Partial Differential Equations for Function Based Geometry Modelling within Visual Cyberworlds

Ugail, Hassan; Sourin, Alexei

doi:10.1109/cw.2008.42

Cited by 5 publications

(3 citation statements)

References 26 publications

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“…One major use of the Bloor et al's PDE method was to develop computer aided manufacturing tools by which many industrial models, such as the marine propeller [7], the swirl port [31] and aircraft geometry [6], can be easily mimicked. Moreover, it has also been demonstrated that the PDE method can be applied to shape morphing [8], geometric modelling for web visualisation [9], mesh reconstruction [10], etc.…”

Section: Pde Methodsmentioning

confidence: 99%

“…Moreover, the behaviour of PDE surfaces has been proven compatible with those underlying tensor-product surfaces, such as Bezier surface [2], B-splines [3], etc. Taken together, these advantages have contributed to a widespread adoption of the PDE methods in a range of disciplines, such as free-form surface design [4], solid modelling [5], computer aided manufacturing [6,7], shape morphing [8], web visualisation [9], mesh reconstruction [10], etc. In this paper, we address a prolonged topic, facial geometry parameterisation, by exploring and examining the feasibility of one PDE method in face modelling and facial animation.…”

Section: Introductionmentioning

confidence: 99%

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Facial geometry parameterisation based on Partial Differential Equations

Willis

Castro

et al. 2011

Mathematical and Computer Modelling

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a b s t r a c tGeometric modelling using Partial Differential Equations (PDEs) has been gradually recognised due to its smooth instinct, as well as the ability to generate a variety of geometric shapes by intuitively manipulating a relatively small set of PDE boundary curves. In this paper we explore and demonstrate the feasibility of the PDE method in facial geometry parameterisation. The geometry of a generic face is approximated by evaluating spectral solutions to a group of fourth order elliptic PDEs. Our PDE-based parameterisation scheme can produce and animate a high-resolution 3D face with a relatively small number of parameters. By taking advantage of parametric representation, the PDE method can use one fixed animation scheme to manipulate the facial geometry in varying Levels of Detail (LODs), without any further process.

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Section: Pde Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Facial geometry parameterisation based on Partial Differential Equations

Willis

Castro

et al. 2011

Mathematical and Computer Modelling

Self Cite

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“…Using PDEs for defining complex geometry was proposed and further developed in [2,3,4]. Later on in [5] we proposed to extend using of PDEs within VRML and X3D virtual worlds.…”

Section: Introductionmentioning

confidence: 98%

Towards a Definition of Virtual Objects Using Partial Differential Equations

Ugail

Castro

Sourin

et al. 2009

2009 International Conference on CyberWorlds

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We propose an efficient alternative to commonly used parametric surfaces such as NURBS surfaces for definition of complex geometry in shared virtual spaces. Our mathematical model allows to define objects by only providing coordinates of the section curves in 3-space. The resulting parametric functions allow fast calculation of the coordinates of the points on the surface of the objects. We devise an algorithm which evaluates the coefficients of these functions in real time. Given the small size of the resulting formulas and interactive rates for their calculation, we are able to efficiently use such PDE-based models for making virtual objects in shared virtual spaces. We describe the modeling framework and illustrate the proposed theoretical concepts with our function-based extension of VRML and X3D.

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Reconstructing Multiresolution Mesh for Web Visualization Based on PDE Resampling

Pang

Sourin

et al. 2011

Lecture Notes in Computer Science

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Partial Differential Equations for Function Based Geometry Modelling within Visual Cyberworlds

Cited by 5 publications

References 26 publications

Facial geometry parameterisation based on Partial Differential Equations

Facial geometry parameterisation based on Partial Differential Equations

Towards a Definition of Virtual Objects Using Partial Differential Equations

Reconstructing Multiresolution Mesh for Web Visualization Based on PDE Resampling

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