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Computing real inflection points of cubic algebraic curves
2003
Computer Aided Geometric Design
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In this paper we present an algorithm for computing the real inflection points of a real planar cubic algebraic curve. ...
Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. ...
This article is about computing the real inflection points of an irreducible planar cubic algebraic curve. ...
doi:10.1016/s0167-8396(03)00022-0
fatcat:wzxfoplrajdhnoonrq6qlrd2om
Page 3268 of Mathematical Reviews Vol. , Issue 2004d
[page]
2004
Mathematical Reviews
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; Hong Kong) Computing real inflection points of cubic algebraic curves. ...
In this paper we present an al- gorithm for computing the real inflection points of a real planar cubic algebraic curve. ...
Distance Product Cubics
2020
KoG
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All distance product cubics share the real points of inflection which lie on the line at infinity. ...
The locus of points that determine a constant product of their distances to the sides of a triangle is a cubic curve in the projectively closed Euclidean triangle plane. ...
The sextic curves (7) have three real and six complex cusps corresponding to the three real and six complex points of inflection on the cubics (2). ...
doi:10.31896/k.24.3
fatcat:46akfkh6ijajza6nyxx5glorg4
On algebraically integrable outer billiards
[article]
2007
arXiv
pre-print
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We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain non-degenerate sense then the oval is an ellipse. ...
Kharlamov for providing a proof of Lemma 3 and to Rich Schwartz for interest and criticism. The author was partially supported by an NSF grant DMS-0555803. ...
Unless C is a conic, this curve has inflection points (not necessarily real). Let d be the degree of C. ...
arXiv:0708.0255v1
fatcat:4o2iakyxprelponyt2mbd2nfqi
Characterization of Planar Cubic Alternative curve
[article]
2013
arXiv
pre-print
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In this paper, we analyze the planar cubic Alternative curve to determine the conditions for convex, loops, cusps and inflection points. ...
Thus cubic curve is represented by linear combination of three control points and basis function that consist of two shape parameters. ...
The necessary condition for the occurrence of the inflection points along with numbers of inflection points of cubic Alternative curve can now be stated. where cusp occur at that value. ...
arXiv:1304.7848v1
fatcat:uqoh7cfmrvg6jf5jnun6y6wrg4
On algebraically integrable outer billiards
2008
Pacific Journal of Mathematics
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We prove that if the outer billiard map around a plane oval is algebraically integrable in a certain nondegenerate sense then the oval is an ellipse. ...
Kharlamov for providing a proof of Lemma 3, to R. Schwartz for interest and criticism, and to the referee for helpful suggestions. ...
We use the notation C for the complex algebraic curve given by the homogenized polynomialf (x : y : z) = f (x/z, y/z). Unless C is a conic, this curve has inflection points (not necessarily real). ...
doi:10.2140/pjm.2008.235.89
fatcat:ijmszoeu3bdcpc6tfeednfg26a
Real Polynomials with a Complex Twist
[article]
2018
arXiv
pre-print
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In order to fully appreciate the Fundamental Theorem of Algebra, and the non-real solutions of a polynomial equation, traditional graphs are inadequate. ...
Advancements in computer graphics allow us to easily illustrate a more complete graph of polynomial functions that is still accessible to students of many different levels. ...
All cubics have one inflection point, where the second derivative is equal to zero. This hyperbola is centered at the point of inflection, where = − 3 . ...
arXiv:1805.05321v1
fatcat:fijjhfixqbcgza6ofl45na6yti
Hermite Interpolation by Pythagorean Hodograph Quintics
1995
Mathematics of Computation
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" cubics. ...
We show that formulating PH quintics as complex-valued functions of a real parameter leads to a compact Hermite interpolation algorithm and facilitates an identification of the "good" interpolant (in terms ...
cubic in its number of inflections. ...
doi:10.2307/2153373
fatcat:p45qeoad2rawfhktxr7nej3q5m
Self-conjugate vectors of immersed 3-manifolds in R6
2012
Topology and its Applications
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We classify the possible generic algebraic structures of the asymptotic vectors at a parabolic point or an inflection point, and we classify the generic topological structures of the parabolic surface. ...
a r t i c l e i n f o a b s t r a c t MSC: 58K30 14E20 53A07 58K05 This paper generalizes the notion of asymptotic vectors, parabolic curves, and inflection points on surfaces in R 4 to n-manifolds in ...
We find normal forms for these quadratic triples and the cubic curves, and we relate the structure of the cubic to the type of point on the manifold. ...
doi:10.1016/j.topol.2011.09.019
fatcat:nmxo4drn4vgshbdaqn73xfu4yq
Auxetic deformations and elliptic curves
2018
Computer Aided Geometric Design
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A fast algorithm for recognizing auxetic capabilities is obtained via the classical Aronhold invariants of the cubic form defining the curve. A related alternative is also considered. ...
We show that the existence of auxetic deformations is related to properties of an associated elliptic curve. ...
The authors are grateful for the hospitality of the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University during the Fall 2016, when this work was completed. ...
doi:10.1016/j.cagd.2018.02.003
pmid:30643352
pmcid:PMC6329461
fatcat:mbnqxbrtxzbptkjh7mx54filvy
Real inflections of hinged planar four-bar coupler curves
1995
Mechanism and Machine Theory
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Plücker's and Klein's equations provide an upper bound on the number of real inflections on the coupler curve of a hinged planar four-bar mechanism. ...
This enables us to locate coupler curves exhibiting the maximum possible number of inflections. ...
. §5 Computer Graphics The realisation of coupler curves with various numbers of inflection points up to the maximum 12 was completed by computer. ...
doi:10.1016/0094-114x(95)00047-3
fatcat:rficqayynjftlikumj3lut4q3i
Auxetic deformations and elliptic curves
[article]
2016
arXiv
pre-print
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A fast algorithm for recognizing auxetic capabilities is obtained via the classical Aronhold invariants of the cubic form defining the curve. ...
We show that the existence of auxetic deformations is related to properties of an associated elliptic curve. ...
The authors are grateful for the hospitality of the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University during the Fall 2016, when this work was completed. ...
arXiv:1612.02100v1
fatcat:lfl2hjzihzf3lm6chn5pif5k4y
Questions and Discussions
1927
The American mathematical monthly
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A StmpLE Way To Discuss Points OF INFLECTION ON PLANE CuBIC CURVES
ALAN D. ...
CAMPBELL, Syracuse University
In this paper we show by means of illustrations a simple but very effective way to discuss points of inflection on plane cubic curves. ...
doi:10.1080/00029890.1927.11986741
fatcat:7mfb2i366fgepfgrh5kd6qdvoy
Hermite interpolation by Pythagorean hodograph quintics
1995
Mathematics of Computation
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" cubics. ...
We show that formulating PH quintics as complex-valued functions of a real parameter leads to a compact Hermite interpolation algorithm and facilitates an identification of the "good" interpolant (in terms ...
cubic in its number of inflections. ...
doi:10.1090/s0025-5718-1995-1308452-6
fatcat:ew7spddaojaonhnawe7bbsahqa
Elliptic curves in honeycomb form
[article]
2012
arXiv
pre-print
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of the tropical group law on such a curve. ...
We explicitly compute such representations from a given j-invariant with negative valuation, we give an analytic characterization of elliptic curves in honeycomb form, and we offer a detailed analysis ...
Acknowledgments This project grew out of discussions we had with Spencer Backman and Matt Baker. We are grateful for their contributions and help with the analytic theory of elliptic curves. ...
arXiv:1203.2356v1
fatcat:xz43orkc7veptn3tcmvuug2ks4
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