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{{redirect2|Moiré|Moire||Moire (disambiguation)}}
Nakład 3D wskazywany inaczej wydawaniem przestrzennym owe przebieg tworzenia celów fizycznych w trójwymiarze na przyczynie sformowanego oraz napisanego w pamięci komputera kroju.<br><br>
{{Multiple issues|refimprove = May 2012|lead too short = May 2012}}


{{double image|right|Moiré pattern.svg|160|Divers - Illustrated London News Feb 6 1873-2.PNG|160|A moiré pattern, formed by two sets of parallel lines, one set inclined at an angle of 5° to the other|The fine lines that make up the sky in this image create moiré patterns when shown at some resolutions for the same reason that photographs of televisions exhibit moiré patterns: The lines are not absolutely level.||}}
Użycie nakładu 3d istnieje przeróżne. Technologia druku 3D umożliwia aktywowanie celów np części zapasowych, form. Technika owa może być z powodzeniem skorzystania do okazale rozumianego prototypowania. W sytuacji gdy żądamy kilku kilkunastu biegłości wiadomego obiektu, uruchomianie okazałej pracy zdoła okazać się nielukratywne, acz  [http://games.cool-radio.in/profile/kalawhorn projektowanie 3d] w relatywnie naskórkowym czasie możemy wyprodukować te tematy za pomocą nakładu 3d.<br><br>Sukcesywnym przykładem gdzie wolno wyzyskać technikę 3d są figury dokonywujące odnowy starych przedmiotów. Oczekując wyrównać, np stary zegar, jakiego części nie ma na rynku możemy założyć starodawną frakcja oraz wydrukować przydatny nam egzemplarz. Obfite nadzieje z nakładem 3d pakuje medycyna. Prominentne są już przypadki dokąd z powodzeniem wydrukowano protezę dopasowaną do potrzeb pacjenta. Hiszpańscy doktorzy zdobyli nie niski sukces usuwając operacyjnie guza, który był uważany za nieoperacyjnego. Przed rozpoczęciem do operacji pozostawał utworzony skrupulatny projekt 3d guza na, jakim syndrom operacyjny trenował przed rozpoczęciem do odpowiedniego zabiegu.<br><br>My website :: [http://mw1.wikinect.hucompute.org/index.php/6_Winning_Strategies_To_Use_For_Druk_3d projektowanie 3d]
 
In physics, mathematics, and art, a '''moiré pattern''' ({{IPAc-en|m|w|ɑr|ˈ|eɪ}}; French: {{IPA-fr|mwaˈʁe|}}) is a secondary and visually evident superimposed pattern created, for example, when two identical  (usually transparent) patterns on a flat or curved surface (such as closely spaced straight lines drawn radiating from a point or taking the form of a grid) are overlaid while displaced or rotated a small amount from one another.
 
== Etymology ==
The term originates from [[Moire (fabric)|moire]] (''moiré'' in its French adjectival form), a type of [[textile]], traditionally of [[silk]] but now also of [[cotton]] or [[synthetic fiber]], with a rippled or 'watered' appearance.
 
The history of the word ''moiré'' is complicated.  The earliest agreed{{By whom|date=June 2012}} origin is the Arabic ''mukhayyar'' (مُخَيَّر in Arabic, which means ''chosen''), a cloth made from the wool of the [[Angora goat]], from ''khayyara'' (خيّر in Arabic), 'he chose' (hence 'a choice, or excellent, cloth').  It has also been suggested that the Arabic word was formed from the Latin ''marmoreus'', meaning 'like marble'.  By 1570 the word had found its way into English as ''[[mohair]]''. This was then adopted into French as ''mouaire'', and by 1660 (in the writings of [[Samuel Pepys]]) it had been adopted back into English as ''moire'' or ''moyre''.  Meanwhile the French ''mouaire'' had mutated into a verb, ''moirer'', meaning 'to produce a watered textile by weaving or pressing', which by 1823 had spawned the adjective ''moiré''. ''Moire'' (pronounced "mwar") and ''moiré'' (pronounced "mwar-ay") are now used somewhat interchangeably in English, though ''moire'' is more often used for the cloth and ''moiré'' for the pattern.
 
"Watered textile" refers to laying part of the textile on top of another part, and pressing the two layers when wet. The similarity of the spacing of individual threads (warp and woof), which is, however, not perfect spacing, creates characteristic patterns when the layers are pressed together; when dry, the patterns remain.
 
== Pattern formation ==
 
Moiré patterns are often an undesired [[Artifact (observational)|artifact]] of [[digital image|images]] produced  by various [[digital imaging]] and [[computer graphics]] techniques, for example when [[Image scanner|scanning]] a [[halftone]] picture or [[Ray tracing (graphics)|ray tracing]] a checkered plane (the latter being a special case of [[aliasing]], due to [[undersampling]] a fine regular pattern).<ref>[http://www.scantips.com/basics06.html Moire in scanning], scantips.com, accessed July 2009</ref>  This can be overcome in texture mapping through the use of [[mipmapping]] and [[anisotropic filtering]].
 
The drawing on the upper right shows a moiré pattern.  The lines could represent fibers in moiré silk, or lines drawn on paper or on a computer screen. The [[nonlinear]] interaction of the optical patterns of lines creates a real and visible pattern of roughly parallel dark and light bands, the moiré pattern, superimposed on the lines.<ref>{{cite book
| title = Energy Minimization Methods in Computer Vision and Pattern Recognition
| author = Anil K. Jain, Mário Figueiredo, and Josiane Zerubia (editors)
| publisher = Springer
| year = 2001
| url = http://books.google.com/books?visbn=3540425233&id=yb8otde21fcC&pg=RA1-PA198&lpg=RA1-PA198&dq=%22moire+pattern%22+nonlinear}}</ref>
 
More complex [[line moiré]] patterns are created if the lines are curved or not exactly parallel. Moiré patterns revealing complex shapes, or sequences of symbols embedded in one of the layers (in form of periodically repeated compressed shapes) are created with [[shape moiré]], otherwise called [[band moiré]] patterns. One of the most important properties of [[shape moiré]] is its ability to magnify tiny shapes along either one or both axes, that is, stretching. A common 2D example of moiré magnification occurs when viewing a [[chain-link fence]] through a second chain-link fence of identical design.  The fine structure of the design is visible even at great distances.
 
== Calculations ==
 
=== Moiré of parallel patterns ===
 
==== Geometrical approach ====
 
{{double image|right|Moire parallel.svg|160|Moire ecart angulaire.png|160|the patterns are superimposed in the mid-width of the figure|Moiré obtained by the superimposition of two similar patterns rotated by an angle α||}}
 
Let us consider two patterns made of parallel and equidistant lines, e.g., vertical lines. The step of the first pattern is <math>p</math>, the step of the second is <math>p+\delta p</math>, with <math>0 < \delta < 1</math>.
 
If the lines of the patterns are superimposed at the left of the figure, the shift between the lines increase when going to the right. After a given number of lines, the patterns are opposed: the lines of the second pattern are between the lines of the first pattern. If we look from a far distance, we have the feeling of pale zones when the lines are superimposed, (there is white between the lines), and of dark zones when the lines are "opposed".
 
The middle of the first dark zone is when the shift is equal to <math>\frac{p}{2}</math>. The <math>n</math><sup>th</sup> line of the second pattern is shifted by <math>n \cdot \delta p</math> compared to the <math>n</math><sup>th</sup> line of the first network. The middle of the first dark zone thus corresponds to
: <math>n \cdot \delta p = \frac{p}{2}</math>
that is
: <math>n = \frac{p}{2 \delta p}</math>.
The distance ''d'' between the middle of a pale zone and a dark zone is
: <math>d = n \cdot p = \frac{p^2}{2 \delta p}</math>
the distance between the middle of two dark zones, which is also the distance between two pale zones, is
: <math>2d = \frac{p^2}{\delta p}</math>
From this formula, we can see that :
* the bigger the step, the bigger the distance between the pale and dark zones;
* the bigger the discrepancy <math>\delta p</math>, the closer the dark and pale zones; a great spacing between dark and pale zones mean that the patterns have very close steps.
Of course, when <math>\delta p = \frac{p}{2}</math>, we have a uniformly grey figure, with no contrast.
 
The principle of the moiré is similar to the [[Vernier scale]].
 
==== Mathematical function approach ====
[[File:Moiré grid.svg|thumb|upright|Moiré pattern (bottom) created by superimposing two grids (top and middle)]]
 
 
The essence of the moiré effect is the (mainly visual) perception of a distinctly different third pattern which is caused by inexact superimposition of two similar patterns.  The mathematical representation of these patterns is not trivially obtained and can be somewhat arbitrary. In this section we shall give a mathematical example of two parallel patterns whose superimposition forms a moiré pattern, and show one way (of many possible ways) these patterns and the moiré effect can be rendered mathematically.
 
The visibility of these patterns is dependent on the medium or substrate in which they appear, and these may be opaque (as, e.g. on paper) or transparent (as, e.g., in plastic film).  For purposes of discussion we shall assume the two primary patterns are each printed in grey scale ink on a white sheet, where the opacity (e.g., shade of grey) of the "printed" part is given by a value between 0 (white) and 1 (black) inclusive, with 1/2 representing neutral grey.  Any value less than 0 or greater than 1 using this grey scale is essentially "unprintable". 
 
We shall also choose to represent the opacity of the pattern resulting from printing one pattern atop the other at a given point on the paper as the average (i.e. the arithmetic mean) of each pattern's opacity at that position, which is half their sum, and, as calculated, does not exceed 1.  (This choice is not unique.  Any other method to combine the functions that satisfies keeping the resultant function value within the bounds [0,1] will also serve;  arithmetic averaging has the virtue of simplicity -- with hopefully minimal damage to one's concepts of the printmaking process.)
 
We now consider the "printing" superimposition of two almost similar, sinusoidally varying, grey-scale patterns to show how they produce a moiré effect in first printing one pattern on the paper, and then printing the other pattern over the first, keeping their coordinate axes in register.  We represent the grey intensity in each pattern by a positive opacity function of distance along a fixed direction (say, the x-coordinate) in the paper plane, in the form
 
:  <math>f = \frac{1 + \sin(k x)}{2}</math>
 
where the presence of 1 keeps the function positive definite, and the divide by 2 prevents function values greater than 1. 
 
The quantity <math>k</math> represents the periodic variation (i.e., spatial frequency) of the pattern's grey intensity, measured as the number of intensity cycles per unit distance. Since the sin function is cyclic over argument changes of <math>2 \pi</math>, the distance increment <math>\Delta x</math> per intensity cycle (the wavelength) obtains when <math>k \Delta x = 2 \pi</math>, or <math>\Delta x = \frac{2 \pi}{k}</math>.  
 
Consider now two such patterns where one has a slightly different periodic variation from the other:
 
:  <math>f_1 = \frac{1 + \sin(k_1 x)}{2}</math>
 
:  <math>f_2 = \frac{1 + \sin(k_2 x)}{2}</math>
 
such that <math>k_1 \approx k_2</math>.
 
The average of these two functions, representing the superimposed printed image, evaluates as follows:
 
:  <math>f_3 = \frac{f_1 + f_2}{2}</math>
 
:  <math>= \frac12 + \frac{\sin(k_1 x) + \sin(k_2 x)}{4}</math> 
 
:  <math>= \frac{1 + \sin(A x) \cos(B x)}{2}</math>
 
where it is easily shown that
 
: <math>A = \frac{k_1 + k_2}{2}</math>
 
and
 
: <math>B = \frac{k_1 - k_2}{2}</math>.
 
This function average, <math>f_3</math>, clearly lies in the range [0,1]. Since the periodic variation <math>A</math> is the average of and therefore close to <math>k_1</math> and <math>k_2</math>, the moiré effect is distinctively demonstrated by the sinusoidal envelope "beat" function <math>\cos(B x)</math>, whose periodic variation is half the difference of the periodic variations <math>k_1</math> and <math>k_2</math> (and evidently much "slower").
 
Other one-dimensional moire effects include the classic beat frequency tone which is heard when two pure notes of almost identical pitch are sounded simultaneously. This is an acoustic version of the moiré effect in the one dimension of time: the original two notes are still present  -- but the listener's ''perception'' is of two pitches that are the average of and half the difference of the frequencies of the two notes.  Aliasing in sampling of time-varying signals also belongs to this moiré paradigm.
 
A concluding note for this section: it is popularly thought that the moiré effect results from "interference" between two superimposed patterns.  However, [[Interference (wave propagation)|interference]] (as understood in the physics sense) requires the summing and squaring of dynamically moving wave amplitudes, and these superposed amplitudes and their products can also have negative values.  Those dynamic attributes are never present in the static patterns printed on opaque or transparent sheets which are superimposed to produce a moiré effect.  That is, superimposition is not the same as superposition.  The moiré effect is therefore not a true interference phenomenon, even though its appearance can sometimes seem similar to pictures of actual visible fringe patterns produced by combining (and interfering) physical waves taken at any one instant of time.
 
=== Rotated patterns ===
Let us consider two patterns with the same step <math>p</math>, but the second pattern is turned by an angle <math>\alpha</math>. Seen from far, we can also see dark and pale lines: the pale lines correspond to the lines of [[Node (physics)|nodes]], that is, lines passing through the intersections of the two patterns.
 
If we consider a cell of the "net", we can see that the cell is a [[rhombus]]: it is a [[parallelogram]] with the four sides equal to <math>d = \frac{p}{\sin \alpha}</math>; (we have a right [[triangle]] which hypothenuse is <math>d</math> and the side opposed to the <math>\alpha</math> angle is <math>p</math>).
 
{{double image|right|Moire calcul angle.png|160|Moire02.gif|160|Unit cell of the "net"; "''ligne claire''" means "pale line"|Effect of changing angle.||}}
 
The pale lines correspond to the small [[diagonal]] of the rhombus. As the diagonals are the [[Bisection|bisectors]] of the neighbouring sides, we can see that the pale line makes an angle equal to <math>\frac{\alpha}{2}</math> with the perpendicular of the lines of each pattern.
 
Additionally, the spacing between two pale lines is <math>D</math>, the half of the big diagonal. The big diagonal <math>2 D</math> is the hypothenuse of a right triangle and the sides of the right angle are <math>d (1 + \cos \alpha)</math> and <math>p</math>. The [[Pythagorean theorem]] gives:
: <math>(2 D)^2 = d^2 (1 + \cos \alpha)^2 + p^2</math>
''id est''
:<math>(2D)^2 = \frac{p^2}{\sin^2 \alpha}(1+ \cos \alpha)^2 + p^2
= p^2 \cdot \left ( \frac{(1 + \cos \alpha)^2}{\sin^2 \alpha} + 1\right )</math>
thus
:<math>(2D)^2 = 2 p^2 \cdot \frac{1+\cos \alpha}{\sin^2 \alpha}</math> or <math>D = \frac{p}{2} / \sin\frac{\alpha}{2}</math>.
 
{{double image|right|Moire Circles.svg|150|Moire Lines.svg|150|Effect on curved lines|||}}
 
When <math>\alpha</math> is very small (<math>\alpha < \frac{\pi}{6}</math>), the following approximations can be done:
: <math>\sin \alpha \approx \alpha</math>
: <math>\cos \alpha \approx 1</math>
thus
: <math>D \approx \frac{p}{\alpha}</math>.
 
We can see that the smaller the <math>\alpha</math>, the farthest the pale lines; when the both patterns are parallel (<math>\alpha = 0</math>), the spacing between the pale lines is "infinite" (there is no pale line).
 
There are thus two ways to determine <math>\alpha</math>: by the orientation of the pale lines and by their spacing
: <math>\alpha \approx \frac{p}{D}</math>
If we choose to measure the angle, the final error is proportional to the measurement error. If we choose to measure the spacing, the final error is proportional to the inverse of the spacing. Thus, for the small angles, it is best to measure the spacing.
 
== Implications and applications ==
 
=== Printing full-color images ===
[[File:BeatTrackMoirePattern.ogg|thumb|The product of two "beat tracks" of slightly different speeds overlaid, producing an audible moiré pattern; if the beats of one track correspond to where in space a black dot or line exists and the beats of the other track correspond to the points in space where a camera is sampling light, because the frequencies are not exactly the same and aligned perfectly together, beats (or samples) will align closely at some moments in time and far apart at other times. The closer together beats are, the darker it is at that spot; the farther apart, the lighter. The result is periodic in the same way as a graphic moiré pattern. See: [[phase (music)]].]]
In [[graphic arts]] and [[prepress]], the usual technology for printing full-color images involves the superimposition of [[halftone]] screens. These are regular rectangular dot patterns—often four of them, printed in cyan, yellow, magenta, and black. Some kind of moiré pattern is inevitable, but in favorable circumstances the pattern is "tight;" that is, the spatial frequency of the moiré is so high that it is not noticeable. In the graphic arts, the term ''moiré'' means an ''excessively visible'' moiré pattern. Part of the prepress art consists of selecting screen angles and halftone frequencies which minimize moiré. The visibility of moiré is not entirely predictable. The same set of screens may produce good results with some images, but visible moiré with others.
 
In [[manufacturing]] industries, these patterns are used for studying microscopic [[Strain (materials science)|strain]] in materials: by deforming a grid with respect to a reference grid and measuring the moiré pattern, the stress levels and patterns can be deduced. This technique is attractive because the scale of the moiré pattern is much larger than the deflection that causes it, making measurement easier.
 
=== Television screens and photographs ===
{{double image|right|Moire on parrot feathers.jpg|160|Moiré fringes IMG 3712.jpg|160|Strong moiré visible in this photo of a parrot's feathers (more pronounced in the full-size image)|Moiré pattern seen over a cage in the San Francisco Zoo||}}
Moiré patterns are commonly seen on television screens when a person is wearing a shirt or jacket of a particular weave or pattern, such as a [[houndstooth]] jacket. This is due to interlaced scanning in televisions and non-film cameras, referred to as [[Interline_twitter#Interline_twitter|Interline Twitter]].  As the person moves about, the Moiré pattern is quite noticeable.  Because of this, newscasters and other professionals who appear on TV regularly are instructed to avoid clothing which could cause the effect.
 
Photographs of a [[Television|TV]] screen taken with a [[digital camera]] often exhibit moiré patterns.
 
=== Marine navigation ===
The Moiré effect is used in shoreside beacons to mark underwater hazards (usually pipelines or cables).<ref>{{cite web|author=Alexander Trabas |url=http://www.online-list-of-lights.info/html/enleuchtfeuer.html |title=Beacons |publisher=Online-list-of-lights.info |date= |accessdate=2012-10-30}}</ref> The Moiré effect creates arrows that 'point' towards an imaginary line marking the hazard; as navigators pass over the hazard, the arrows on the beacon appear to become vertical bands before 'changing' back to arrows pointing in the reverse direction. An example can be found in the UK on the East shore of Southampton water, opposite Fawley oil refinery ({{coord|50|51|21.63|N|1|19|44.77|W|type:landmark_region:GB|display=inline}}). Similar Moiré effect beacons can be used to guide mariners to the centre point of an oncoming bridge; when the vessel is aligned with the centreline, vertical lines are visible.
 
=== Strain measurement ===
[[Image:Moire extensometrie.png|thumb|Use of the moiré effect in strain measurement: case of uniaxial traction (top) and of pure shear (bottom); the lines of the patterns are initially horizontal in both cases]]
 
The moiré effect can be used in [[Strain (materials science)|strain]] measurement: the operator just has to draw a pattern on the object, and superimpose the reference pattern to the [[Deformation (engineering)|deformed]] pattern on the deformed object.
 
A similar effect can be obtained by the superposition of an [[hologram|holographic]] image of the object to the object itself: the hologram is the reference step, and the difference with the object are the deformations, which appear as pale and dark lines.
 
''See also: [[theory of elasticity]], [[strain tensor]] and [[holographic interferometry]].''
 
=== Image processing ===
Some [[image scanner]] [[device driver|driver]] [[computer program|program]]s provide an optional [[filter (software)|filter]], called a "descreen" filter, to remove Moiré-pattern artifacts which would otherwise be produced when scanning printed [[halftone]] images to produce [[digital image]]s.<ref>[http://www.scantips.com/basics6c.html Scanning Images in magazines/books/newspapers] at scantips.com; visited 22 April 2010.</ref>
 
=== Currency ===
Many currencies exploit the tendency of digital scanners to produce moiré patterns by including fine circular or wavy designs that are likely to exhibit a moiré pattern when scanned and printed.
 
=== Animation ===
The Moiré pattern can be used to animate images. An acetate overlay containing vertical stripes is placed over the image and slowly moved from right to left. These are sold in sets under the brand name Scanimation. It was invented by Rufus Butler Seder,<ref>http://scanimationbooks.com/about-scanimation/</ref> and patented in 2006 under US Patent #7151541.<ref>http://www.archpatent.com/patents/7151541</ref>
 
=== Super-resolution microscopy ===
The Moiré pattern can be used to obtain images with a resolution higher than the diffraction limit using a technique known as [[Super resolution microscopy|Structured Illumination Microscopy]].
 
== See also ==
* [[Aliasing]]
* [[Angle-sensitive pixel]]
* [[Beat frequency]]
* [[Kan't Kopy paper]]
* [[Multidimensional sampling]]
 
== References ==
{{reflist}}
 
== External links ==
{{commons}}
* [http://www.pip-dickens.com/moire.html A series of oil paintings based on Moiré principles by British artist, Pip Dickens]
* [http://www.mathematik.com/Moire/ A live demonstration of the Moiré effect that stems from interferences between circles]
* [http://www.kirl.nl/moireGen.swf An interactive example of various Moiré patterns] Use arrow keys and mouse to manipulate layers.
 
{{DEFAULTSORT:Moire Pattern}}
[[Category:Printing]]
[[Category:Geometry]]
[[Category:Interference]]
[[Category:Patterns]]

Latest revision as of 10:54, 20 December 2014

Nakład 3D wskazywany inaczej wydawaniem przestrzennym owe przebieg tworzenia celów fizycznych w trójwymiarze na przyczynie sformowanego oraz napisanego w pamięci komputera kroju.

Użycie nakładu 3d istnieje przeróżne. Technologia druku 3D umożliwia aktywowanie celów np części zapasowych, form. Technika owa może być z powodzeniem skorzystania do okazale rozumianego prototypowania. W sytuacji gdy żądamy kilku kilkunastu biegłości wiadomego obiektu, uruchomianie okazałej pracy zdoła okazać się nielukratywne, acz projektowanie 3d w relatywnie naskórkowym czasie możemy wyprodukować te tematy za pomocą nakładu 3d.

Sukcesywnym przykładem gdzie wolno wyzyskać technikę 3d są figury dokonywujące odnowy starych przedmiotów. Oczekując wyrównać, np stary zegar, jakiego części nie ma na rynku możemy założyć starodawną frakcja oraz wydrukować przydatny nam egzemplarz. Obfite nadzieje z nakładem 3d pakuje medycyna. Prominentne są już przypadki dokąd z powodzeniem wydrukowano protezę dopasowaną do potrzeb pacjenta. Hiszpańscy doktorzy zdobyli nie niski sukces usuwając operacyjnie guza, który był uważany za nieoperacyjnego. Przed rozpoczęciem do operacji pozostawał utworzony skrupulatny projekt 3d guza na, jakim syndrom operacyjny trenował przed rozpoczęciem do odpowiedniego zabiegu.

My website :: projektowanie 3d