Old problems and new challenges in subdivision

Autor: Malcolm A. Sabin, Ulrich Reif
Rok vydání: 2019
Předmět:
Zdroj: Journal of Computational and Applied Mathematics. 349:523-531
ISSN: 0377-0427
Popis: Subdivision has been an active research topic for about 40 years, and it has seen commercial exploitation in animated Computer Graphics. The question has to be asked: ‘Is there anything left to do research-wise?’ This note contains the authors’ responses. Yes, much has been learnt and does not need to be relearnt, but there are still results that we cannot prove, properties of specific schemes that we cannot compute exactly, and there are still ways in which we need to improve the technology to make it useful in the more demanding contexts of CAD, CAM, and CAE. We have approached the subject by looking first at curves, then at surfaces, and finally at the trivariate structures which are required for CAE. For each dimension we identify first what is already established, and then proceed to suggest directions for further research. Three different labels indicate, for each useful piece of work, the relative difficulty and hence the prospects of success: Download : Download high-res image (24KB) Download : Download full-size image Download : Download high-res image (25KB) Download : Download full-size image Download : Download high-res image (40KB) Download : Download full-size image Of course, these ratings are just our personal estimates. We will only know for sure how hard the questions were when the work has been done. Further, we do not claim completeness of the list of topics discussed here. Also the list of references selects only a few samples from the vast literature.
Databáze: OpenAIRE
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