Minkowski sum is an important operation. It is used in many domains such as: computer-aided design, robotics, spatial planning, mathematical morphology, and image processing. We propose a novel algorithm, named the Contributing Verticesbased Minkowski Sum (CVMS) algorithm for the computation of the Minkowski sum of convex polyhedra. The CVMS algorithm allows to easily obtain all the facets of t...

PURPOSE To evaluate the association of acromial morphology and subacromial impingement. METHODS Bilateral shoulder computed tomography was performed in 138 patients who received shoulder arthroscopy. Measured parameters included: acromial tilt (AT), modified acromial tilt (mAT), acromial slope (AS), acromiohumeral interval (AHI), lateral acromial angle (LAA), acromial index (AI), critical sho...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

This paper presents the results of an extensive laboratory set tests aimed to study failure downstream shoulder highly permeable rockfill subjected overflow. The experimental research comprised testing 114 physical models by varying following elements: (i) median size uniform gravels (7 45 mm); (ii) configuration dam, i.e., upstream and shoulders crest or just shoulder; (iii) dam height (from 0...

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

In this article we propose the novel approach to measure anthropometrical features such as height, width of shoulder, circumference of the chest, hip and waist. The sub-pixel processing and convex hull technique are used to efficiently measure the features from 2d image. The SVM technique is used to classify men and women based on measured features. The results of real data processing are prese...

Kaltenborn's convex-concave rule is a familiar concept in joint treatment techniques and arthrokinematics. Recent investigations on the glenohumeral joint appear to question this rule and thus accepted practice guidelines. An evidence-based systematic review was conducted to summarize and interpret the evidence on the direction of the accessory gliding movement of the head of the humerus (HOH) ...

Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, |ζ| is convex, and that in the region 0 < <(s) ≤ 0.5, |ζ| has a negative slope. In each case, analytical formulae are established, and numerical examples are presented to validate these formulae.

The metric subregularity of multifunctions is a key notion in Variational Analysis and Optimization. In this paper, we establish firstly a cretirion for metric subregularity of multifunctions between metric spaces, by using the strong slope. Next, we use a combination of abstract coderivatives and contingent derivatives to derive verifiable first order conditions ensuring the metric subregulari...

In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume, volume and surface area related to the Brunn-Minkowski theory. All measures considered are invariant under translations; furthermore, they may also be invariant under subgroups of the aane transformation group. For the case of rotation and scale ...