There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Photoplethysmography and its application in clinical physiological measurement

This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For hexahedral meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of quadrilateral/hexahedral meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.

Surface Smoothing and Quality Improvement of Quadrilateral/Hexahedral Meshes with Geometric Flow

(1977). Markov Chains — Theory and Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 236-237.

Markov Chains — Theory and Applications

This article is to review the published works related to the CAD/CAM and in vitro finishing of bioceramics in restorative dentistry over the last two decades. Bioceramics with a wide spectrum of glass–ceramics, reinforced porcelains, zirconias, aluminas, fiber-reinforced ceramic composites and multi-layered ceramic structures are firstly classified with two categories based on their machinabilities. The investigations on the restorative performance with respect to wear, fatigue and durability are then summarized. Next, the technological challenges in dental CAD/CAM processes for rapid generation of crowns, inlays/onlays and bridges are reviewed. Furthermore, the research on the clinically applied abrasive finishing of bioceramics for intraoral final adjustments using high speed dental handpieces and diamond burs is addressed. Finally, the critical research issues relating to manufacturing are highlighted as future research trends for better applications of dental bioceramics in restorations.

An overview of in vitro abrasive finishing & CAD/CAM of bioceramics in restorative dentistry

In this paper, we present an application of numerical optimization for surface reconstruction (more precisely: reconstruction of missing parts of a real geometric object represented by volume data) by employing a specially designed genetic algorithm to solve a problem concerning computer-aided design in dentistry. Using a space mapping technique the surface of a given model tooth is fitted by a shape transformation to extrapolate (or reconstruct) the remaining surface of a patient's tooth with occurring damage such as a “drill hole.” Thereby, the genetic algorithm minimizes the error of the approximation by optimizing a set of control points that determine the coefficients for spline functions, which in turn define a space transformation. The fitness function to be minimized by the genetic algorithm is the error between the transformed occlusal surface of the model tooth and the remaining occlusal surface of the damaged (drilled) tooth. The algorithm, that is used, is based upon a proposal by Mahfoud and Goldberg. It uses a simulated-annealing type selection scheme, which is applied sequentially (pair-wise, or one-by-one) to the members in the parent generation and their respective offspring generated by mutation-crossover. We outline a proof of convergence for this algorithm. The algorithm is parallel in regard to computing the fitness-values of creatures.

Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection

In this paper we present two novel techniques to improve the quality of triangle surface meshes while preserving surface characteristics as much as possible. In contrast to previous approaches we do not tend to preserve mesh nodes on the original discrete surface. Instead, we propose two techniques, which allow to keep resulting mesh close to the smooth surface approximated by the original mesh. The first technique called trapezium drawing (TD) is iterative and can be easy implemented for all types of meshes. It does not use any information about surface geometry. On the contrary, in the second technique to find new location each node of the mesh we use value of maximum curvature defined at this node. We show that the second approach called curvature-based mesh improvement (CBMI) gives the best results in the sense of keeping new mesh very close to the original surface and preserving surface characteristics such as normals and curvatures. But unlike TD it can be applied only for meshes representing smooth surfaces without sharp edges and corners. Several quantitative measures are presented to demonstrate the effectiveness of both proposed techniques.

Two Techniques to Improve Mesh Quality and Preserve Surface Characteristics.

In this work we investigate the effect of diffusive voltage and current couplings between natural pacemaker oscillators in the heterogeneous coupled oscillator model of ECG signals. We study the synchronization behavior of the oscillator system for normal and fast cardiac sinus rhythms and reproduce different mode-locked cases which correspond to known incomplete atrioventricular blocks. The obtained results may help to choose reasonable coupling configurations to study heart rhythm dynamics coupled oscillator models.

http://ieeexplore.ieee.org/iel7/7033073/7047454/07047503.pdf

Effect of coupling on the pacemaker synchronization in coupled oscillator ECG model

In the paper we present a novel algorithm for collision detec tion between complex geometric objects represented by polygonal models and undergoing rigid motions and deform ations. Most algorithms described in the literature deal with rigid bodies and are based on some kind of hierarchi cal representations. We present the alternative approach. The algorithm relies on the idea of "sensor partic les": interacting particles distributed on a surface. Two types of particles that interact in a special way are usedfor determining the minimum distance between two models. The algorithm has been implemented and used in real‐ time simulation of dynamic interaction between geometric objects. A detailed description of the algorithm , animation examples, and benchmarks are included in the paper. A potential application of this software algorit hm is collision detection for animation of bodies with deformable surfaces.

/pdf/particle-based-collision-detection-5cobfgmwve.pdf

Particle-based Collision Detection

This paper presents an approach for interactive and intuitive deformation of 3D shapes. The approach combines a fast and efficient 3D free form deformation algorithm with a high degrees-offreedom input device of hand joint angles, namely, the CyberGlove. The deformation algorithm employs compactly supported radial basis functions (CSRBFs) to produce reasonable shape deformations quickly. However, positioning and moving CSRBFs properly to create a desired shape deformation is not a trivial task. In our approach, the 10 CSRBFs are virtually attached to the fingertips of the CyberGloves worn on both hands of the user. This allows the user an intuitive manipulation of 3D shapes in a manner somewhat similar to clay modeling. While the shape deformation algorithm is not physically-based, the shape deformation created by the algorithm is plausible and quite useful. In terms of speed, deformations involving all the 15k vertices of a 32k triangle mesh model can be produced at speed of about 30 frames-per-second.

Vladimir Savchenko

Papers

Reconstructing occlusal surfaces of teeth using a genetic algorithm with simulated annealing type selection

Two Techniques to Improve Mesh Quality and Preserve Surface Characteristics.

Effect of coupling on the pacemaker synchronization in coupled oscillator ECG model

Particle-based Collision Detection

3D freeform design: interactive shape deformations by the use of CyberGlove