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By using the support functions on the $xy$-plane, we show the necessary and sufficient conditions for the existence of envelopes of horizontal lines in the 3D-Heisenberg group. A method to construct horizontal envelopes from the given ones is also derived, and we classify the solutions satisfying the construction.
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참고문헌 (27)
참고문헌 신청
V. I. Arnold / 1989 / Graduate Texts in Mathematics, 60 / Springer-Verlag
V. I. Arnold / 1990 / Mathematics and its Applications (Soviet Series), 62 / Kluwer Academic Publishers Group :62
V. I. Arnold / 1993 / Singularity Theory. II, Dynamical Systems VIII / Encyclopaedia Math. Sci. 39
V. I. Arnold / 1985 / Monographs in Mathematics / Birkhauser Boston, Inc :82
J. -D. Boissonnat / 1996 / On-line construction of the upper envelope of triangles and surface patches in three dimensions / Comput. Geom. 5(6):303~320
V. I. Arnold / 1990 / Mathematics and its Applications (Soviet Series), 62 / Kluwer Academic Publishers Group :62
V. I. Arnold / 1993 / Singularity Theory. II, Dynamical Systems VIII / Encyclopaedia Math. Sci. 39
V. I. Arnold / 1985 / Monographs in Mathematics / Birkhauser Boston, Inc :82
J. -D. Boissonnat / 1996 / On-line construction of the upper envelope of triangles and surface patches in three dimensions / Comput. Geom. 5(6):303~320
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