Multiresolution methods
For many purposes it is desirable to dynamically adapt the quality of the mathematical description used to the requirements a specialized use impose in a work process. To satisfy this requirement the organization of the mathematical description has to allow for retrieval of descriptions with the quality controlled by a user specified tolerance. Further the response of the model has to be so fast that the momentarily accuracy requirements of the user can be satisfied.
Wavelet decomposition is a well-known method creating multi resolution representation of a structured data set. However, hierarchies can also be created based on spline functions, where every level is a refinement of the level above. When multi-resolution technology is used then the upper levels represent the rough structure of the model. Going deeper into the hierarchy smaller details are introduced. When including the finest levels the original data set can be reconstructed.
Multi-resolution representation used in a proper way can significantly improve the performance of client-server type of applications were the data sent to the client depends on user action at the client.
