Wyniki wyszukiwania - Biblioteka Nauki

1

Determination of surface waviness using radius of curvature measurement with laser scanning technique

100%

Pieńkos T. , Gładyszewski L. , Prószyński A. , Chocyk D. , Gładyszewski G.

Optica Applicata

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2005

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tom Vol. 35, nr 3

503-507

EN

A method for obtaining the shape of a surface investigated with a laser scanning curvature measurement is presented. Additional simple analysis of raw experimental data allows one to determine waviness of the sample. The accuracy of the method and comparison of the results obtained with the method and commercial profilometer are also described.

2

On the Curvature and Heat Flow on Hamiltonian Systems

100%

Ohta S.-i.

Analysis and Geometry in Metric Spaces

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2014

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tom 2

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nr 1

EN

We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

3

Curvature of optimal control: Deformation of scalar-input planar systems

100%

Kawski M. , Maxwell P. T.

Control and Cybernetics

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2008

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tom Vol. 37, no 2

353-367

EN

The Pontryagin Maximum Principle and high-order open-mapping theorems generalize elementary first-derivative tests to nonlinear optimal control. They provide necessary conditions for a trajectory-control-pair to be optimal, or sufficient conditions for local controllability. Sufficient conditions for optimality (and necessary conditions for nonlinear controllability) are harder to obtain. Like the Legendre-Clebsch condition, they generally take the form of tests for definiteness of second order derivatives. Recently, Agrachev introduced an attractive alternative by developing a notion of curvature of optimal control that generalizes classical Gauss (and Ricci) curvatures. This theory naturally applies to systems whose controls take values on a circle or sphere. In this article we present initial studies of how this notion of curvature provides insight into the limiting case when the circles become degenerate ellipses in the form of closed intervals. Of particular interest are well studied accessible, but uncontrollable, nonlinear systems, and systems that exhibit conjugate points, in which the control takes values in a closed interval u = (u1, u2) ∈ [-1,1] x {0} ⊆ R². We focus on systems that are well-known models for the analysis of small-time local controllability and time-optimal control.

4

Adsorption efficiency of selected natural and synthetic sorbents

100%

Pavolova H. , Bakalar T. , Puskarova P.

Geology, Geophysics and Environment

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2016

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tom Vol. 42, no. 1

114--115

EN

Sorbents are substances binding other substances on their surface. Effective sorbents have a porous surface. The adsorption activity of the surface is closely related to the local radius of curvature of surface irregularities. Suitable sorbents are natural and synthetic solids of amorphous or microcrystalline structure (Kyncl et al. 2008). Globally, the following adsorbents are the most used: activated carbon, zeolites, silica gel, activated alumina (Bakalár et al. 2005). A characteristic of effective adsorbents is large surface area of hundreds of square meters multiply by gram to the power of minus one [m 2 ∙g −1 ]. Other important features of adsorbents include specific volume, porosity, average pore diameter, pore distribution, etc. Some natural materials or industrial waste with high adsorption capacity, which naturally reduces the overall cost of their disposal, can be used for adsorption of heavy metal cations. Some of low-cost sorbents are: lignin, chitin, seaweed/ algae, zeolites, clays, fly-ash, peat, sand grains coated with iron oxide, modified cotton and wool (Pavolová et al 2006). In experiments of Cu and Zn removal from wastewater the following adsorbents were used (Bakalár et al. 2005): - Lewatit S100, which is strongly acidic, gel-like cationic ion exchange resin with particles of equal size based on styrene-divinylbenzene copolymers. Monodisperse beads are chemically and osmotically highly stable. - Chitosan, which is prepared from chitin, naturally occurring in the shells of crustaceans, by deacetylation using strongly alkaline solution. Chitin is a homopolymer composed of β-(1-4)- -N-acetyl-D-glucosamine. The ability of crustaceans shells to bind metal ions is assigned to the presence of exoskeleton in the molecule of chitin and chitosan. - Synthetic zeolite, which is included in the group of aluminosilicates, was prepared by zeolitization of fly-ash from energy industry. - Bentonite, which is included in the group of hydrated aluminosilicates, the main ingredient is mineral montmorillonite. - Slovakit, which is an inorganic composite sorbent made from pure natural ingredients. Its composition is a subject of patent protection. The aspect of time, i.e. the time the specific sorbent reaches the maximum adsorption capacity for the heavy metal removed, is also important in removal of Cu 2+, Zn 2+ and Pb 2+ cations. The experimental measurements of cations adsorption using the above mentioned sorbents are made at the initial concentration of 10 mg∙L −1 of heavy metal. The time to reach the equilibrium for all sorbent during separation of Cu 2+ cations from model solutions of wastewater was about 60 seconds except for chitosan for which it was almost 2 minutes. This is relatively very good result. The equilibrium of Zn 2+ cations adsorption at the experimental measurements for all the selected sorbents was reached in about 80 seconds except for chitosan for which this time was 2 minutes 5 seconds. This time was on average around 20 minutes longer compared to the adsorption of Cu 2+ ions. The adsorption of Pb 2+ cations was carried out at the experimental measurements in about 83 seconds for all the selected sorbents, except for synthetic zeolite for which the time was 1 min 15 seconds. The adsorption of Pb 2+ cations compared to the cations of Cu 2+ was 23 seconds faster and compared to the cations of Zn 2+ was 3 seconds longer. The most appropriate for the removal of Cu 2+, Zn 2+, and Pb 2+ is Lewatit S100 among the used sorbents; the equilibrium was reached in approximately 35 seconds, 45 seconds, and 83 seconds for Zn 2+, Cu 2+, and Pb 2+, respectively. According to the experimental measurements the longest adsorption time was for chitosan – about 2 minutes for Cu 2+ and Zn 2+, and about 1.5 minutes for Pb 2+.

5

Curvature

100%

Gitis A. K.

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

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2005

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tom Vol. 15

5--8

EN

The problem discussed in this paper concerns the curvature of the surface of our globe. The measure of the globe curvature will be determined by a relative growth of the relative change of linear distance between two geodesics which are parallel at their origin but converge when approaching to the Pole. A sphere and an ellipsoid of revolution will be taken as models for further consideration.

PL

Zagadnienie rozważane w niniejszej pracy dotyczy krzywizny na powierzchni kuli ziemskiej. Miarą krzywizny jest względny przyrost względnej miary odległości między dwie-ma geodezyjnymi początkowo idealnie równoległymi. Występujące zagadnienie porównano dla powierzchni kuli i dla elipsoidy obrotowej.

6

Modele wyznaczania promieni krzywizny w strefie kontaktu elementów rolkowej przekładni tocznej

100%

Warchoł S.

Mechanik

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2016

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tom R. 89, nr 5-6

488--489

PL

Przedstawiono dwa modele wyznaczania promieni krzywizny elementów rolkowej przekładni tocznej w strefie ich styku. Pierwszy model wykorzystuje oprogramowanie CATIA, a drugi bazuje na metodzie analitycznej.

EN

Described are two procedures providing for calculation of the curvature radii values within the zone of rolling contact between the elements of thread roller screw. The first method is by using CATIA software while the other is making use of mathematical model.

7

A new method of balanced edge detection based on curvature for gravity data

88%

Dandan J. , Qi Z. , Hairong Z.

Acta Geophysica

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2023

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tom Vol. 71, no. 4

1705--1715

EN

The edge detection method can be used to delineate the position of the structural boundary of the geological body, and it occupies an important position in the processing of gravity data. The shortcomings of traditional edge detection methods are that the output boundary is divergent, the Strength and weak anomalies cannot be balanced, or false boundaries appear in the recognition results. There is a close connection between gravity anomaly and its curvatures and subsurface geological formations. Thus they can be used to describe the geometry of subsurface formations. In this paper, a new method of balanced edge detection based on curvature is proposed by combining the fusion formula of average curvature, vertical curvature, and the degree of curvature. Model tests show that the method proposed in this paper has obvious advantages compared with the recognition effects of several traditional curvature and equalization filtering methods. The edge detection results of the proposed method have good convergence. When both positive and negative anomalies exist, this method is less affected and has anti-noise capabilities. Applying the method to real field data, the results show that the identified geological body structural boundaries are clearer and more accurate, and can be applied to more complex geological environments.

8

New estimate for the curvature of an order-convex set and related questions

88%

Ramazanov A. B.

Control and Cybernetics

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2020

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tom Vol. 49, No. 2

233--240

EN

It is well known that in discrete optimization problems, gradient (local) algorithms do not always guarantee an optimal solution. Therefore, the problem arises of finding the accuracy of the gradient algorithm. This is a fairly well-known problem and numerous publications have been devoted to it. In establishing accuracy, various approaches are used. One of these approaches is to obtain guaranteed estimates of the accuracy of the gradient algorithm in terms of the curvature of the admissible domain. With this approach, it is required to find the curvatures of the admissible region. Since finding the exact value of curvature is a difficult problem to solve, curvature estimates in terms of more or less simply calculated parameters of the problem are relevant. A new improved bound for the curvature of an order-convex set is found and is presented in this paper in terms of the steepness and parameters of strict convexity of the function.

9

Curvature of line in the theory of plane flexion

88%

Anfilofiev A. V.

Applied Mechanics and Engineering

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1999

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tom Vol. 4, no spec.

259-262

EN

The estimations of simplifications in the tasks of definition of lines with a small flexure in theory of bending. Establishments of liaison between the simplified and exact definitions of the curvature of lines and forming allowable spectrum of its approached expressions. The approached expression is considered as result of association of exact expression with a simplifying functional multiplier. With reduction of meaning a simplifying functional multiplier the requirement of a measure of curvature of line also is reduced and in it there are opportunities of definition of lines with the large curvature.

10

Differential geometric approach to the stress aspect of a fault: Airy stress function surface and curvatures

88%

Yamasaki K. , Yajima T.

Acta Geophysica

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2012

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tom Vol. 60, no. 1

4-23

EN

We considered the two-dimensional stress aspect of a fault from the viewpoint of differential geometry. For this analysis, we concentrated on the curvatures of the Airy stress function surface. We found the following: (i) Because the principal stresses are the principal curvatures of the stress function surface, the first and the second invariant quantities in the elasticity correspond to invariant quantities in differential geometry; specifically, the mean and Gaussian curvatures, respectively; (ii) Coulomb's failure criterion shows that the coefficient of friction is the physical expression of the geometric energy of the stress function surface; (iii) The differential geometric expression of the Goursat formula shows that the fault (dislocation) type (strike-slip or dip-slip) corresponds to the stress function surface type (elliptic or hyperbolic). Finally, we discuss the need to use non-biharmonic stress tensor theory to describe the stress aspect of multi-faults or an earthquake source zone.

11

The quick measure of a NURBS surface curvature for accurate triangular meshing

88%

Kniat A.

Polish Maritime Research

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2014

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tom nr 2

41--44

EN

NURBS surfaces are the most widely used surfaces for three-dimensional models in CAD/ CAE programs. When a model for FEM calculation is prepared with a CAD program it is inevitable to mesh it finally. There are many algorithms for meshing planar regions. Some of them may be used for meshing surfaces but it is necessary to take the curvature of the surface under consideration to avoid poor quality mesh. The mesh must be denser in the curved regions of the surface. In this paper, instead of analysing a surface curvature, the method to assess how close is a mesh triangle to the surface to which its vertices belong, is presented. The distance between a mesh triangle and a parallel tangent plane through a point on a surface is the measure of the triangle quality. Finding the surface point whose projection is located inside the mesh triangle and which is the tangency point to the plane parallel to this triangle is an optimization problem. Mathematical description of the problem and the algorithm to find its solution are also presented in the paper.

12

Curvatures of single-input control systems

88%

Jakubczyk B.

Control and Cybernetics

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2009

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tom Vol. 38, no 4B

1375-1391

EN

We introduce invariants of control-affine systems which we call curvatures. They are defined by the drift and the control distribution, given by the system. The curvatures allow us to analyse the variational equation along a given trajectory, as well as existence of conjugate points.

13

The tensile test curvw of wire after its curvature changing

75%

Knap F. , Cieślak Ł.

Archives of Metallurgy

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2002

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tom Vol. 47, iss. 4

421-432

EN

Stress and strain state during the curvature change are characterized by great nonuniformity. There are circumferential tensile stresses in the external elongated zone and compressive ones in the internal zone. Both zones are separated by the neutral surface where circumferential stresses equal zero. Circumferential strains during curvature change can be determined from: (...) In the neighbourhood of the neutral surface the material is in the elastic state and the circumferential stresses can be calculated on the basis on equation: (...). Range of the elastic zone can be determined from the condition that the circumferential stresses reach the value of yield stress. (...) As a result of superimposing of the unloading stresses on the stresses appearing during the active phase of the process some stresses called residual stresses will remain after the process is finished. During tension of a wire having the residual stresses first elastic deformation is observed in the wire, and the tensile force changes linearly depending on the deformation. When sum of the stresses resulting from the external loading and residual stresses reaches the yield stress value, the material is in the plastic condition. With the increase of the stress resulting from the external loading the plastic zone is gradually expanding. In the elastic zone stresses grow proportionally to the strain while in the plastic zone rise in stresses will occur in the range from residual stresses to the yield stress value. Borders between the zones can be determined from the boundary conditions saying that sum of stresses from external loading and residual stresses reaches value of yield stress. On the basis of given equations first distribution of the residual stresses on the cross-section of the wire and then values of forces for the elastic and plastic zones were determined. Considering the peculiarity of the change of stresses in the elastic and plastic zones equations describing tensile force for elastoplastic stage of tension were derived and compared with forces observed in the experiment.

PL

Podczas zmiany krzywizny stan naprężenia i odkształcenia charakteryzuje się dużą nierównomiernością. W zewnętrznej wydłużonej strefie naprężenia obwodowe są rozciągające, natomiast w wewnętrznej są ściskajace. Obie te strefy oddziela od siebie powierzchnia obojętna, w której naprężenia obwodowe są równe zeru. Odkształcenia obwodowe podczas zmiany krzywizny można wyznaczyć ze wzoru (...). W pobliżu powierzchi obojętnej materiał znajduje się w stanie sprężystym, a naprężenia obwodowe można wyznaczyć ze wzoru (...).Zasięg strefy sprężystej może być wyznaczony z warunku, że naprężenia obwodowe osiągają wartość naprężenia uplastyczniającego (...). W wyniku nałożenia sie naprężeń odciążających na naprężenia występujące podczas czynnej fazy procesu pozostaną po jego zakończeniu pewne naprężenia zwane naprężeniami własnymi. Podczas rozciągania drutu, w którym występują naprężenia własne drut początkowo odkształca się sprężyście, a siła rozciągająca zmienia się liniowo w zależności od odkształcenia. Uplastycznienie nastapi wówczas, gdy suma naprężeń od obciażenia zewnętrznego oraz naprężeń własnych osiągnie wartość naprężenia uplastyczniającego. W miarę przykładania coraz to większych naprężeń zewnętrznych rozszerza się zasięg uplastycznionej strefy. W strefie sprężystej naprężenia rosną proporcjonalnie do zachodzących odkształceń, natomiast wzrost naprężeń w strefie uplastycznionej będzie zachodził w zakresie od wartościnaprężeń własnych do wartości naprężenia uplastyczniającego. Granice stref wyznacza się z warunków brzegowych, zgodnie z którymi suma naprężeń własnych oraz naprężeń od obciążenia zewnętrznego osiaga wartość równą naprężeniu uplastyczniającemu. W oparciu o podane wzory wyznaczono rozkład naprężeń własnych na przekroju poprzecznym drutu a nastepnie wartość siły dla strefy sprężystej i plastycznej. Uwzględniając specyfikę zmian naprężeń w strefie sprężystej i plastycznej wprowadzono wzory do określenia siły rozciągania dla sprężysto-plastycznego etapu rozciągania oraz porównano je z siłami wyznaczonymi doświadczalnie.

14

Effect of Curvature Shape of Transparent COVID-19 Protective Face Shields on the Speech Signal

75%

Bjelić M. , Mijić M. , Miljković T. , Šumarac Pavlović D.

Archives of Acoustics

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2024

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tom Vol. 49, nr 1

27--35

EN

Recent papers and studies over the course of last three years have shown that COVID-19 has a negative impact on the speech communication quality between people. This paper presents an influence analysis of the curvature shape of protective transparent shields on the speech signal. Five shields made of the same material and dimensions but with different curvatures were analyzed, from a completely flat to a very curved shield which has the same shape of curvature at its top and bottom and covers the entire face. The influence of the shield is analyzed with two types of experiments – one using dummy head with integrated artificial voice device, and the other using real speakers (female and male actors). It has been shown that usage of protective shields results in a relative increase in the speech signal level, in the frequency range of around 1000 Hz, compared to the situation when protective shields are not used. The relative increase in speech signal levels for large-curvature shields can be up to 8 dB. The possible causes of this phenomenon have been analyzed and examined.

15

Wkład profesora A. Rozenbluma w teorię żelbetu

75%

Nakas A.

Zeszyty Naukowe Politechniki Białostockiej. Budownictwo

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2005

|

tom Z. 26

221-229

PL

Urodzony w Białymstoku wybitny litewski inżynier budowlany, doktor habilitowany, prof. Anatol Rozenblum zaprojektował konstrukcje wielu ważnych dla Litwy budowli. Był autorem podręczników, opracował oryginalną teorię obliczania zarysowania i deformacji konstrukcji żelbetowych. Teoria ta spotkała się z pozytywną oceną wybitnych rosyjskich i zagranicznych specjalistów w zakresie konstrukcji budowlanych, była omawiana na konferencjach oraz w publikacjach naukowych. Prace inżynierów ze szkoły naukowej A. Rozenbluma miały wielki wpływ na dalszy rozwój nauki o konstrukcjach żelbetowych na Litwie.

EN

Professor, Doctor Habil Anatolijus Rozenbliumas created an original theory of calculating the reinforced concrete deformations. The theory was recognized by the most outstanding specialists in this field in the former Soviet Union and abroad. The professor raised a school of researchers on based reinforced concrete structures, the members of which have developed research on structural engeneering in Lithuania. .

16

Curvature Concentrations on the HIV-1 Capsid

75%

Liu J. , Sadre-Marandi F. , Tavener S. , Chen C.

Molecular Based Mathematical Biology

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2015

|

tom 3

|

nr 1

EN

It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers result in icosahedral, tubular, or conical shaped capsids. These pentamer clusters introduce declination and hence curvature on the capsids. This paper provides explicit and quantitative characterization of curvature on virus capsids. The concept of curvature concentration is also introduced. For the HIV (5,7)-cone, it is shown that the curvature concentration at the narrow end is about at least four times higher than that at the broad end. Our modeling results about curvature concentrations on HIV-1 capsids echo the results in the literature that the pentamers are in the regions with the highest stress, although the connection between the two approaches (curvature concentration and stress) is to be explored. This also leads to a conjecture that “HIV-1 capsid narrow end may close last during maturation but open first during entry into a host cell".

17

Wpływ temperatury zbrojenia na sztywność belek żelbetowych w warunkach pożarowych

63%

Głowacki M. , Abramowicz M. , Kowalski R.

Budownictwo i Architektura

|

2013

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tom Vol. 12, nr 1

115--122

PL

W referacie przedstawiono analizę w zakresie wpływu wysokiej temperatury na belki z ogrzewaną strefą rozciąganą. Badania w wysokiej temperaturze przeprowadzono pod działaniem stałego obciążenia, wynoszącego 50 albo 70% siły niszczącej, zapewniającego stałą wartość momentu zginającego w środkowej ogrzewanej części belki. Zbadano belki o dwóch stopniach zbrojenia: 0,44 albo 1,13%. W sumie rozpatrzono cztery serie belek, po trzy w każdej serii (12 elementów). W referacie przeanalizowano względne obniżenie sztywności przekroju belek w zależności od temperatury zbrojenia. Sztywności uzyskane eksperymentalnie, obliczone dwoma sposobami (pomiar maksymalnego ugięcia elementu lub pomiar ugięć w trzech punktach badanego odcinka) porównano z wynikami obliczeń przeprowadzonych według wymagań Eurokodu. Z przeprowadzonej analizy wynika, iż obniżenie sztywności elementu obliczone na podstawie wymagań Eurokodu jest nieco większe od określonego eksperymentalnie.

EN

This paper describes the analysis of high temperature influence on beams with heated tensile zone. High temperature experiments were preformed under the static load of 50 or 70% of the destructive force ensuring constant value of bending moment in the central part of the heated beam. Beams with 2 reinforcement ratios – 0.44 and 1.13% were examined. In total four series of beams, three in each series (12 elements) were used. This paper analyses the reduction of relative beam cross section stiffness depending on reinforcement temperature. Experimentally obtained stiffness values calculated in two ways (element maximal deflection and deflection measured in three points of analysed element) were compared to calculation results made according to Eurocode. The performed analysis shows that reduction of the stiffness of element based on Eurocode calculations is slightly bigger than the experimentally obtained one.

18

Free wool-fibre shapes

63%

Marsh C. , Tsang B. , Wilkins A.

Autex Research Journal

|

2003

|

tom Vol. 3, no. 4

153--159

EN

Eighteen cleaned and degreased Perendale wool fibres, which were as free as possible from external and internal stresses, were photographed, the images scanned to computer, and their space curves reconstructed. Various relations between the fibres' curvature and torsion were discovered which point to the possibility of a statistical description of a free fibre's shape in terms of only a few easily measured quantities, including the mean and RMS curvature. An algorithm is given which allows the generation of realistic wool fibre shapes for use in computer simulations.

19

Probabilistyczna ocena wpływu krzywizn powierzchni na budynki

63%

Kwiatek J.

Zeszyty Naukowe. Górnictwo / Politechnika Śląska

|

2005

|

tom z. 270

131-140

PL

W ocenie wpływu podziemnej eksploatacji górniczej na budynki na terenach górniczych na ogół pomija się wpływ krzywizn powierzchni. Uzasadnia się to małymi ich wartościami. Doświadczenia wskazują jednak na występowanie uszkodzeń budynków, przypisywanych krzywiznom powierzchni. Wykazano, że wobec dużego losowego rozproszenia krzywizn, jest możliwe wystąpienie na terenach górniczych krzywizn na tyle dużych, aby ich szkodliwość dla budynków była niepomijalna.

EN

In assessment of underground mining impact on buildings on mining terrain the impact of surface curvatures is generally omitted. It finds its justification on their small values. Howeover, an extended experience shows that the occurrence of damages of building structures, which are attributed to the surface curvature has place. It was shown that in the presence of great random curvature distribution the occurrance of so big curvatures on the mining terrain is possible which makes their adverse effects for buildings non-neglected.

20

Nowe metody geometryczne w wieloskalowej analizie topografii powierzchni: nachylenie i krzywizna

63%

Bartkowiak T.

Mechanik

|

2018

|

tom R. 91, nr 11

966--969

PL

Przedmiotem artykułu jest przedstawienie nowych, geometrycznych metod wielkoskalowych w opisie topografii powierzchni. Istotnym zagadnieniem w inżynierii powierzchni jest znalezienie zależności funkcyjnych między procesem wytwarzania a uzyskaną topografią lub między topografią a zjawiskami występującymi w trakcie jej oddziaływania z otoczeniem (np. tarciem, wytrzymałością zmęczeniową czy refleksyjnością). Właściwości geometryczne chropowatych powierzchni zmieniają się wraz ze skalą obserwacji, wynikającą z pomiaru lub obliczeń. Skoncentrowano się na dwóch nowych metodach analizujących nachylenie i krzywiznę. Krzywizna jest przedstawiana jako tensor, którego komponenty opisują maksymalną i minimalną krzywiznę, w tym ich wartości i kierunki. Nachylenie jest rozumiane jako orientacja w przestrzeni wektora normalnego do powierzchni. Przedstawiono przykładowe korelacje między nachyleniem i krzywizną a parametrami opisującymi ich oddziaływanie z otoczeniem i proces wytwarzania, wskazując na ich duży potencjał w rozwoju wieloskalowego opisu topografii powierzchni.

EN

The aim of this paper is to demonstrate the use of novel geometric multiscale methods in the characterization of surface topographies with a view to establishing functional relations between formation processes and resulted topography or between topography and its performance during interaction with the environment (e.g. friction, fatigue or gloss reflectance). Geometric properties of rough surfaces change with the scale of observation, i.e., measurement or calculation. In this paper, I focus on two novel method, which analyse slope and curvature in multiple scales. The digital nature of measured surfaces is recognized and is not smoothed to fit a continuous function to the measured heights. Curvature is represented as a second order tensor, which components describe maximal and minimal curvatures and their directions. In order to describe curvature distributions for analyzed regions, statistical parameters, such as: mean and standard deviation, are used. Those measures are utilized to find correlations between them and certain formation or performance parameters. The other method described here bases on slope. In this work, two calculation techniques are presented using orientation normal vectors estimated through covariance matrix method or cross product. As a result of further processing, 3D distributions of direction cosines are obtained, based on which multivariate statistical parameters are calculated (incl. measures of dispersion and higher statistical moments). This paper also presents the sample strong correlations between slope or curvature, for actual measured textures, and manufacturing or performance parameters. This indicates a great potential of those two methods in the development of multiscale characterization of surface topographies.