Ten lectures on wavelets
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Area preserving deformation of multiresolution curves
Computer Aided Geometric Design
Curve modeling with constrained B-spline wavelets
Computer Aided Geometric Design
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We have created an interactive map that can smoothly zoom to any region. The core of our system utilizes wavelets to achieve this effect. The system is implemented to view hydrographic flowline data, such as in the USGS National Hydrography Dataset (NHD). The map demonstrates that a wavelet-based approach is well suited for basic generalization operations. It provides smoothing and pruning that is continuously dependent on map scale. The method is applied to the Vermont river network, with the goal of creating an interactive map visualization. The process involves removing cycles from the network, prioritizing the segments according to their Strahler numbers, and extracting tributaries. Then each tributary is decomposed into wavelet details. When the user requests a map of a region B, the window size infers the scale s. Functions ε(s) and σ(s) determine the accuracy and the pruning level. The tributaries that are visible in B are synthesized to the required accuracy ε(s) and displayed according to the pruning function σ(s). In our system, the pruning is designed to be continuous with respect to the scale. Our implementation shows that the interactive map renders views in subsecond time. We have determined experimentally that the FBI (9--7) biorthogonal wavelet family provides the best compromise between quality of approximation and computation time.