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A shape design system using volumetric implicit PDEs

Haixia Du, Hong Qin
2004 Computer-Aided Design  
We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of  ...  To maximize the modeling potential of PDEbased methodology, in this paper we tightly couple PDEs with volumetric implicit functions in order to achieve interactive, intuitive shape representation, manipulation  ...  An example of shape blending is shown in Fig. 4 including blended results using different order PDEs, where the fourth-order blended shape is smoother than the second-order result.  ... 
doi:10.1016/j.cad.2004.01.009 fatcat:oxr2sie7ezcctoflengofporiq

A shape design system using volumetric implicit PDEs

Haixia Du, Hong Qin
2005 ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05  
We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of  ...  To maximize the modeling potential of PDEbased methodology, in this paper we tightly couple PDEs with volumetric implicit functions in order to achieve interactive, intuitive shape representation, manipulation  ...  An example of shape blending is shown in Fig. 4 including blended results using different order PDEs, where the fourth-order blended shape is smoother than the second-order result.  ... 
doi:10.1145/1198555.1198647 dblp:conf/siggraph/DuQ05 fatcat:2tler2xeq5asxcai6wi7pzykfq

Discrete surface modelling using partial differential equations

Guoliang Xu, Qing Pan, Chandrajit L. Bajaj
2006 Computer Aided Geometric Design  
We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N -sided hole filling and free-form surface fitting.  ...  The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows.  ...  The authors are grateful to the referees for their carefully reading of the manuscript and for their helpful comments on improving the final version of this paper.  ... 
doi:10.1016/j.cagd.2005.05.004 pmid:19830268 pmcid:PMC2760856 fatcat:74ryy3jcwzeipa6tizdjk6kpm4

Interactive shape design using volumetric implicit PDEs

Haixia Du
2003 Proceedings of the eighth ACM symposium on Solid modeling and applications - SM '03  
We make use of a fourth-order elliptic PDE to define the volumetric implicit function.  ...  We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of  ...  The implicit PDE model can be defined as the solution of the fourth order elliptic PDE over a scalar intensity field with either scatteredpoint datasets or a set of sketch curves as generalized boundary  ... 
doi:10.1145/781606.781642 dblp:conf/sma/Du03 fatcat:rtuponqmhnh6xjrzvone5ondoa

Interactive shape design using volumetric implicit PDEs

Haixia Du
2003 Proceedings of the eighth ACM symposium on Solid modeling and applications - SM '03  
We make use of a fourth-order elliptic PDE to define the volumetric implicit function.  ...  We use the finite-difference discretization and variational interpolating approach with the localized iterative solver for the numerical integration of our PDEs in order to accommodate the diversity of  ...  The implicit PDE model can be defined as the solution of the fourth order elliptic PDE over a scalar intensity field with either scatteredpoint datasets or a set of sketch curves as generalized boundary  ... 
doi:10.1145/781640.781642 fatcat:j26phfaeizhbrddwpum6lu7sri

Free-Form Geometric Modeling by Integrating Parametric and Implicit PDEs

Haixia Du, Hong Qin
2007 IEEE Transactions on Visualization and Computer Graphics  
The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.  ...  The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form  ...  Sloan Fellowship, Honda Initiation Award, and an appointment to the NLM Research Participation Program sponsored by the National Library of Medicine and administered by the Oak Ridge Institute for Science  ... 
doi:10.1109/tvcg.2007.1004 pmid:17356220 fatcat:npos3gbaevg2nhphesvfonik3u

A survey of partial differential equations in geometric design

Gabriela González Castro, Hassan Ugail, Philip Willis, Ian Palmer
2007 The Visual Computer  
This work summarises the uses given to PDE surfaces as a surface generation technique together with some other applications to computer graphics.  ...  Computer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required.  ...  Acknowledgements The authors wish to acknowledge the support received from the UK Engineering and Physical Sciences Research Council through the grants EP/C015118/1 and EP/D000017/1 by which this work  ... 
doi:10.1007/s00371-007-0190-z fatcat:zts5cx3b7baczaioyuvxjrgbc4

A PDE patch-based spectral method for progressive mesh compression and mesh denoising

Qiqi Shen, Yun Sheng, Congkun Chen, Guixu Zhang, Hassan Ugail
2017 The Visual Computer  
PDE solution.  ...  In our new method an arbitrary mesh model is partitioned into patches, each of which can be represented by a small set of coefficients of its PDE spectral solution.  ...  Acknowledgement The authors would like to thank the reviewers for their constructive comments.  ... 
doi:10.1007/s00371-017-1431-4 fatcat:vbv2eigmwnf43banegoydowah4

A general framework for surface modeling using geometric partial differential equations

Guoliang Xu, Qin Zhang
2008 Computer Aided Geometric Design  
Recently, fourth order flows have been used to solve the problems of surface blending and free-form surface design.  ...  In this paper, we present a general framework for surface modeling using geometric PDEs. Starting with a general integral functional, we then derive an Euler-Lagrange equation and a geometric PDE.  ... 
doi:10.1016/j.cagd.2007.06.002 fatcat:6ts4k4ngmvbfxpzyjknb7so4qq

Dynamic PDE-based surface design using geometric and physical constraints

Haixia Du, Hong Qin
2005 Graphical Models  
PDE surfaces, which are defined as solutions of partial differential equations (PDEs), offer many modeling advantages in surface blending, free-form surface modeling, and specifying surfaceÕs aesthetic  ...  This paper presents an integrated approach that can incorporate PDE surfaces into the powerful physics-based modeling framework, to realize the full potential of PDE methodology.  ...  We would also like to thank the anonymous reviewers for their valuable suggestions that greatly improve this paper.  ... 
doi:10.1016/j.gmod.2004.06.002 fatcat:55et3dpwxrey7jjpwqimspjjna

Minimal Mean-Curvature-Variation Surfaces and Their Applications in Surface Modeling [chapter]

Guoliang Xu, Qin Zhang
2006 Lecture Notes in Computer Science  
We apply our equation to solving several surface modeling problems, including surface blending, N-sided hole filling and point interpolating.  ...  The illustrative examples provided show that this sixth-order flow yields high quality surfaces.  ...  The surfaces (c), (f) and (i) are the blending meshes generated using our sixth-order flow.  ... 
doi:10.1007/11802914_25 fatcat:j7rawjw2azbdvgqnm27ga3geka

surface modeling using minimal mean-curvature-variation flow

Guoliang Xu, Qin Zhang
2007 Computer-Aided Design  
We apply our equation to solving several surface modeling problems, including surface blending, N-sided hole filling and point interpolating, with G 2 continuity.  ...  Physical and geometric based variational techniques for surface construction have been shown to be advanced methods for designing high quality surfaces in the fields of CAD and CAGD.  ...  The surfaces (c), (f) and (i) are the blending meshes generated using our sixthorder flow. These figures show the results after 60 iterations with time step sizes 0.01.  ... 
doi:10.1016/j.cad.2007.02.007 fatcat:zrwo2r6ozjea3mgf4wspbtg5pi

Deformation of Dynamic Surfaces [chapter]

L. H. You, Jian J. Zhang
2006 Lecture Notes in Computer Science  
Based on dynamic fourth order partial differential equations, we present an iterative finite difference algorithm.  ...  external forces into user handles for dynamic manipulation of surface deformations.  ...  Dynamic PDEs Considering the influences of density and damping on deformations and motion, dynamic surfaces can be described with the solution to the following dynamic fourth order partial differential  ... 
doi:10.1007/11758525_31 fatcat:3k54dnm64rdtzfoolzecddixra

G1 surface modelling using fourth order geometric flows

Guoliang Xu, Qing Pan
2006 Computer-Aided Design  
We use two fourth order geometric partial differential equations to efficiently solve several surface modelling problems, including the surface blending, the N -sided hole filling and the free-form surface  ...  fitting with the G 1 boundary continuity.  ...  Recently, the fourth order geometric flows have been used to solve the surface blending and the free-form surface fitting problems (see [6, 17, 18, 23] ).  ... 
doi:10.1016/j.cad.2005.11.002 fatcat:souh5r7tibdrvhgibzkuar344i

Efficient parametrization of generic aircraft geometry

Malcolm I. G. Bloor, Michael J. Wilson
1995 Journal of Aircraft  
Derivative Boundary Conditions for PDE Solution Equation (2) is fourth-order, hence, we require boundary conditions on the normal derivatives of X(u, v) in the (u, v) parameter plane, which in this case  ...  The method views surface generation as a boundary-value problem and produces surfaces as the solutions to elliptic partial differential equations, hence its name, the PDE method.  ... 
doi:10.2514/3.46874 fatcat:72hkgsjtojhqzefwdjqo7pua3u
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