منابع مشابه
Numerical Implicitization for Macaulay2
We present the Macaulay2 package NumericalImplicitization, which allows for user-friendly computation of the basic invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This package relies on methods of numerical algebraic geometry, such as homotopy continuation and monodromy. Introduction. Many varieties of interest in algebraic geometry and its a...
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In geometric modelling surfaces can be given essentially in two ways: implicit and parametric form. The automatic transition between the implicit and the parametric representations of surfaces is of fundamental importance. In the literature there are several symbolic/numeric implicitization techniques based on resultants [1], Gröbner–basis [2], moving surfaces [3], linear algebra [4], but the n...
متن کاملNumerical Implicitization of Parametric Hypersurfaces with Linear Algebra
We present a new method for implicitization of parametric curves, surfaces and hypersurfaces using essentially numerical linear algebra. The method is applicable for polynomial, rational as well as trigonometric parametric representations. The method can also handle monoparametric families of parametric curves, surfaces and hypersurfaces with a small additional amount of human interaction. We i...
متن کاملImplicitization using Moving Lines
where the equations a0x+ b0y + c0 = 0 and a1x+ b1y + c1 = 0 define any two distinct lines. It is known that any conic section can be “generated by the intersection of corresponding lines of two related pencils in a plane” [Som51], p.388. In other words, given two distinct pencils, (a00x+b00y+c00)(1−t)+(a10x+b10y+c10)t = 0 and (a01x+b01y+c01)(1−t)+(a11x+b11y+c11)t = 0, to each value of t corresp...
متن کاملImplicitization and Distance Bounds
We address the following problem: given a curve in parametric form, compute the implicit representation of another one that approximates the parametric curve on a certain domain of interest. We study this problem from the numerical point of view: what happens with the output curve if the input curve is slightly changed? It is shown that for any approximate parameterization of the given curve, t...
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ژورنال
عنوان ژورنال: Journal of Software for Algebra and Geometry
سال: 2019
ISSN: 1948-7916
DOI: 10.2140/jsag.2019.9.55