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In the area of geometric modeling in 3D [[computer animation]], '''curve-controlled modeling'''<ref name="CurveControl">Ding, H., Hong, Y. (2003), NURBS curve-controlled modeling for facial animation, ''Computers and Graphics'', 27(3):373-385</ref> is known as a 3D computer animation method that makes use of the [[Non-uniform rational B-spline]] ('''NURBS''') curve.  Here, a NURBS curve, a specific form of parametric representation, is used as an underlying control mechanism to simulate muscle movements. Currently, NURBS curves are used in computer animation with applications limited to traditional methods of creating surfaces, key framing and setting motion paths.


The principles of curve-controlled modeling rest on the analogy of the modification of rational curves and the complexity of muscle movement.  Curve-controlled modeling is implemented in commercial packages used in the entertainment industry (movies, games) as well as in education.


==Principles of curve-controlled modeling==
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The techniques involved in curve-controlled modeling are based on the analogy between the modification of rational curves and the movement of muscles. These techniques use the curve as a control mechanism to change the shape of a 3D model. This is an approach that is definitively different from the traditional one that uses curved surfaces to model the surface of 3D objects.
 
=== Complexity of muscle movement===
 
The '''muscles of the human body'''<ref>{{cite web|url=http://www.colorado.edu/intphys/iphy3415rheisler/oia3e.pdf |title=Nature, origin, insertion, action of human muscles |accessdate=31 July 2013}}</ref> (ex. thoracic wall, facial expression, limbs, and hands) can be characterized by their movement (extension, contraction/flexion) and the end points - called origin and insertion - of attachment to the supporting bone. For a linear muscle, the origin and insertion can be considered as points whereas for a sphincter muscle or a sheet muscle, they can be approximated as a series of points. During a [[muscle contraction]], a local area of the surface will be pulled toward the muscle origin.
 
=== NURBS curve modification principles===
 
When a weight of a NURBS curve increases, the affected segment of the curve moves toward the control point. For the NURBS curve, control point repositioning can produce the same effect as weight changing.
 
According to the known definition of NURBS curves:
 
Given a set of n+1 control points '' P<sub>0</sub>, P<sub>1</sub>, … ,P<sub>n</sub>'' to which are affected the weight '' w<sub>i</sub>'', and vector '' U '' = {''u<sub>0</sub>, u<sub>1</sub>, …, u<sub>m</sub>''}, the NURBS curve of degree p is defined as follows:
 
: <math> C(u)= \sum_{i=0}^{i=n} R_{i,p}(u)P_{i}</math>
where '' R<sub>i,p</sub>'' is defined as:
 
: <math> R_{i,p}(u) = </math>  <math>N_{i,p}(u)w_{i}\over{\sum_{j=0}^{j=n} N_{j,p}(u)w_{j}}</math>
 
with '' N<sub>i,p</sub>'' as the B-spline basis function.
 
From this definition, we can examine the impact of weight variation of a given control point.
 
: <math> C(u)= </math> <math> 1\over{\sum_{i=0}^{i=n} N_{i,p}(u)w_{i}}</math>  <math>\sum_{i=0}^{i=n} N_{i,p}(u)w_{i}P_{i}</math>
 
Given control point P<sub>k</sub>, what is the impact of changing w<sub>k</sub>? In the following, we assume u is in [u<sub>k</sub>, u<sub>k+p+1</sub>), the non-zero domain of its coefficient N<sub>k,p(u)</sub>. When we single out terms involving w<sub>k</sub>, we have:
 
: <math> C(u) = </math> <math> 1\over{N_{k,p}(u)w_{k} + \sum_{i=0, i\ne k}^{i=n} N_{i,p}(u)w_{i}}</math>  <math>(N_{k,p}(u)w_{k} P_{k} + \sum_{i=0, i\ne k}^{i=n} N_{i,p}(u)w_{i}P_{i})</math>
 
We realize three notable events:
 
* Increasing the value of the weight w<sub>i</sub> pulls the curve toward control point Pi
 
* Decreasing the value of the weight w<sub>i</sub> pushes the curve away from control point P<sub>i</sub>
 
* When w<sub>i</sub> tends toward infinity, the curve gets closer to and passes through control point P<sub>i</sub> whereas when w<sub>i</sub> becomes zero, the curve has no relation with the control point P<sub>i</sub>
 
In a typical simulation of a sheet muscle, the modification of a NURBS curve consists in two neighbouring control points being repositioned or their weights modified. When the two neighbouring control points move in parallel, the affected curve segment also moves in the same direction.  When their respective weights increase, the segment moves toward the connection between the two control points.
 
===Similarities===
 
The geometric similarity between curve modification and muscle movement suggests that the modification of NURBS curves may simulate the movement of muscles. Since a NURBS curve is a 3D curve and a virtual facial model can be presented by a polygon mesh, the curve may act as a control mechanism to model the [[deformation]] of the virtual model.
 
Therefore, curve-controlled modeling uses NURBS curves to model a facial movement in three consecutive procedures:
 
* Construction of NURBS curves based on the similarity
 
* Association of NURBS curves with the virtual face
 
* Animation controlled by NURBS curves
 
== Applications ==
 
[[3D modeling]] and animation is widely used in making movies,TV programs, computer games, advertisements and education. Currently, many commercial animation packages also use [[parametric surface]]s like NURBS patches, to model and animate characters. These packages approximate the human body using the parametric patches like in engineering CAD. In contrast, curve-controlled modeling does not require any approximation of a real-world 3D object with parametric patches.
 
This technology is being commercialized by a number of companies which propose 3D facial animation <ref name=" Comp. Facial Anim">Ding, Zhigang D. and Junyong N. (2003), Computer Facial Animation: A Survey, ''Computers and Graphics'', 27(3):373-385</ref> to be realistically generated in real-time. In this case, there is no need for any of the traditional techniques, such as [[rigging]], [[morphing]], key-framing, and [[motion capture]].
 
Therefore, curve-controlled modeling can greatly improve the process of computer facial animation in terms of time and cost unlike any other existing approaches in 3D facial animation.
 
==See also==
 
{{colbegin|2}}
 
* [[Computer graphics]]
 
* [[Animation]]
 
* [[Computer animation]]
 
* [[Facial expression]]
* [[Face Modeling Language]]
* [[Emotion classification]]
* [[Facial Action Coding System]], Paul Ekman
* [[Morphing]]
* [[Parametric surface]]
 
{{colend}}
 
==References==
{{reflist}}
 
==External links==
* [http://www.naturalfront.com/Index.aspx  NaturalFront], Realistic 3D Facial Animation
* [http://channel9.msdn.com/posts/TechFest-2012-3D-Facial-Animation TechFest 2012]: 3D Facial Animation - Future of 3D facial animation
* [http://www.cubicmotion.com/ Facial Animation Specialist]
* [http://mambo.ucsc.edu/psl/sig97/siggraph97-panel.html SIGGRAPH 97], Panel on Facial Animation: Past, Present and Future
 
<!--- STOP! Be warned that by using this process instead of Articles for Creation, this article is subject to scrutiny. As an article in "mainspace", it will be DELETED if there are problems, not just declined. If you wish to use AfC, please return to the Wizard and continue from there. --->
 
[[Category:Software architecture]]
[[Category:3D graphics software]]

Latest revision as of 02:35, 7 December 2014


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