Construction of Bézier rectangles and triangles on the symmetric Dupin horn cyclide by means of inversion
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Cited by (12)
Representation of Dupin cyclides using quaternions
2015, Graphical ModelsCitation Excerpt :The interest in Dupin cyclides was revived in 1984 by Martin [17] who proposed to use their principal patches for modeling applications. Since then there were many attempts to integrate Dupin cyclides into geometric modeling: blending applications were developed in [11,20,21], smooth patchworks of Dupin cyclides were considered in [3,22], rational biquadratic Bézier representation was studied by [1,10,13,24]. One can find a good survey on Dupin cyclides and their applications in [6,9].
Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides
2014, Computers and Mathematics with ApplicationsCitation Excerpt :On the other hand, the parametric representation fits better the editing, animation, and visualization of surfaces. Another important argument encouraging Dupin cyclides use is their well-established conversions to other parametric surfaces, such as Bézier curves, B-splines, and NURBS [4,11–15]. This point bridges the gap between the different types of surfaces and may accelerate the introduction of Dupin cyclides into modeling systems based on parametric surfaces.
Studying cyclides with Laguerre geometry
2000, Computer Aided Geometric DesignApplications of Laguerre geometry in CAGD
1998, Computer Aided Geometric DesignSubdivisions of ring dupin cyclides using bézier curves with mass points
2021, WSEAS Transactions on MathematicsConstruction of 3D triangles on Dupin cyclides
2013, Intelligent Computer Vision and Image Processing: Innovation, Application, and Design
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Present address: Mathematisches Institut, Technische Universität München, D-80290 München, Germany