Approximate Rational Parameterization of Implicitly Defined Surfaces

2005 ◽  
pp. 434-447 ◽  
Author(s):  
Elmar Wurm ◽  
Bert Jüttler ◽  
Myung-Soo Kim
Keyword(s):  
Implicitly Defined Surfaces ◽  
Rational Parameterization

Blending Cylinders and Cones using Canal Surfaces

2000 ◽  
Vol 5 ◽  
pp. 77-89 ◽  
Author(s):  
M. Kazakevičiūtė ◽  
R. Krasauskas
Keyword(s):  
Canal Surface ◽  
Variable Radius ◽  
Rolling Ball ◽  
Canal Surfaces ◽  
Rational Parameterization

There is reviewed the construction of a rational blending surface between cylinders and cones in some interlocation cases. This surface is constructed as a patch of rolling ball envelope, i.e. as a patch of tangent canal surface of rational-variable radius. This construction defines rational parameterization of a blending surface. The constructed surface is Laguerre invariant.

scholarly journals A Priori Anisotropic Mesh Adaptation on Implicitly Defined Surfaces

2015 ◽  
Vol 37 (6) ◽  
pp. A2758-A2782 ◽  
Author(s):  
Franco Dassi ◽  
Simona Perotto ◽  
Luca Formaggia
Keyword(s):  
A Priori ◽  
Mesh Adaptation ◽  
Anisotropic Mesh ◽  
Anisotropic Mesh Adaptation ◽  
Implicitly Defined Surfaces

scholarly journals Rational quartic spectrahedra

2021 ◽  
Vol 127 (1) ◽  
pp. 79-99
Author(s):  
Martin Helsø ◽  
Kristian Ranestad
Keyword(s):  
Necessary Conditions ◽  
Zariski Closure ◽  
Rational Parameterization ◽  
Exhaustive List ◽  
Convex Subsets

Rational quartic spectrahedra in $3$-space are semialgebraic convex subsets in $\mathbb{R} ^3$ of semidefinite, real symmetric $(4 \times 4)$-matrices, whose boundary admits a rational parameterization. The Zariski closure in $\mathbb{C}\mathbb{P} ^3$ of the boundary of a rational spectrahedron is a rational complex symmetroid. We give necessary conditions on the configurations of singularities of the corresponding real symmetroids in $\mathbb{R} \mathbb{P} ^3$ of rational quartic spectrahedra. We provide an almost exhaustive list of examples realizing the configurations, and conjecture that the missing example does not occur.

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