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    Radial Basis Functions Applied to Integral Interpolation, Piecewise Surface Reconstruction and Animation Control

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    Author
    Langton, Michael Keith
    Date
    2009
    Permanent Link
    http://hdl.handle.net/10092/4078
    Thesis Discipline
    Mathematics
    Degree Grantor
    University of Canterbury
    Degree Level
    Doctoral
    Degree Name
    Doctor of Philosophy

    This thesis describes theory and algorithms for use with Radial Basis Functions (RBFs), emphasising techniques motivated by three particular application areas.

    In Part I, we apply RBFs to the problem of interpolating to integral data. While the potential of using RBFs for this purpose has been established in an abstract theoretical context, their use has been lacking an easy to check sufficient condition for finding appropriate parent basic functions, and explicit methods for deriving integral basic functions from them. We present both these components here, as well as explicit formulations for line segments in two dimensions and balls in three and five dimensions. We also apply these results to real-world track data.

    In Part II, we apply Hermite and pointwise RBFs to the problem of surface reconstruction. RBFs are used for this purpose by representing the surface implicitly as the zero level set of a function in 3D space. We develop a multilevel piecewise technique based on scattered spherical subdomains, which requires the creation of algorithms for constructing sphere coverings with desirable properties and for blending smoothly between levels. The surface reconstruction method we develop scales very well to large datasets and is very amenable to parallelisation, while retaining global-approximation-like features such as hole filling. Our serial implementation can build an implicit surface representation which interpolates at over 42 million points in around 45 minutes.

    In Part III, we apply RBFs to the problem of animation control in the area of motion synthesis---controlling an animated character whose motion is entirely the result of simulated physics. While the simulation is quite well understood, controlling the character by means of forces produced by virtual actuators or muscles remains a very difficult challenge. Here, we investigate the possibility of speeding up the optimisation process underlying most animation control methods by approximating the physics simulator with RBFs.

    Subjects
    Radial Basis Functions
     
    RBFs
     
    Approximation
     
    Integral Interpolation
     
    Surface Reconstruction
     
    Surface Fitting
     
    Hermite RBFs
     
    Piecewise RBFs
     
    Piecewise Approximation
     
    Hole Filling
     
    Animation Control
     
    Motion Synthesis
    Collections
    • Engineering: Theses and Dissertations [2271]
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