maps using frameless stereotaxic transcranial magnetic stimulation

The recent enhanced sophistication of non-invasive mapping of the human motor cortex using MRI-guided Transcranial Magnetic Stimulation (TMS) techniques, has not been matched by refinement of methods for generating maps from motor evoked potential (MEP) data, or in quantifying map features. This is despite continued interest in understanding cortical reorganization for natural adaptive processes such as skill learning, or in the case of motor recovery, such as after lesion affecting the corticospinal system. With the observation that TMS-MEP map calculation and quantification methods vary, and that no readily available commercial or free software exists, we sought to establish and make freely available a comprehensive software package that advances existing methods, and could be helpful to scientists and clinician-researchers. Therefore, we developed NeuroMeasure, an open source interactive software application for the analysis of TMS motor cortex mapping data collected from Nexstim® and BrainSight®, two commonly used neuronavigation platforms. NeuroMeasure features four key innovations designed to improve motor mapping analysis: de-dimensionalization of the mapping data, fitting a predictive model, reporting measurements to characterize the motor map, and comparing those measurements between datasets. This software provides a powerful and easy to use workflow for characterizing and comparing motor maps generated with neuronavigated TMS. The software can be downloaded on our github page: https://github.com/EdwardsLabNeuroSci/NeuroMeasure Aim This paper aims to describe a software platform for quantifying and comparing maps of the human primary motor cortex, using neuronavigated transcranial magnetic stimulation, for the purpose of studying brain plasticity in health and disease

Bad pixel modified interpolation for astronomical images

We present a new method of interpolation for the pixel brightness estimation in astronomical images. Our new method is simple and easily implementable. We show the comparison of this method with the widely used linear interpolation and other interpolation algorithms using one thousand astronomical images obtained from the Sloan Digital Sky Survey. The comparison shows that our method improves bad pixels brightness estimation with four times lower mean error than the presently most popular linear interpolation and has a better performance than any other examined method. The presented idea is flexible and can be also applied to presently used and future interpolation methods. The proposed method is especially useful for large sky surveys image reduction but can be also applied to single image correction.Comment: 16 pages, 10 figures. Printed in PASP, September 201