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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