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Generalised cyclidic nets for shape modelling in architecture

Romain Mesnil, Cyril Douthe, Olivier Baverel, Bruno Léger
2017 International Journal of Architectural Computing  
Indeed, Dupin's cyclides do not have umbilical points: their lines of curvature and therefore the edges of the cyclidic patches are thus strictly perpendicular.  ...  The extension of these findings for other patterns, like the tri-hex pattern, should also be Figure 3 : 3 Dupin's cyclide parameterised by its lines of curvature (in order top, front and perspective views  ...  Pre-print submitted to The International Journal of Architectural Computing (2017) 20 studied.  ... 
doi:10.1177/1478077117714917 fatcat:62cgg7ukbvbg3d5suktzop5yue

On the geometry of Dupin cyclides

V. Chandru, D. Dutta, C. M. Hoffmann
1989 The Visual Computer  
., variable radius blending) and require a deep understanding of the geometry of the cyclide.  ...  We also discuss the morphology of cyclides and present a new classification scheme.  ...  ,ey 1871J and [Darboux 1887) . have analyzed and generalized Dupin's cyclide in various ways.  ... 
doi:10.1007/bf01914786 fatcat:uspf3ntol5hrtaqzl3inu43zu4

Page 3913 of Mathematical Reviews Vol. , Issue 91G [page]

1991 Mathematical Reviews  
Summary: “Dupin’s cyclides are useful in blending conventional solids in solid modeling.  ...  It covers the construc- tion of the Bézier presentation of a simple basic patch as well as the double-cyclide blend of two conics, a solution of the Cranfield problem and the blend of a tripod.”  ... 

Circular arc structures

Pengbo Bo, Helmut Pottmann, Martin Kilian, Wenping Wang, Johannes Wallner
2011 ACM SIGGRAPH 2011 papers on - SIGGRAPH '11  
We study remarkable special cases of circular arc structures which possess simple supporting elements or repetitive edges, we present the first global approximation method for principal patches, and we  ...  The most important guiding principle in computational methods for freeform architecture is the balance between cost efficiency on the one hand, and adherence to the design intent on the other.  ...  Acknowledgments This research has been supported by the Austrian Science Fund (FWF) under grants No. S92-06 and S92-09 (National Research Network Industrial Geometry).  ... 
doi:10.1145/1964921.1964996 fatcat:djkjmr7mircflo7aorcucrkbyu

Circular arc structures

Pengbo Bo, Helmut Pottmann, Martin Kilian, Wenping Wang, Johannes Wallner
2011 ACM Transactions on Graphics  
We study remarkable special cases of circular arc structures which possess simple supporting elements or repetitive edges, we present the first global approximation method for principal patches, and we  ...  The most important guiding principle in computational methods for freeform architecture is the balance between cost efficiency on the one hand, and adherence to the design intent on the other.  ...  Acknowledgments This research has been supported by the Austrian Science Fund (FWF) under grants No. S92-06 and S92-09 (National Research Network Industrial Geometry).  ... 
doi:10.1145/2010324.1964996 fatcat:6elcuwy7wfenva7zrnppgshpre

Möbius-invariant curve and surface energies and their applications

Shin Yoshizawa, Alexander Belyaev
2013 Science China Information Sciences  
We also study connections of CI-MVS with the cyclides of Dupin. In addition, we consider several other conformal-invariant curve and surface energies involving curvatures and curvature derivatives.  ...  In computer-aided geometric design, the Willmore surfaces and the so-called minimum variation surfaces (MVS) are widely used for shape modeling purposes.  ...  The MVS energy (2) also measures deviation from special surfaces called Dupin's cyclides (see Figure 1 ) which are characterized by the conditions e max = 0 = e min and which are often used as CAD primitives  ... 
doi:10.1007/s11432-013-4997-0 fatcat:5fbagtxuyrghvom2xsnso76dii

Fast, robust, and faithful methods for detecting crest lines on meshes

Shin Yoshizawa, Alexander Belyaev, Hideo Yokota, Hans-Peter Seidel
2008 Computer Aided Geometric Design  
The methods exploit intrinsic geometric properties of the curvature extrema and provide with an inherent level-of-detail control of the detected crest lines.  ...  , and visualization purposes.  ...  We would like to thank the anonymous reviewers of this paper for their helpful comments and suggestions.  ... 
doi:10.1016/j.cagd.2008.06.008 fatcat:zxmbxtdz6berxpiq3brbeqnzrq

Closed rational trigonometric curves and surfaces

Imre Juhász, Ágoston Róth
2010 Journal of Computational and Applied Mathematics  
We also present the exact control point based description of some famous curves (Lemniscate of Bernoulli, Zhukovsky airfoil profile) and surfaces (Dupin cyclide and the smooth transition between the Boy  ...  surface and the Roman surface of Steiner) to illustrate the usefulness of the proposed tool.  ...  Fig. 6 . 6 cos u cos v) + b 2 cos u a − c cos u cos v , The three different basic cases of Dupin's cyclide (a = 6, b = 4 √ 2, c = 2): (a) ring (µ = 3); (b) horn (µ = 1.5); and (c) spindle (µ = 12).y (u  ... 
doi:10.1016/j.cam.2010.03.009 fatcat:k7xnqryguzal7jnt2e6vlk7cky

Book reports

1993 Computers and Mathematics with Applications  
Dupin's cyclide and the cyclide patch. 23 . Geometric reasoning in a parallel network. 24. SMS: A suggestive modelling system for object recognition. 25.  ...  MIT Press, Cambridge, MA and London, England. The develol~nent of and dissemination of engineering knowledge. 6. The mal~g of an engineer. 7. The gap between promise and performance.  ... 
doi:10.1016/0898-1221(93)90315-m fatcat:tnmkz3axfnekvgr4srsgsivuvy

Dupin cyclidic systems geometrically revisited [article]

Gudrun Szewieczek
2022
The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate systems with Dupin cyclides and spheres as coordinate surfaces, were provided by Darboux.  ...  Here we take a more geometric point of view and discuss how Dupin cyclides and Lamé families of Dupin cyclidic systems can be obtained by suitably evolving an initial circle or a Dupin cyclide, respectively  ...  The author would like to thank Udo Hertrich-Jeromin, María Lara Miró and Martin Peternell for fruitful and pleasurable discussions around the subject.  ... 
doi:10.48550/arxiv.2201.08576 fatcat:lmighiycybgrpgdg55pljf3yia

The development of computing tools to approximate doubly curved surfaces with quadrilateral planar facets

Florian Gauss, Technische Universität Berlin, Klaus Rückert
2020
Free form architectural design created with the aid of digital media requires a fundamental change of the approach to the entire planning and building process as it might not involve the use of actual  ...  The triangulation of a surface is a well-documented process however from an architectural and economical point of view the planar quadrilateral (PQ) tessellation of a surface offers several advantages.  ...  The patch cut out from a sphere S is called spherical patch and similar geometric properties apply as for the cyclidic patch: Just like for the cyclidic patch the boundary curves of a spherical patch are  ... 
doi:10.14279/depositonce-10435 fatcat:jvaspd62dfcr7f7kbuaitdw2aa

Societies and Academies

1923 Nature  
Dupin’s cyclid.  ...  They are characterised by the presence of highly corroded xenocrysts of quartz and felspar, and by the occurrence of variolitic and glassy patches in the ground-mass. Linnean Society, November 15.  ... 
doi:10.1038/112813a0 fatcat:7qi7lqo5lfa7jk53dtxjakkw7y

PHYSICS BASED GEOMETRIC DESIGN

HONG QIN
1996 International journal of shape modeling  
To o vercome the disadvantages of this indirect process, we summarize the prior work of physics-based modeling and review dynamic NURBS (D-NURBS) as a physics-based generalization of geometric NURBS for  ...  graphics, vision, and scienti c visualization.  ...  Dutta, Martin and Pratt 30] used piecewise Dupin's quartic cyclides for (a) (b) Figure 9 : Tension e ect on curve shape (a) the curve is generated by c o n trol polygon (b) the curve i s generated through  ... 
doi:10.1142/s0218654396000099 fatcat:ctnoubb7vvaubpbxuiev5dpmpe

Extracting lines of curvature from noisy point clouds

Evangelos Kalogerakis, Derek Nowrouzezahrai, Patricio Simari, Karan Singh
2009 Computer-Aided Design  
The extraction of curvature information can benefit many applications in CAD, computer vision and graphics for point cloud shape analysis, recognition and segmentation.  ...  First, we show a novel approach to denoising the input point cloud using robust statistical estimates of surface normal and curvature which automatically rejects outliers and corrects points by energy  ...  We thank Hanson Robotics for the Einstein's head dataset. We acknowledge the AIM@SHAPE 3D library and its authors for the use of 3D models and point clouds.  ... 
doi:10.1016/j.cad.2008.12.004 fatcat:pcvkzignsjgxtplil7c6sjw35q

Normals of the butterfly subdivision scheme surfaces and their applications

P. Shenkman, N. Dyn, D. Levin
1999 Journal of Computational and Applied Mathematics  
Two applications of these formulas are presented: building offsets to surfaces generated by the butterfly scheme and Gouraud shading of surfaces generated by this scheme as well as shading of their offsets  ...  The paper presents explicit formulas for calculating normals to surfaces generated by the butterfly interpolatory subdivision scheme from a general initial triangulation of control points.  ...  Acknowledgements We thank Gershon Elber for bringing to our attention the Gouraud shading.  ... 
doi:10.1016/s0377-0427(98)00213-1 fatcat:c2ckpo2xsrbvxk2ktktzx4rvvq
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