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Shape transformation using compactly supported radial basis functions

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https://ir.library.oregonstate.edu/concern/graduate_projects/cz30q221d

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  • Shape transformation is a technique for gradually changing one geometric shape to another. A recent approach presents the use of thin-plate radial basis functions as opposed to traditional "blobby sphere" implicit functions. Without the explicit evaluation of he energy function, this approach combined the two traditional steps into one by using the calculus of variation. However. this method has the disadvantage of requiring a lot of time and space. This paper illustrates a technique for speedup up this recent shape transformation technique. Rather than using thin-plate radial basis functions, I use compactly­-supported radial basis functions. While thin-plate radial basis functions globally influence each other, compactly-supported radial basis functions locally do so. This local characteristic makes them much faster to evaluate for modeling and rendering. I will demonstrate time and space savings using compactly-supported radial basis functions.
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