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Constraints on Curve Networks Suitable for G 2 Interpolation [chapter]

Thomas Hermann, Jorg Peters, Tim Strotman
2010 Lecture Notes in Computer Science  
Prescribing a network of curves to be interpolated by a surface model is a standard approach in geometric design.  ...  Here we prove the existence of an additional, more subtle constraint that governs the admissibility of curve networks for G 2 interpolation.  ...  Section 5 provides a sufficient geometric condition for the existence of a G 2 patch network interpolating a curve network.  ... 
doi:10.1007/978-3-642-13411-1_6 fatcat:7n32xwj2yvgiteqq7fgd5qsdsa

Functional optimization for fair surface design

Henry P. Moreton, Carlo H. Séquin
1992 Proceedings of the 19th annual conference on Computer graphics and interactive techniques - SIGGRAPH '92  
The surfaces are specified through interpolated geometric constraints consisting of positions and, optionally, surface normals and surface curvatures.  ...  With more efficient optimization algorithms and with the ever increasing processing power available on every desk-top, the techniques described here will provide the basis for a new class of practical  ...  Acknowledgments The authors thank Silicon Graphics Inc. for its generous support. We would also like to thank Tony DeRose and the reviewers for their many helpful comments on this paper.  ... 
doi:10.1145/133994.134035 dblp:conf/siggraph/MoretonS92 fatcat:unjfvbaeurhjrnpv7zsmayvn4a

Blending, smoothing and interpolation of irregular meshes using N-sided Varady patches

Xuefu Wang, Fuhua (Frank) Cheng, Brian A. Barsky
1999 Proceedings of the fifth ACM symposium on Solid modeling and applications - SMA '99  
The new approach treats all these problems as a surface fitting problem by first restructuring the given mesh to obtain a new mesh suitable for network curves construction, and then filling all the holes  ...  Several new techniques are introduced; these include restructuring techniques for a given mesh regarding blending and interpolation problems, ,a network curves construction technique, an energy formulation  ...  Yong Zhou for providing us with the rendering package. We thank all the anonymous reviewers for their comments.  ... 
doi:10.1145/304012.304034 dblp:conf/sma/WangCB99 fatcat:dsk7bjszzzdk7bzwj5xwx6tddi

Surface design with minimum energy networks

Henry Moreton, Carlo Séquin
1991 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications - SMA '91  
Previous methods for scattered data interpolation use linearized strain energy to produce a G1 network of curves which are subsequently blended.  ...  We describe a method for free form surface design that uses a mesh formed by networks of curves of minimum energy to define surfaces satisfying position, normal, and curvature constraints.  ...  Curve Minimization In this section we present a method for computing minimal energy curves subject to geometric constraints.  ... 
doi:10.1145/112515.112553 dblp:conf/sma/MoretonS91 fatcat:gdfs5qfuvnchtor6m7n4q2q5mi

Page 6784 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
{For the entire collection see MR 91¢:65004.} 91m:65050 65D17 68U07 Varady, Tamas (H-AOS-C) Overlap patches: a new scheme for interpolating curve networks with n-sided regions. Comput. Aided Geom.  ...  (UAE-UAE) Surface interpolation on irregular networks with normal conditions. Comput. Aided Geom. Design 8 (1991), no. 1, 89-96.  ... 

Smooth 3D Dubins Curves Based Mobile Data Gathering in Sparse Underwater Sensor Networks

Wenyu Cai, Meiyan Zhang
2018 Sensors  
This paper proposes a smooth 3D Dubins curves based mobile data gathering mechanism to overcome the kinematic nonholonomic constraints of AUVs.  ...  Extensive simulation results verify that the proposed method has a more efficient performance in terms of path smoothness and energy consumption; thus it is very suitable for mobile data collection in  ...  Acknowledgments: The authors would like to thank the anonymous reviewers for their helpful and constructive comments that greatly contributed to improving the final version of the paper.  ... 
doi:10.3390/s18072105 pmid:29966362 pmcid:PMC6069250 fatcat:7yzc4rc6n5af3dg5hsj4qbk5sa

Splines and geometric modeling [chapter]

Chandrajit Bajaj
2004 Handbook of Discrete and Computational Geometry, Second Edition  
Necessary and su cient vertex enclosure constraints on a mesh of polynomial curves that guarantees the existence of a regular smooth interpolant are given.  ...  The scheme is based on a su cient constraint that forces the mesh curves to interpolate second order data at the mesh points.  ... 
doi:10.1201/9781420035315.ch53 fatcat:e7evq2b77ba5lj3vxlcxwxxzda

Approximate implicitization of parametric surfaces by using compactly supported radial basis functions

Jinming Wu, Renhong Wang
2008 Computers and Mathematics with Applications  
It is primarily based on multivariate interpolation of scattered data by using compactly supported radial basis functions.  ...  In this paper, a new approach is proposed to solve the approximate implicitization of parametric surfaces.  ...  Acknowledgements We are very grateful to the referees for their careful reading of the manuscript and many valuable comments and remarks, which greatly improved this paper.  ... 
doi:10.1016/j.camwa.2008.09.016 fatcat:clyetid6zrbfbgti6567ygbyza

PHYSICS BASED GEOMETRIC DESIGN

HONG QIN
1996 International journal of shape modeling  
During the past several decades, numerous geometric formulations have been proposed for a large variety of geometric modeling applications.  ...  We demonstrate that D-NURBS can not only serve as a basis for the future research o f physics-based geometric design but also become readily appropriate for a large variety of important applications in  ...  Therefore, both the monomial and the Lagrangian forms are not suitable for the construction of piecewise smooth curves.  ... 
doi:10.1142/s0218654396000099 fatcat:ctnoubb7vvaubpbxuiev5dpmpe

Laplacian-based Design: Sketching 3D Shapes

Bin Sheng, Enhua Wu
2006 International Journal of Virtual Reality  
In this paper, we present an interactive modeling system for generating free-form surfaces using a 2D sketch interface.  ...  Finally, the shape of the triangular surface mesh that follows the 3D profile curves is computed using harmonic interpolation by solving Laplacian equations.  ...  ACKNOWLEDGEMENT We would like to thank the anonymous reviewers for their valuable comments. This work was supported by University of Macau.  ... 
doi:10.20870/ijvr.2006.5.3.2700 fatcat:2zqeectovjgt3jgbcjctpodw5y

Triangular bubble spline surfaces

Mario Kapl, Marek Byrtus, Bert Jüttler
2011 Computer-Aided Design  
The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves.  ...  a r t i c l e i n f o Keywords: G n -surface Triangular bubble patch Network of compatible surface strips Gordon-Coons interpolation for triangles a b s t r a c t We present a new method for generating  ...  For instance, [15, 16] describe geometric constraints on a network of curves which have to be satisfied for the case of G 1 and G 2 -smooth surfaces.  ... 
doi:10.1016/j.cad.2011.08.021 pmid:22267872 pmcid:PMC3257880 fatcat:nw73yezbkrgoxgzmc7utyiawdm

Freeform vector graphics with controlled thin-plate splines

Mark Finch, John Snyder, Hugues Hoppe
2011 Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11  
Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines.  ...  The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.  ...  Acknowledgments We manually traced curves over public-domain art in http://www. openclipart.org/tags/line_art for the "hat", "puppy", "girl", "French", and "rose" examples.  ... 
doi:10.1145/2070752.2024200 fatcat:6o32dlsq4nhfromj4wkwugii2u

Freeform vector graphics with controlled thin-plate splines

Mark Finch, John Snyder, Hugues Hoppe
2011 Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11  
Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines.  ...  The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.  ...  Acknowledgments We manually traced curves over public-domain art in http://www. openclipart.org/tags/line_art for the "hat", "puppy", "girl", "French", and "rose" examples.  ... 
doi:10.1145/2024156.2024200 fatcat:eaq563b3fjgvfhx56mum3v4zei

Freeform vector graphics with controlled thin-plate splines

Mark Finch, John Snyder, Hugues Hoppe
2011 ACM Transactions on Graphics  
Our system lets a user sketch discontinuity curves without fixing their colors, and sprinkle color constraints at sparse interior points to obtain smooth interpolation subject to the outlines.  ...  The vector constraints are discretized over an image grid, and satisfied using a hierarchical solver. We demonstrate interactive authoring on a desktop CPU.  ...  Acknowledgments We manually traced curves over public-domain art in http://www. openclipart.org/tags/line_art for the "hat", "puppy", "girl", "French", and "rose" examples.  ... 
doi:10.1145/2070781.2024200 fatcat:7ureenchkjfhveioopjrwnxvze

Smoothing polyhedra using implicit algebraic splines

Chandrajit L. Bajaj, Insung Ihm
1992 Computer graphics  
Polyhedron "smoothing" is an efficient construction scheme for generating complex boundary models of solid physical objects.  ...  This paper presents efficient algorithms for generating families of curved solid objects with boundaty topology related to an input polyhedron.  ...  Acknowledgements : We are grateful to Vinod Anupam, Andrew Royappa and Dan Schikore for their assistance in the implementation of the smoothing algorithms.  ... 
doi:10.1145/142920.134014 fatcat:7whadzf2z5hnfcbmaz5cmpiu5m
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