Surface Modeling Using Partial Differential Equations: A Survey

You, Lihua; Jin, Xiaogang; You, X. Y.; Zhang, Jian Jun

doi:10.1109/iv.2013.62

2013 17th International Conference on Information Visualisation 2013

DOI: 10.1109/iv.2013.62

|View full text |Cite

Surface Modeling Using Partial Differential Equations: A Survey

Lihua You

Xiaogang Jin

X. Y. You

et al.

Abstract: Partial differential equation-based surface modelling is a new approach of creating and manipulating threedimensional geometric models. It uses the solution to a vector-valued partial differential equation subjected to suitably defined boundary constraints to carry out surface modeling. This paper provides a survey on this approach which summarizes various mathematical models of partial differential equation-based surface modelling, accurate and approximate analytical solutions as well as numerical solutions o… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2019

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Optimal NURBS conversion of PDE surface-represented high-speed train heads

et al. 2019

View full text Add to dashboard Cite

The head shape of high-speed trains has become a critical factor in boosting the speed further. Aerodynamic simulation-based optimization is a dominant method to obtain the optimal head shape which relies on detailed train head models defined by a lot of design variables. Since aerodynamic simulation-based optimization involves heavy calculations, too many design variables not only causes high computational costs, but also makes the optimal solution difficult to obtain. Therefore, how to use few design variables to define detailed train head model is the key to success. Partial differential equation (PDE)-based geometric modelling which creates a complicated PDE patch with few design variables provides an effective solution to this problem. In addition, it also has the advantage of naturally maintaining any high-order continuities between two adjacent surfaces which is very important in designing highly smooth train heads to achieve excellent aerodynamic performance. At the present time, PDE-based geometric modelling cannot be directly applied in computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) since it has not become an industrial standard. In contrast, non-uniform rational B-splines (NURBS) are commonly used in CAD, CAM, CAE, and many other engineering fields. They have already become part of industry wide standards. In order to apply PDE-based geometric modelling in shape design of high-speed train heads for CAD etc., how to optimally convert PDE surfaces into NURBS surfaces must be addressed. In this paper, a new method of achieving optimal conversion of PDE surfaces representing high-speed train heads into NURBS surfaces is developed. It takes control points and weight deformations of NURBS surfaces to be design variables, and the error between NURBS surfaces and PDE surfaces as the objective function. The least squares fitting and the genetic algorithm are combined to obtain the optimal conversion between PDE surfaces and NURBS surfaces. The application examples demonstrate the effectiveness of the developed method.

show abstract

Optimal NURBS conversion of PDE surface-represented high-speed train heads

et al. 2019

View full text Add to dashboard Cite

show abstract

Mathematical Modelling in Nanotechnology Using Calculus of Variations

Alshammari¹

2017

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Surface Modeling Using Partial Differential Equations: A Survey

Cited by 2 publications

References 44 publications

Optimal NURBS conversion of PDE surface-represented high-speed train heads

Optimal NURBS conversion of PDE surface-represented high-speed train heads

Mathematical Modelling in Nanotechnology Using Calculus of Variations

Contact Info

Product

Resources

About