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Discrete fairing and variational subdivision for freeform surface design

Leif P. Kobbelt
2000 The Visual Computer  
Conclusion In this paper, we have given a survey of discrete fairing and variational subdivision methods that combine several powerful techniques for free-form surface design.  ...  Key words: Free-form surface design -Fairing -Variational subdivisions -Geometric modeling There are several standard representations for surface geometry, each of which is appropriate for specific tasks  ...  KOBBELT is a Senior Researcher at the Max Planck Institute for computer sciences in Saarbrücken, Germany.  ... 
doi:10.1007/s003710050204 fatcat:i4llkif4iveb7nxjd5taz2zwh4

Geometric modeling with conical meshes and developable surfaces

Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang, Wenping Wang
2006 ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06  
Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant  ...  The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass  ...  Markus Forstner is the designer of both the conical mesh in Fig. 15 and the developables in Fig. 16 .  ... 
doi:10.1145/1179352.1141941 fatcat:ba2eibmuj5cotg7j5iwdqktkia

Geometric modeling with conical meshes and developable surfaces

Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang, Wenping Wang
2006 ACM Transactions on Graphics  
Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant  ...  The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass  ...  Markus Forstner is the designer of both the conical mesh in Fig. 15 and the developables in Fig. 16 .  ... 
doi:10.1145/1141911.1141941 fatcat:qa5atp6y7vepxa6iusskyrewja

Feature-based 3D non-manifold freeform object construction

Charlie C. L. Wang, Yu Wang, Matthew M.F. Yuen
2003 Engineering with Computers  
This paper presents a novel technique for modeling a 3D non-manifold freeform model around a 3D reference model.  ...  In order to represent both the design abstractions and the incomplete topological information, first of all, a new non-manifold data structure is defined.  ...  subdivision scheme [37] , which is discrete fairing based.  ... 
doi:10.1007/s00366-003-0251-5 fatcat:o45fbhw3orcgzla2g3nkisg7wq

Multiresolution Analysis [chapter]

2010 Fundamentals of Wavelets  
transmission and LOD editing.  ...  They are now considered a powerful tool for efficiently representing functions at multiple levels-of-detail with many inherent advantages, including compression, Level-Of-Details (LOD) display, progressive  ...  Variational Shape Design Although it is difficult to define exactly, in mathematical terms, what fairness of a curve or surface is, it is commonly accepted that smooth and graceful shapes are obtained  ... 
doi:10.1002/9780470926994.ch5 fatcat:bbd2jxurcnbz5hurv4vudpkj2y

Architectural Geometry and Fabrication-Aware Design

Helmut Pottmann
2013 Nexus Network journal  
Freeform shapes and structures with a high geometric complexity play an increasingly important role in contemporary architecture.  ...  The present paper provides a short survey of research in Architectural Geometry and shows how this field moves towards a new direction in Geometric Modeling which aims at combining shape design with important  ...  Thanks go also to the team of Evolute for their insights and feedback from real-world projects and for help with several figures.  ... 
doi:10.1007/s00004-013-0149-5 fatcat:wj5w4fiaerfa3b6f33yndc7bjm

Freeform surfaces from single curved panels

Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner
2008 ACM SIGGRAPH 2008 papers on - SIGGRAPH '08  
This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces.  ...  Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels.  ...  Acknowledgments This work was supported by grants S92-06, S92-09, and P-19214 of the Austrian Science Fund (FWF). We want to thank Benjamin Schneider for his help in preparing illustrations.  ... 
doi:10.1145/1399504.1360675 fatcat:ye2fpwiowzctrhbywfcczoc2pe

Freeform surfaces from single curved panels

Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner
2008 ACM Transactions on Graphics  
This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces.  ...  Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels.  ...  Acknowledgments This work was supported by grants S92-06, S92-09, and P-19214 of the Austrian Science Fund (FWF). We want to thank Benjamin Schneider for his help in preparing illustrations.  ... 
doi:10.1145/1360612.1360675 fatcat:ghe4q7loffbgrjbw7rpr3qmz6e

Geometric Modeling Based on Polygonal Meshesv [article]

Leif P. Kobbelt, Stephan Bischoff, Mario Botsch, Kolja Kähler, Christian Rössl, Robert Schneider, Jens Vorsatz
2000 Eurographics State of the Art Reports  
Those techniques address important issues such as surface generation from discrete samples (e.g. laser scans) or from control meshes (ab initio design); complexity control by adjusting the level of detail  ...  While traditional computer aided design (CAD) is mainly based on piecewise polynomial surface representations, the recent advances in the efficient handling of polygonal meshes have made available a set  ...  Freeform modeling can be implemented based on subdivision schemes or based on discrete fairing techniques (Section 6).  ... 
doi:10.2312/egt.20001033 fatcat:ys2bwbqzzbg2zm4jb45d2cbvfi

Planar Hexagonal Meshing for Architecture

Yufei Li, Yang Liu, Wenping Wang
2015 IEEE Transactions on Visualization and Computer Graphics  
This understanding enables us to develop an effective method for paneling freeform architectural surfaces with PH meshes.  ...  We have developed several novel and effective techniques for improving undesirable mesh layouts caused by singular behaviors of surface curvature.  ...  Cutler and Whiting [11] employed the variational surface approximation approach [22] to compute planar panels for a given surface.  ... 
doi:10.1109/tvcg.2014.2322367 pmid:26357024 fatcat:kq35wuj4pbftxa2cvxopwtj2pe

A unified method for hybrid subdivision surface design using geometric partial differential equations

Qing Pan, Guoliang Xu, Yongjie Zhang
2014 Computer-Aided Design  
h i g h l i g h t s • We composite surface subdivision and the GPDE to form a unified method for freeform surface design. • We present a novel technique to evaluate the finite element basis functions.  ...  In this paper, we composite these two ingredients to form a unified method for freeform surface design.  ...  This example shows the power of our approach for the freeform shape design.  ... 
doi:10.1016/j.cad.2013.08.023 fatcat:v7wysnjelzgp3j236uma7rlgqy

Architectural geometry

Helmut Pottmann, Michael Eigensatz, Amir Vaxman, Johannes Wallner
2015 Computers & graphics  
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however  ...  For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint.  ...  The authors would like to thank Philippe Bompas and Jacques Raynaud for helpful discussions. We are very grateful to the anonymous reviewers for their extensive and helpful comments.  ... 
doi:10.1016/j.cag.2014.11.002 fatcat:m72hdwved5dx5izrtbjsk6m7gi

Feature based 3D garment design through 2D sketches

Charlie C.L. Wang, Yu Wang, Matthew M.F. Yuen
2003 Computer-Aided Design  
, a smooth mesh surface interpolating the specified profiles is constructed by a modified variational subdivision scheme.  ...  The result mesh surface can be cut and flattened into 2D patterns to be manufactured.  ...  Luo Zegang, and Dr. Au Chi Kit.  ... 
doi:10.1016/s0010-4485(02)00091-x fatcat:i7bppuuy5jg47abs62wl4ai3wy

Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing

Peter Schröder, Martin Rumpf, Ulrich Reif, Gerhard Dziuk
2005 Oberwolfach Reports  
and surface fairing, physical modeling of surfaces, the restoration of images and surfaces using higher order variational formulations.  ...  The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image  ...  In particular we derive variational problems and geometric evolutions problems for image and surface fairing, restoration and matching.  ... 
doi:10.4171/owr/2005/10 fatcat:lxgstanio5bafdcbv4fzkrqmgi

G1 surface modelling using fourth order geometric flows

Guoliang Xu, Qing Pan
2006 Computer-Aided Design  
These nonlinear equations are discretized using the mixed finite element method based on the combination of the Loop's basis and the linear basis.  ...  The nonlinear equations used include the surface diffusion flow and the Willmore flow.  ...  The mean curvature flow (MCF) and its various variations have been intensively used to smooth or fair noisy surfaces (see [2, 7, 9, 14] for references).  ... 
doi:10.1016/j.cad.2005.11.002 fatcat:souh5r7tibdrvhgibzkuar344i
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