Aberrations of holographic lens recorded on surface of revolution with shifted pupil

1991 ◽  
Author(s):  
Jan Masajada
Keyword(s):  
Surface Of Revolution ◽  
Holographic Lens

Real-time CAD-level surface of revolution reconstruction on visual slam

2020 ◽  
Author(s):  
Feng Li ◽  
Bin He ◽  
Gang Li ◽  
Ming Ma ◽  
Jian Li ◽  
...  
Keyword(s):  
Real Time ◽  
Level Surface ◽  
Visual Slam ◽  
Surface Of Revolution

scholarly journals Darboux Transforms of a Harmonic Inverse Mean Curvature Surface

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Katsuhiro Moriya
Keyword(s):  
Mean Curvature ◽  
Curvature Surface ◽  
Surface Of Revolution ◽  
Darboux Transforms

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.

scholarly journals On the Affine Image of a Rational Surface of Revolution

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2061
Author(s):  
Juan G. Alcázar
Keyword(s):  
Differential Geometry ◽  
Affine Transformation ◽  
Rational Surface ◽  
Affine Differential Geometry ◽  
Affine Mapping ◽  
Surfaces Of Revolution ◽  
Surface Of Revolution ◽  
Affine Image ◽  
Fixed Line ◽  
The Given

We study the properties of the image of a rational surface of revolution under a nonsingular affine mapping. We prove that this image has a notable property, namely that all the affine normal lines, a concept that appears in the context of affine differential geometry, created by Blaschke in the first decades of the 20th century, intersect a fixed line. Given a rational surface with this property, which can be algorithmically checked, we provide an algorithmic method to find a surface of revolution, if it exists, whose image under an affine mapping is the given surface; the algorithm also finds the affine transformation mapping one surface onto the other. Finally, we also prove that the only rational affine surfaces of rotation, a generalization of surfaces of revolution that arises in the context of affine differential geometry, and which includes surfaces of revolution as a subtype, affinely transforming into a surface of revolution are the surfaces of revolution, and that in that case the affine mapping must be a similarity.

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