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Interactive skeleton-driven simulation (orInteractive skeleton-driven dynamic deformations) is a scientificcomputer simulation technique used to approximate realistic physicaldeformations of dynamic bodies inreal-time. It involves usingelasticdynamics andmathematical optimizations to decide the body-shapes during motion and interaction withforces. It has various applications within realistic simulations formedicine, 3Dcomputer animation andvirtual reality.

Methods for simulating deformation, such as changes of shapes, of dynamic bodies involve intensive calculations, and several models have been developed. Some of these are known asfree-form deformation,skeleton-driven deformation,dynamic deformation andanatomical modelling.Skeletal animation is well known incomputer animation and 3D character simulation. Because of the calculation insensitivity of the simulation, few interactive systems are available which realistically can simulate dynamic bodies inreal-time. Being able tointeract with such arealistic 3D model would mean that calculations would have to be performed within the constraints of aframe rate which would be acceptable via auser interface.

Recent research has been able to build on previously developed models and methods to provide sufficiently efficient and realistic simulations. The promise for this technique can be as widespread asmimicking humanfacial expressions forperception of simulating a human actor in real-time or othercellorganisms. Using skeletal constraints and parameterized force to calculate deformations also has the benefit of matching how a single cell has a shapingskeleton, as well as how a larger living organism might have an internal bone skeleton - such as thevertebrae. The generalized external body force simulations makeselasticity calculations more efficient, and means real-timeinteractions are possible.

There are several components to such a simulation system:

• apolygon mesh defining the body shape of the model
• a coarse volumetric mesh usingfinite element methods to ensure complete integration over the model
• line constraints corresponding to internal skeleton and instrumented to the model
• linearizing of equations of motion to achieve interactive rates
• hierarchical regions of the mesh associated with skeletal lines
• blending of locally linearlized simulations
• a control lattice throughsubdivision fitting the model by surrounding and covering it
• a hierarchical basis containing functions which will provide values for deformation of each lattice

domain with calculations of these hierarchical functions similar to that oflazywavelets

Rather than fitting the object to the skeleton, as is common, the skeleton is used to set constraints for deformation. Also the hierarchical basis means that detail levels can be introduced or removed when needed - for example, observing from a distance or hidden surfaces.

Pre-calculatedposes are used to be able to interpolate between shapes and achieve realistic deformations throughout motions. This means traditionalkeyframes are avoided.

There areperformance tuning similarities between this technique andprocedural generation,wavelet anddata compression methods.

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To achieve interactivity there are several optimizations necessary which are implementation specific.

Start by defining the object you wish to animate as a set (i.e. define all the points):${\displaystyle p:\mathrm{\Omega }\times \mathbb{R}\to {\mathbb{R}}^3:(x,t)\mapsto p(x,t)}$ .

Then get a handle on it.Let${\displaystyle p_S:S\times \mathbb{R}\to {\mathbb{R}}^3}$

Then you need to define the rest state of the object (the non-wobble point):${\displaystyle r(x)=\sum _a{r}_a{\mathrm{\varnothing }}^a(x)=r_a{\mathrm{\varnothing }}^a(x)=x}$

Projects are taking place to further develop this technique and presenting results toSIGGRAPH, with available reference of details. Academic institutions and commercial enterprises likeAlias Systems Corporation (the makers of theMaya rendering software),Intel andElectronic Arts are among the known proponents of this work. There are also videos available showcasing the techniques, with editors showing interactivity in real-time with realistic results. Thecomputer gameSpore also has showcased similar techniques.

• Kinematics
• Dynamics
• Computer animation
• Skeletal animation
• Morph target animation
• 3D computer graphics
• Development of Spore

• Interactive Character Animation Using Dynamic Elastic Simulation, 2004, Steve Capell Ph.D. dissertation.
• Interactive Skeleton-Driven Dynamic Deformations, 2002SIGGRAPH. Authors: Steve Capell, Seth Green, Brian Curless, Tom Duchamp and Zoran Popović.
• A Multiresolution Framework for Dynamic Deformations, 2002SIGGRAPH.Authors: Steve Capell, Seth Green, Brian Curless, Tom Duchamp and Zoran Popović.
• Physically Based Rigging for Deformable Characters, 2005SIGGRAPH. Authors: Steve Capell, Matthew Burkhart, Brian Curless, Tom Duchamp and Zoran Popović.
• Skeleton-driven Deformation - lecture on physically-based modelling, simulation and animation, 2005,Ming C. Lin, University of North Carolina, USA.

• Video of an interactive skeletal and model editor with introduction to the basic theory, University of Washington, USA.
• Deformable Objects and Characters project, University of Washington, USA. Has example videos of the techniques.
• Motion Libraries for Character Animation project, University of Washington, USA. Has example videos of the techniques.

• Animation techniques
• 3D computer graphics
• Anatomical simulation

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