Abstract
Developable surfaces are a subset of ruled surfaces, which can be mapped onto a plane without deformation. Due to this property, they have considerable relevance in several applications. In the medical area, regarding information visualization along sections of organs, they could be useful in clinical diagnosis. They have also industrial applications, including footwear and clothing industries, where three-dimensional (3D) designs are made from flat materials.
In this research, we consider the issue of approximating developable surfaces with segments of circular cones, with the aim of constructing splines that model interesting surfaces. Our emphasis will be in the odontological area. We present examples of “panoramic views” of curved sections of human jaw which contain information about all the dental pieces. Moreover, the process allows for the simultaneous display of these pieces in a flat surface, without metric distortion.
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Notes
- 1.
Actually for multiple root teeth, there might be more than one plane choices. These stem from the fact the best plane for clinical inspection could approximate any of the root pairs.
- 2.
If we have two adjacent contact elements \(({e}_{i},\tau_{i})\) and \(({e}_{i+1},\tau_{i+1})\), “jum** over a contact element” means omitting \(({e}_{i+1},\tau_{i+1})\) and considering instead \(({e}_{i},\tau_{i})\) and \(({e}_{i+2},\tau_{i+2})\).
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Acknowledgments
We wish to thank José F. Ramírez Huaca for Fig. 11.
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González, C., Paluszny, M. (2015). Odontological Information Along Cone Splines. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_15
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DOI: https://doi.org/10.1007/978-3-319-12583-1_15
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