Abstract
In computer graphics and scientific visualization, B-splines are common geometric representations. A typical display method is to render a piecewise linear (PL) approximation that lies within a prescribed tolerance of the curve. In dynamic applications it is necessary to perturb specified points on the displayed curve. The distance between the perturbed PL structure and the perturbed curve it represents can change significantly, possibly changing the underlying topology and introducing unwanted artifacts to the display. We give a strategy to perturb the curve smoothly and keep track of the error introduced by perturbations. This allows us to refine the PL curve when appropriate and avoid spurious topological changes. This work is motivated by applications to visualization of Big Data from simulations on high performance computing architectures.
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Notes
- 1.
There is an obvious typographical error [8, Proposition 5.2].
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Acknowledgements
The authors thank the referees, both for the conference presentation, as well as for this final book, for their helpful and constructive comments, which led to many improvements. The three UConn authors were partially supported by NSF grants CMMI 1053077 and CNS 0923158. T. J. Peters was also partially supported by an IBM Faculty Award and IBM Doctoral Fellowships. All statements here are the responsibility of the author, not of the National Science Foundation nor of IBM.
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Cassidy, H.P., Peters, T.J., Ilies, H., Jordan, K.E. (2014). Topological Integrity for Dynamic Spline Models During Visualization of Big Data. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_11
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DOI: https://doi.org/10.1007/978-3-319-04099-8_11
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