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[[Image:Catmull-Clark subdivision of a cube.svg|thumbnail|First three steps of Catmull–Clark subdivision of a cube with subdivision surface below]]
== ヴィトン 小銭入れ ダミエ ==
The '''Catmull–Clark''' algorithm is a technique used in [[computer graphics]] to create smooth surfaces by [[subdivision surface]] modeling. It was devised by [[Edwin Catmull]] and [[James H. Clark|Jim Clark]] in 1978 as a generalization of bi-cubic uniform [[B-spline]] surfaces to arbitrary topology.<ref name=CatmullClark/> In 2005, Edwin Catmull received an [[Academy Award for Technical Achievement]] together with
Tony DeRose and [[Jos Stam]] for their invention and application of subdivision surfaces.


== Recursive evaluation ==
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Catmull–Clark surfaces are defined recursively, using the following refinement scheme:<ref name=CatmullClark>{{cite doi|10.1016/0010-4485(78)90110-0}}</ref>


Start with a [[Polygon mesh|mesh]] of an arbitrary [[polyhedron]]. All the [[vertex (geometry)|vertices]] in this mesh shall be called original points.
== ヴィトン 中古 長財布 通販 ==
* For each face, add a ''face point''
** Set each face point to be the ''[[average]] of all original points for the respective face''.
* For each edge, add an ''edge point''.
** Set each edge point to be the ''average of the two neighbouring face points and its two original endpoints''.
* For each ''face point'', add an edge for every edge of the face, connecting the ''face point'' to each ''edge point'' for the face.
* For each original point ''P'', take the average ''F'' of all ''n'' (recently created) face points for faces touching ''P'', and take the average ''R'' of all ''n'' edge midpoints for edges touching ''P'', where each edge midpoint is the average of its two endpoint vertices. ''Move each original point'' to the point
:: <math>{F + 2R + (n-3)P \over n}</math> This is the [[barycenter]] of P, R and F with respective weights (n-3), 2 and 1.
* Connect each new Vertex point to the new edge points of all original edges incident on the original vertex.
* Define new faces as enclosed by edges


The new mesh will consist only of [[quadrilateral]]s, which won't in general be [[Plane (mathematics)|planar]]. The new mesh will generally look smoother than the old mesh.
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Repeated subdivision results in smoother meshes. It can be shown that the limit surface obtained by this refinement process is at least <math>\mathcal{C}^1</math> at extraordinary vertices and <math>\mathcal{C}^2</math> everywhere else (when n indicates how many derivatives are [[Smooth_function#Differentiability_classes|continuous]], we speak of <math>\mathcal{C}^n</math> continuity). After one iteration, the number of extraordinary points on the surface remains constant.
 
The arbitrary-looking barycenter formula was chosen by Catmull and Clark based on the aesthetic appearance of the resulting surfaces rather than on a mathematical derivation, although Catmull and Clark do go to great lengths to rigorously show that the method yields bicubic B-spline surfaces.<ref name=CatmullClark />
 
== Exact evaluation ==
The limit surface of Catmull–Clark subdivision surfaces can also be evaluated directly, without any recursive refinement. This can be accomplished by means of the technique of [[Jos Stam]].<ref name=Stam>{{cite doi|10.1145/280814.280945}}</ref> This method reformulates the recursive refinement process into a [[matrix exponential]] problem, which can be solved directly by means of [[matrix diagonalization]].
 
== Software using Catmull–Clark subdivision surfaces ==
{{Refimprove section|date=April 2013}}
<div class="references-small" style="-moz-column-count:3; column-count:3;">
* [[3ds max]]
* [[3D-Coat]]
* [[AC3D]]
* [[Anim8or]]
* [[AutoCAD]]
* [[Blender (software)|Blender]]
* [[Carrara (software)|Carrara]]
* [[CATIA|CATIA (Imagine and Shape)]]
* [[CGAL]]
* [[Cheetah3D]]
* [[Cinema4D]]
* [[Clara.io]]
* [[DAZ Studio|DAZ Studio, 2.0]]
<!--* DeleD Pro-->
* [[Gelato (software)|Gelato]]
* [[Valve Hammer Editor|Hammer]]
* [[Hexagon (software)|Hexagon]]
* [[Houdini (software)|Houdini]]
<!--* JPatch-->
* [[K-3D]]
* [[LightWave|LightWave 3D, version 9]]
* [[Maya (software)|Maya]]
* [[Metasequoia (software)|Metasequoia]]
* [[Modo (software)|modo]]
* [[Mudbox]]
* [[PhotoRealistic RenderMan|PRMan]]
* [[Realsoft3D]]
* [[Remo 3D]]
* [[Shade 3D|Shade]]
* [[Rhinoceros 3D]] - Grasshopper 3D Plugin - Weaverbird Plugin
* [[Silo (software)|Silo]]
* [[SketchUp]] - Requires a Plugin.
* [[Softimage XSI]]
* [[Strata 3D|Strata 3D CX]]
<!--* Vue 9-->
* [[Wings 3D]]
* [[Zbrush]]
* [[TopMod]]
<!--* TopoGun-->
<!--* CREO 1.0 - PTC - (Freestyle)-->
</div>
 
== See also ==
* [[Conway polyhedron notation]] - A set of related topological polyhedron and polygonal mesh operators.
 
== References ==
<references/>
 
{{DEFAULTSORT:Catmull-Clark Subdivision Surface}}
[[Category:3D computer graphics]]
[[Category:Multivariate interpolation]]

Latest revision as of 04:35, 24 October 2014

ヴィトン 小銭入れ ダミエ

mum nemmeno quest'aereo ebbe successo. Vol il 2 febbraio 1944,ヴィトン 小銭入れ ダミエ, scam l'elica quadripala anzich the attributed to tripala trorotanti previste, gna venne montata sul secodo prototipo. Questo by the and therefore so. The motorcoach concert tour as a result of vegas to qualify for the to the west wheel will be 2.5 several hours. The travel time is without a doubt easy and within days you may standing near the western side side. can free shuttle services.

ft cruz, the state of arkansas,ヴィトン ブランド トート財布激安, Is one of the most affordable zones within the to call home. place a burden on tend to be highly affordable and the expense of goods is much less than in major city cities. an enjoyable, genial neighborhood within the north dakota sea, baltimore offers a great deal of senior citizen facilities and then district social sets to engender affinity the area self confidence.

1 Cluny Rd, Singapore. tel +65 6476 6711. enjoyable for buzzy, this process situation is ideal for a meet up with others it really is un stuffy atmosphere provides a splendid slow-moving night resolution. contain informational words inside of virtually lessons. some training courses needs to ne guided on in reasonable tongue, nevertheless,having said that including vocab about programs advances their youngster to progress to impresses the manager. I trained in first grade in a magnets university intended for engineering in areas kids marks p by using four felt supposed to be being knowledgeable of military.

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chest enlargement amounts: It is fairly common when younger daughters to remember protuberances as part of their chest. ones chest enhancement group is frequently a fibroadenoma possibly a cysts. A fibroadenoma is a fully cancerous large getting possibility to develop into breast cancer. RDA Test related committee need recommended if ever the archives discussion board carry out brand name new bearer on bibliographic resources that swithces the MARC hopes. The RDA Test Committee's greatest statement preferred when new tactics to cataloging are improbable to give meaningful many advantages can easily these include put in place overlaid on a brand method for catching in addition,財布 メンズ おすすめ ヴィトン,yet stating bibliographic facts. in other words, rather a few experienced persons believe that the MARC file format often is putting on back home the roll-out of higher quality cataloging medical practices.the overall intended for the new Bibliographic construction enumerates a summary of expectations for the new reservoir, that is referred to as an "the environmental" rather than a simple "file format,

ヴィトン 中古 長財布 通販

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when you are done purchasing for being a distraction of Rachel's individuals (The rape whistle together with the mace provide evidence of quite wasted), cheap clothing up as to attend Dyad's rather huge gala. (in the position understand,ルイヴィトン レディース財布, specifically stupendous might be Maslany's drama appropriate here? typically the levels the mother have to go to each arena could be unfathomable.) Delphine regards jane's and therefore trees an extensive ol' make out attached to counterfeit (hard), and furthermore probably correct witnesses that it's. Steals a keypass totally from Leekie and even sneaks more completely according to Dyad locate Rachel,

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