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Smooth Orthogonal Layouts

Michael A. Bekos, Michael Kaufmann, Stephen G. Kobourov, Antonios Symvonis
2013 Journal of Graph Algorithms and Applications  
We study the problem of creating smooth orthogonal layouts for planar graphs.  ...  We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3.  ...  Vertices of degree four have perfect angular resolution in traditional orthogonal layouts, by virtue of construction.  ... 
doi:10.7155/jgaa.00305 fatcat:cpyhzz7ks5gqrim3xsxpu3nqpy

Smooth Orthogonal Layouts [chapter]

Michael A. Bekos, Michael Kaufmann, Stephen G. Kobourov, Antonios Symvonis
2013 Lecture Notes in Computer Science  
We study the problem of creating smooth orthogonal layouts for planar graphs.  ...  We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3.  ...  Vertices of degree four have perfect angular resolution in traditional orthogonal layouts, by virtue of construction.  ... 
doi:10.1007/978-3-642-36763-2_14 fatcat:5zg4c4omgrekrmuocaklaaqxha

Smooth Orthogonal Drawings of Planar Graphs [chapter]

Muhammad Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G. Kobourov, Alexander Wolff
2014 Lecture Notes in Computer Science  
We say that a graph has smooth complexity k-for short, an SC k -layout-if it admits a smooth orthogonal drawing of edge complexity at most k.  ...  In this paper, we study the problem of finding smooth orthogonal layouts of low edge complexity, that is, with few segments per edge.  ...  We seek for drawings of 4-planar graphs with low smooth complexity. Our Contribution. Known results and our contributions to smooth orthogonal drawings are shown in Table 1 .  ... 
doi:10.1007/978-3-642-54423-1_13 fatcat:p4w3km6ylncl7dnqb2xf2jjhwi

Smooth Orthogonal Drawings of Planar Graphs [article]

Md. Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G. Kobourov, Alexander Wolff
2013 arXiv   pre-print
We say that a graph has smooth complexity k---for short, an SC_k-layout---if it admits a smooth orthogonal drawing of edge complexity at most k.  ...  In this paper, we study the problem of finding smooth orthogonal layouts of low edge complexity, that is, with few segments per edge.  ...  We seek for drawings of 4-planar graphs with low smooth complexity. Our Contribution. Known results and our contributions to smooth orthogonal drawings are shown in Table 1 .  ... 
arXiv:1312.3538v1 fatcat:skwfkgwec5hmlazmh6dbuorheq

True2Form

Baoxuan Xu, William Chang, Alla Sheffer, Adrien Bousseau, James McCrae, Karan Singh
2014 ACM Transactions on Graphics  
Our approach to infer 3D form from 2D drawings is a novel mathematical framework of insights derived from perception and design literature.  ...  Many thanks to Xch'e' Hernandez Simper, and Cloud Shao for generating input drawings. Inria acknowledges generous support from Adobe.  ...  To start the process we recall that orthogonality at smooth crossings is one regularity that always applies.  ... 
doi:10.1145/2601097.2601128 fatcat:ef365m3lafaypiqsrzvmvltrya

BendFields

Emmanuel Iarussi, David Bommes, Adrien Bousseau
2015 ACM Transactions on Graphics  
Designers frequently draw curvature lines to convey bending of smooth surfaces in concept sketches.  ...  Our algorithm first estimates the projection of this cross field in the drawing, which is non-orthogonal due to foreshortening.  ...  Fig. 16 :Fig. 17 :Fig. 18 : 161718 Fig.16: The stroke smoothness and constrain weights offer a trade-off between fidelity to the input drawing and smoothness of the normal field.  ... 
doi:10.1145/2710026 fatcat:qxoikkatzvd4ni2nohrax5vdwe

Angular measures and Birkhoff orthogonality in Minkowski planes [article]

Márton Naszódi and Vilmos Prokaj and Konrad Swanepoel
2019 arXiv   pre-print
We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc.  ...  A B-measure (Fankhänel 2011) is an angular measure μ on the unit circle for which μ(C)=π/2 whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points.  ...  Acknowledgement KS thanks Adam Ostaszewski for enlightening conversations and for drawing his attention to [Par05] .  ... 
arXiv:1909.07905v1 fatcat:t4lvxoanpneifnwbvmq7xmgwwi

Patterns from photograph: Reverse-engineering developable products

Amélie Fondevilla, Adrien Bousseau, Damien Rohmer, Stefanie Hahmann, Marie-Paule Cani
2017 Computers & graphics  
[33] derive an orthogonality constraint from crosssection lines that designers draw to convey curvature directions on smooth surfaces. Iarussi et al.  ...  Moreover, one can check that every smooth surface satisfies S ,uv · n = −S ,v · n ,u , which leads to the expected conclusion that S ,v is orthogonal to n ,u .  ... 
doi:10.1016/j.cag.2017.05.017 fatcat:z4a3ka6i6fawtmj2jtckpgvnay

Page 506 of Journal of Polymer Science. Part B, Polymer Physics Vol. 31, Issue 5 [page]

1993 Journal of Polymer Science. Part B, Polymer Physics  
In this orthogonal coordinate sys- tem, the y axis is chosen orthogonal to the film plane.  ...  These layers had been deposited mechanically (e.g., by friction ) on a smooth support like glass.  ... 

Standard special generic maps of homotopy spheres into Euclidean spaces

Dominik J. Wrazidlo
2018 Topology and its Applications  
A so-called special generic map is by definition a map of smooth manifolds all of whose singularities are definite fold points.  ...  The Morse perfection of M n is the greatest integer k ≥ −1 for which there exists a smooth map η : S k × M n → R with the following properties: M n → W f is a smooth map satisfying q −1 f (∂W f ) = S(f  ...  Consequently, Theorem 1.2 allows to draw conclusions on the Gromoll filtration of concrete homotopy spheres such as Milnor spheres (compare Proposition 5.3(ii)).  ... 
doi:10.1016/j.topol.2017.11.037 fatcat:omk65gu7t5ehfl44u64lcah53a

A Cylindrical Basis Function for Solving Partial Differential Equations on Manifolds [article]

E.O.Asante-Asamani, Lei Wang, Zeyun Yu
2016 arXiv   pre-print
(in radians) between normals of smoothed sphere (after 10, 30 and 60 steps) and original perfect sphere with 258 points.  ...  We choose not to use the position vectors of the point clouds on the perfect sphere as true normals in order to permit a more uniform comparison with the smoothed sphere.  ... 
arXiv:1407.1303v3 fatcat:zjcaxg3g5jfjddhggimnw4qytu

Loss Landscapes of Regularized Linear Autoencoders [article]

Daniel Kunin, Jonathan M. Bloom, Aleksandrina Goeva, Cotton Seed
2019 arXiv   pre-print
Similarly, the smooth 4-dimensional Poincaré conjecture holds if and only if every smooth 4-sphere admits a perfect Morse function.  ...  A Morse function is F 2 -perfect if this count is always even, in which case ∂ vanishes over the field of two elements.Not all smooth manifolds admit perfect Morse functions.  ... 
arXiv:1901.08168v2 fatcat:u453wlh6m5ckhpkssy4tak3dua

Derived noncommutative schemes, geometric realizations, and finite dimensional algebras [article]

Dmitri Orlov
2018 arXiv   pre-print
It is proved that such noncommutative schemes have special geometric realizations under which the algebra goes to a vector bundle on a smooth projective scheme.  ...  In this paper we discuss some properties of derived noncommutative schemes and draw various analogies with the commutative case.  ...  By Proposition 2.12 all such DG bimodules are perfect because N i are smooth and proper.  ... 
arXiv:1808.02287v1 fatcat:wc2l4hp7hzh3joh6lwm2xx3keu

A Cylindrical Basis Function for Solving Partial Differential Equations on Manifolds

E.O. Asante-Asamani, Lei Wang, Zeyun Yu
2016 Procedia Computer Science  
Recently, the orthogonal gradient method presented in [13] , was introduced to extend this idea to point clouds.  ...  The modified kernel, when used in the representation of smooth functions defined on a closed surface, allows surface differential operators to be replaced by their Cartesian equivalent without the need  ...  steps) and original perfect sphere with 258 points.  ... 
doi:10.1016/j.procs.2016.05.316 fatcat:7ympvefqgvaqzdaghwvtsq7sou

An Interactive Car Drawing System with Tick'n'Draw for Training Perceptual and Perspective Drawing Skills

Seung-Jun Lee, Joon Hyub Lee, Seok-Hyung Bae
2022 CHI Conference on Human Factors in Computing Systems Extended Abstracts  
trains 10 core drawing skills to make them his or her own.  ...  Figure 1 : Our novel interactive system consists of 5 stages for drawing a nice car with an accurate perspective.  ...  a smooth curve connecting the points (Skill 5) to transfer the curve on the orthogonal grid to the perspective grid (Skill 9).  ... 
doi:10.1145/3491101.3519776 fatcat:f3c4clep3nbp3nez3bbke67hou
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