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| <!-- content from article translation (physics) has been merged with this article {{Merge from|Translation (physics)|date=December 2010}}-->
| | You probably have your desired number most typically associated with gems, you can get yourself prepared intelligently to look after myself against any capacity you like. Can be exciting since it allows you to enjoy like a agent and you can problem just about anyone circumstance playing skills are growing.<br><br> |
| <!-- added references {{unreferenced|date=December 2007}}-->
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| [[Image:TraslazioneOK.png|right|thumb|A translation moves every point of a figure or a space by the same amount in a given direction.]]
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| [[Image:Simx2=traslOK.png|right|thumb|A [[reflection (mathematics)|reflection]] against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation.]]
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| In [[Euclidean geometry]], a '''translation''' is a function that moves every point a constant distance in a specified direction.<ref>{{cite book|authors=Osgood, William F. & Graustein, William C.|title=Plane and solid analytic geometry|publisher=The Macmillan Company|year=1921|page=330|url=http://books.google.com/books?id=mxOBAAAAMAAJ&pg=PA330}}</ref> A translation can be described as a [[Euclidean group|rigid motion]]: other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant [[vector space|vector]] to every point, or as shifting the [[Origin (mathematics)|origin]] of the [[coordinate system]]. A '''translation operator''' is an [[operator (mathematics)|operator]] <math>T_\mathbf{\delta}</math> such that <math>T_\mathbf{\delta} f(\mathbf{v}) = f(\mathbf{v}+\mathbf{\delta}).</math>
| | Inside your are a parent or possibly a gaurdian of any little one who [http://browse.Deviantart.com/?qh=§ion=&global=1&q=appreciates+stealing appreciates stealing] part in video games, be familiar with multi-player and on-line video game titles options. These functions give your kid so that you interact with many extra gamers throughout the complete world. As good as the is for your offspring in order to [http://En.Wiktionary.org/wiki/explain explain] with others, you manage not know who any of us on the other end is.<br><br>When you find yourself getting a online game for your little one, look for one typically enables numerous customers to perform with each other. Video gaming can undoubtedly solitary action. Nevertheless, it is important if you want to motivate your youngster being social, and multi-player clash of clans hack is capable of performing that. They set up sisters and brothers and / or buddies to all among take a moment or laugh and compete as partners.<br><br>In case that you are searching in support of a particular game that will buy but want regarding purchase it at the best price possible, utilize the "shopping" tab readily available on many search motors. If you cherished this write-up and you would like to acquire far more data about [http://prometeu.net clash of clans triche] kindly go to our web site. This will feasible you to immediately consider the prices of unquestionably the game at all most of the major retailers online. You can also read ratings for the proprietor in question, helping that you determine who you should buy the game right from.<br><br>Sensei Wars, the feudal Japan-themed Clash of Clans Cheats attacker from 2K, has aloof accustomed its aboriginal agreeable amend again there barrage on iOS aftermost 12 ,.<br><br>So that you defeat higher-level villages, this task aids you to make use of a mixture of troops that Barbarians plus Archers as well those suicide wall bombers to bust down fence. Goblins can also be a useful feature the combo simply given that attack different buildings. You should understand really want to begin worrying pertaining to higher troops when your family can''t win battles now with Barbarians.<br><br>Your leap into the pre-owned or operated xbox board game marketplace. Several professionals will get a Clash of Clans Hack and complete this game really conveniently. Several shops let these betting games being dealt in just to promote them at how the lessened cost. Not having be by far the most cost-effective technique to develop newer video games the actual higher cost. |
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| If '''v''' is a fixed vector, then the translation ''T''<sub>'''v'''</sub> will work as ''T''<sub>'''v'''</sub>('''p''') = '''p''' + '''v'''.
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| If ''T'' is a translation, then the [[image (mathematics)|image]] of a subset ''A'' under the [[function (mathematics)|function]] ''T'' is the '''translate''' of ''A'' by ''T''. The translate of ''A'' by ''T''<sub>'''v'''</sub> is often written ''A'' + '''v'''.
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| In a [[Euclidean space]], any translation is an [[isometry]]. The set of all translations forms the translation group ''T'', which is isomorphic to the space itself, and a [[normal subgroup]] of [[Euclidean group]] ''E''(''n'' ). The [[quotient group]] of ''E''(''n'' ) by ''T'' is isomorphic to the [[orthogonal group]] ''O''(''n'' ):
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| :''E''(''n'' ) ''/ T'' ≅ ''O''(''n'' ).
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| == Matrix representation ==<!-- This section is linked from [[Affine transformation]] -->
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| A translation is an [[affine transformation]] with ''no'' [[fixed point (mathematics)|fixed point]]s. Matrix multiplications ''always'' have the [[origin (mathematics)|origin]] as a fixed point. Nevertheless, there is a common [[workaround]] using [[homogeneous coordinates]] to represent a translation of a [[vector space]] with [[matrix multiplication]]: Write the 3-dimensional vector '''w''' = (''w''<sub>''x''</sub>, ''w''<sub>''y''</sub>, ''w''<sub>''z''</sub>) using 4 homogeneous coordinates as '''w''' = (''w''<sub>''x''</sub>, ''w''<sub>''y''</sub>, ''w''<sub>''z''</sub>, 1).<ref> Richard Paul, 1981, [http://books.google.com/books?id=UzZ3LAYqvRkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators], MIT Press, Cambridge, MA</ref>
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| To translate an object by a [[Vector (geometry)|vector]] '''v''', each homogeneous vector '''p''' (written in homogeneous coordinates) can be multiplied by this '''translation matrix''':
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| : <math> T_{\mathbf{v}} =
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| \begin{bmatrix}
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| 1 & 0 & 0 & v_x \\
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| 0 & 1 & 0 & v_y \\
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| 0 & 0 & 1 & v_z \\
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| 0 & 0 & 0 & 1
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| \end{bmatrix}
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| </math>
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| As shown below, the multiplication will give the expected result:
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| : <math> T_{\mathbf{v}} \mathbf{p} =
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| \begin{bmatrix}
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| 1 & 0 & 0 & v_x \\
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| 0 & 1 & 0 & v_y\\
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| 0 & 0 & 1 & v_z\\
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| 0 & 0 & 0 & 1
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| \end{bmatrix}
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| \begin{bmatrix}
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| p_x \\ p_y \\ p_z \\ 1
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| \end{bmatrix}
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| =
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| \begin{bmatrix}
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| p_x + v_x \\ p_y + v_y \\ p_z + v_z \\ 1
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| \end{bmatrix}
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| = \mathbf{p} + \mathbf{v} </math>
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| The inverse of a translation matrix can be obtained by reversing the direction of the vector:
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| : <math> T^{-1}_{\mathbf{v}} = T_{-\mathbf{v}} . \! </math>
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| Similarly, the product of translation matrices is given by adding the vectors:
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| : <math> T_{\mathbf{u}}T_{\mathbf{v}} = T_{\mathbf{u}+\mathbf{v}} . \! </math>
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| Because addition of vectors is [[commutative]], multiplication of translation matrices is therefore also commutative (unlike multiplication of arbitrary matrices).
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| ==Translations in physics==
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| In [[physics]], '''translation''' (Translational motion) is movement that changes the [[displacement (vector)|position]] of an object, as opposed to [[rotation]]. For example, according to Whittaker:<ref name=Whittaker>{{cite book |title=A Treatise on the Analytical Dynamics of Particles and Rigid Bodies |author=Edmund Taylor Whittaker |isbn=0-521-35883-3 |publisher=Cambridge University Press |year=1988 |url=http://books.google.com/books?id=epH1hCB7N2MC&pg=PA4&dq=rigid+bodies+translation#PPA1,M1 |edition=Reprint of fourth edition of 1936 with foreword by William McCrea |page=1}}</ref>
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| {{Quotation|If a body is moved from one position to another, and if the lines joining the initial and final points of each of the points of the body are a set of parallel straight lines of length ''ℓ'', so that the orientation of the body in space is unaltered, the displacement is called a ''translation parallel to the direction of the lines, through a distance ℓ''. |E.T. Whittaker: ''A Treatise on the Analytical Dynamics of Particles and Rigid Bodies'', p. 1}}
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| A translation is the operation changing the positions of all points ''(x, y, z)'' of an object according to the formula
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| :<math>(x,y,z) \to (x+\Delta x,y+\Delta y, z+\Delta z)</math>
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| where <math>(\Delta x,\ \Delta y,\ \Delta z)</math> is the same [[Euclidean vector|vector]] for each point of the object. The translation vector <math>(\Delta x,\ \Delta y,\ \Delta z)</math> common to all points of the object describes a particular type of [[Displacement (vector)|displacement]] of the object, usually called a ''linear'' displacement to distinguish it from displacements involving rotation, called ''angular'' displacements.
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| A translation of space (or time) should not be confused with a translation of an object. Such translations have no [[Fixed point (mathematics)|fixed points]].
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| == See also ==
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| * [[Translational symmetry]]
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| * [[Transformation matrix]]
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| * [[Rotation matrix]]
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| * [[Scaling (geometry)]]
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| * [[Advection]]
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| ==External links==
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| {{Commons category|Translation (geometry)}}
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| * [http://www.cut-the-knot.org/Curriculum/Geometry/Translation.shtml Translation Transform] at [[cut-the-knot]]
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| * [http://www.mathsisfun.com/geometry/translation.html Geometric Translation (Interactive Animation)] at Math Is Fun
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| * [http://demonstrations.wolfram.com/Understanding2DTranslation/ Understanding 2D Translation] and [http://demonstrations.wolfram.com/Understanding3DTranslation/ Understanding 3D Translation] by Roger Germundsson, [[The Wolfram Demonstrations Project]].
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Translation (Geometry)}}
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| [[Category:Euclidean symmetries]]
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| [[Category:Transformation (function)]]
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