scholarly journals Method of trimming PDE surfaces

2006 ◽  
Vol 30 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Hassan Ugail
Keyword(s):  
Pde Surfaces

scholarly journals Fast character modeling with sketch-based PDE surfaces

2020 ◽  
Vol 79 (31-32) ◽  
pp. 23161-23187
Author(s):  
Lihua You ◽  
Xiaosong Yang ◽  
Junjun Pan ◽  
Tong-Yee Lee ◽  
Shaojun Bian ◽  
...  
Keyword(s):  
Pde Surfaces

Manipulation of PDE surfaces using an interactively defined parameterisation

1999 ◽  
Vol 23 (4) ◽  
pp. 525-534 ◽  
Author(s):  
Hassan Ugail ◽  
Malcolm I.G Bloor ◽  
Michael J Wilson
Keyword(s):  
Pde Surfaces

scholarly journals Spine Based Shape Parameterisation for PDE Surfaces

Computing ◽  
2004 ◽  
Vol 72 (1-2) ◽  
pp. 195-206 ◽  
Author(s):  
Hassan Ugail
Keyword(s):  
Pde Surfaces

Direct Manipulation and Interactive Sculpting of PDE Surfaces

2000 ◽  
Vol 19 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Haixia Du ◽  
Hong Qin
Keyword(s):  
Direct Manipulation ◽  
Pde Surfaces

Spectral approximations to PDE surfaces

1996 ◽  
Vol 28 (2) ◽  
pp. 145-152 ◽  
Author(s):  
IG Malcolm Bloor ◽  
Michael J Wilson
Keyword(s):  
Spectral Approximations ◽  
Pde Surfaces

scholarly journals PDE Surface-Represented Facial Blendshapes

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2905
Author(s):  
Haibin Fu ◽  
Shaojun Bian ◽  
Ehtzaz Chaudhry ◽  
Shuangbu Wang ◽  
Lihua You ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourier Series ◽  
Mathematical Expression ◽  
Second Order ◽  
New Method ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Boundary Curves ◽  
Pde Surfaces

Partial differential equation (PDE)-based geometric modelling and computer animation has been extensively investigated in the last three decades. However, the PDE surface-represented facial blendshapes have not been investigated. In this paper, we propose a new method of facial blendshapes by using curve-defined and Fourier series-represented PDE surfaces. In order to develop this new method, first, we design a curve template and use it to extract curves from polygon facial models. Then, we propose a second-order partial differential equation and combine it with the constraints of the extracted curves as boundary curves to develop a mathematical model of curve-defined PDE surfaces. After that, we introduce a generalized Fourier series representation to solve the second-order partial differential equation subjected to the constraints of the extracted boundary curves and obtain an analytical mathematical expression of curve-defined and Fourier series-represented PDE surfaces. The mathematical expression is used to develop a new PDE surface-based interpolation method of creating new facial models from one source facial model and one target facial model and a new PDE surface-based blending method of creating more new facial models from one source facial model and many target facial models. Some examples are presented to demonstrate the effectiveness and applications of the proposed method in 3D facial blendshapes.

The accuracy of B-spline finite element approximations to PDE surfaces

1998 ◽  
Vol 158 (3-4) ◽  
pp. 221-234 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I.G. Bloor ◽  
M.Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element ◽  
B Spline ◽  
Finite Element Approximations ◽  
Spline Finite Element ◽  
Pde Surfaces
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