Computing the intersection of two ruled surfaces by using a new algebraic approach

Fioravanti, Mario; González-Vega, Laureano; Necula, Ioana

doi:10.1016/j.jsc.2005.02.008

Cited by 16 publications

(17 citation statements)

References 12 publications

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“…Algorithm 2: Intersection of two parameterized curves Input: Two parameterized curves C 1 and C 2 given by (9) and (10). Output: The intersection points of C 1 and C 2 .…”

Section: Extracting the Regular Part Of A Non Square Pencil Of Matricesmentioning

confidence: 99%

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Matrix-based implicit representations of rational algebraic curves and applications

Busé

2010

Computer Aided Geometric Design

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Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: The point-on-curve and inversion problems, the computation of singularities and the calculation of the intersection between two rational curves.

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“…Algorithm 2: Intersection of two parameterized curves Input: Two parameterized curves C 1 and C 2 given by (9) and (10). Output: The intersection points of C 1 and C 2 .…”

Section: Extracting the Regular Part Of A Non Square Pencil Of Matricesmentioning

confidence: 99%

“…It is worth mentioning that the computation of the intersection lines between two ruled surfaces is interesting because it corresponds to the singular case in the methods given in [14] and [10] to compute the complete intersection locus between two ruled surfaces.…”

Section: Extracting the Regular Part Of A Non Square Pencil Of Matricesmentioning

confidence: 99%

Matrix-based implicit representations of rational algebraic curves and applications

Busé

2010

Computer Aided Geometric Design

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“…For the same ruled surface, Fioravanti, et al [16] computed three resultants and their gcd to get the implicit equation.…”

Section: Corollarymentioning

confidence: 99%

Implicitization using univariate resultants

Shen

Yuan

2010

J Syst Sci Complex

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Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univariate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.

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“…In order to find the implicit equation of a surface one may use resultants, a method which can be very appropriate when dealing with revolution, canal or ruled surfaces ( [5,6]), but using in practice the presentation through the Bézout matrix Bez(p, q) when computing such a resultants.…”

Section: The Surface-to-surface Intersection Problem By Using Implicimentioning

confidence: 99%

Mixing symbolic and numerical approaches for the surface‐to‐surface intersection problem

Fioravanti

González-Vega

2007

Proc Appl Math and Mech

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This paper shows how the efficiency of the current methodologies applied to the surface-to-surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output.

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Computing the intersection of two ruled surfaces by using a new algebraic approach

Cited by 16 publications

References 12 publications

Matrix-based implicit representations of rational algebraic curves and applications

Matrix-based implicit representations of rational algebraic curves and applications

Implicitization using univariate resultants

Mixing symbolic and numerical approaches for the surface‐to‐surface intersection problem

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