Progressive Precision Surface Design

We introduce a novel wavelet decomposition algorithm that makes a number of powerful new surface design operations practical. Wavelets, and hierarchical representations generally, have held promise to facilitate a variety of design tasks in a unified way by approximating results very precisely, thus avoiding a proliferation of undergirding mathematical representations. However, traditional wavelet decomposition is defined from fine to coarse resolution, thus limiting its efficiency for highly precise surface manipulation when attempting to create new non-local editing methods. Our key contribution is the progressive wavelet decomposition algorithm, a generalpurpose coarse-to-fine method for hierarchical fitting, based in this paper on an underlying multiresolution representation called dyadic splines. The algorithm requests input via a generic interval query mechanism, allowing a wide variety of non-local operations to be quickly implemented. The algorithm performs work proportionate to the tiny compressed output size, rather than to some arbitrarily high resolution that would otherwise be required, thus increasing performance by several orders of magnitude. We describe several design operations that are made tractable because of the progressive decomposition. Free-form pasting is a generalization of the traditional control-mesh edit, but for which the shape of the change is completely general and where the shape can be placed using a free-form deformation within the surface domain. Smoothing and roughening operations are enhanced so that an arbitrary loop in the domain specifies the area of effect. Finally, the sculpting effect of moving a tool shape along a path is simulated