Algebraic Methods in Computer Aided Geometric Design: Theoretical and Practical Applications

González-Vega, Laureano; Necula, Ioana; Pérez–Díaz, Sonia; Sendra, J. Rafael

doi:10.1142/9789812794833_0001

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2005

2019

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Cited by 6 publications

(2 citation statements)

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“…(1). There are many generic methods for implicitizing rational curves and surfaces such as resultants, Grobner bases, and the method of moving lines and planes (Gonzalez-Vega et al, 2004;Kotsireas, 2004;Sederberg and Chen, 1995;Cox et al, 1998a). Here we shall develop an efficient technique with very little computation to implicitize a rational surface with a planar directrix and a space directrix by using moving planes.…”

Section: Introductionmentioning

confidence: 99%

Using moving planes to implicitize rational surfaces generated from a planar curve and a space curve

Shi

2014

Computer Aided Geometric Design

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Section: Introductionmentioning

confidence: 99%

Using moving planes to implicitize rational surfaces generated from a planar curve and a space curve

Shi

2014

Computer Aided Geometric Design

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“…Some applications in computer-aided geometric design (CAGD) require the manipulation of certain geometric objects called offsets (see [13,5,10]). These objects are algebraic varieties, in fact hypersurfaces, that essentially appear when taking the envelope of a system of hyperspheres with fixed, but probably undetermined, distance and centered at the points of a given hypersurface.…”

Section: Introductionmentioning

confidence: 99%

Degree formulae for offset curves

Segundo

Sendra

2005

Journal of Pure and Applied Algebra

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In this paper, we present three different formulae for computing the degree of the offset of a real irreducible affine plane curve C given implicitly, and we see how these formulae particularize to the case of rational curves. The first formula is based on an auxiliary curve, called S, that is defined depending on a non-empty Zariski open subset of R 2 . The second formula is based on the resultant of the defining polynomial of C, and the polynomial defining generically S. The third formula expresses the offset degree by means of the degree of C and the multiplicity of intersection of C and the hodograph H to C, at their intersection points.

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