Abstract
The concept of envelope of a family of curves or surfaces is a well known idea in Differential Geometry. But, in general, it is used only for families with low degrees of freedom, in whose context it has full sense. Even if for families with higher degrees of freedom, the concept of envelope becomes less evident, we can generalize it for families of hypersurfaces with arbitrary constraints and higher degrees of freedom. We provide theorems showing the scope of the new definition and how it generalizes the known envelope definitions.
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Notes
- 1.
If we do not use the full representation of F but only the generic one, we obtain an extra point y=1, that must be discarded.
- 2.
It is important to choose the order of the ring variables adequately in the definition of the ring in order to obtain this interesting result. We tried other alternatives and the result was not obvious.
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Montes, A. (2018). Geometric Envelopes. In: The Gröbner Cover . Algorithms and Computation in Mathematics, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-030-03904-2_8
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DOI: https://doi.org/10.1007/978-3-030-03904-2_8
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