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Wavelet Subdivision Methods - GEMS for Rendering Curves and Surfaces (Paperback)
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Wavelet Subdivision Methods - GEMS for Rendering Curves and Surfaces (Paperback)
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Prevalent in animation movies and interactive games, subdivision
methods allow users to design and implement simple but efficient
schemes for rendering curves and surfaces. Adding to the current
subdivision toolbox, Wavelet Subdivision Methods: GEMS for
Rendering Curves and Surfaces introduces geometry editing and
manipulation schemes (GEMS) and covers both subdivision and wavelet
analysis for generating and editing parametric curves and surfaces
of desirable geometric shapes. The authors develop a complete
constructive theory and effective algorithms to derive synthesis
wavelets with minimum support and any desirable order of vanishing
moments, along with decomposition filters. Through numerous
examples, the book shows how to represent curves and construct
convergent subdivision schemes. It comprehensively details
subdivision schemes for parametric curve rendering, offering
complete algorithms for implementation and theoretical development
as well as detailed examples of the most commonly used schemes for
rendering both open and closed curves. It also develops an
existence and regularity theory for the interpolatory scaling
function and extends cardinal B-splines to box splines for surface
subdivision. Keeping mathematical derivations at an elementary
level without sacrificing mathematical rigor, this book shows how
to apply bottom-up wavelet algorithms to curve and surface editing.
It offers an accessible approach to subdivision methods that
integrates the techniques and algorithms of bottom-up wavelets.
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