A PDE method for patchwise approximation of large polygon meshes

Yu, Shengkai; Sourin, Alexei; Castro, Gabriela; Ugail, Hassan

doi:10.1007/s00371-010-0456-8

Cited by 16 publications

(28 citation statements)

References 16 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

View full text Add to dashboard Cite

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“…The preservation of irregular and sharp details on the surface will be found by matching the respective patches to the surface at various sizes and orientations. According to [34], a biharmonic-like fourthorder PDE is formulated as follows:…”

Section: Generation Of Pde Patchesmentioning

confidence: 99%

A Lightweight Surface Reconstruction Method for Online 3D Scanning Point Cloud Data Oriented toward 3D Printing

Sheng

Zhao

Yin

et al. 2018

Mathematical Problems in Engineering

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The existing surface reconstruction algorithms currently reconstruct large amounts of mesh data. Consequently, many of these algorithms cannot meet the efficiency requirements of real-time data transmission in a web environment. This paper proposes a lightweight surface reconstruction method for online 3D scanned point cloud data oriented toward 3D printing. The proposed online lightweight surface reconstruction algorithm is composed of a point cloud update algorithm (PCU), a rapid iterative closest point algorithm (RICP), and an improved Poisson surface reconstruction algorithm (IPSR). The generated lightweight point cloud data are pretreated using an updating and rapid registration method. The Poisson surface reconstruction is also accomplished by a pretreatment to recompute the point cloud normal vectors; this approach is based on a least squares method, and the postprocessing of the PDE patch generation was based on biharmonic-like fourth-order PDEs, which effectively reduces the amount of reconstructed mesh data and improves the efficiency of the algorithm. This method was verified using an online personalized customization system that was developed with WebGL and oriented toward 3D printing. The experimental results indicate that this method can generate a lightweight 3D scanning mesh rapidly and efficiently in a web environment.

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“…The solution to the vector-valued ordinary differential equation (23) is (27) where f 51 , f 52 , f 53 and f 54 are unknown vector-valued constants. Substituting Eqs.…”

Section: Accuracy Efficiency and Shape Controlmentioning

confidence: 99%

“…Apart from the applications in surface blending, partial differential equations have also been applied in interactive surface design [24], free-form surface modeling [25], cyclic animation [26], patchwise approximation of large polygon meshes [27], and solid modeling [28].…”

Section: Related Workmentioning

confidence: 99%

Controllable C1 continuous blending of time-dependent parametric surfaces

2012

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This paper proposes the concept of blending timedependent varying surfaces, and develops a new method to create a controllable C1 continuous blending surface between primary parametric surfaces whose position and shape change with time. We treat it as a boundary-valued problem defined by the mathematical model of a vectored dynamic fourth-order partial differential equation subjected to time-dependent C1 continuous blending boundary constraints. High performance blending surface generation is achieved through the development of an approximate analytical solution of the mathematical model. We investigate the accuracy and efficiency of the solution, study the effective shape control of the blending surfaces, and apply the obtained solution to tackle surface blending problems. The applications demonstrate that our proposed approach is very effective and efficient in dealing with controllable C1 continuous surface blending between time-dependent varying parametric surfaces.

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A PDE method for patchwise approximation of large polygon meshes

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Cited by 16 publications

References 16 publications

Facial geometry parameterisation based on Partial Differential Equations

Facial geometry parameterisation based on Partial Differential Equations

A Lightweight Surface Reconstruction Method for Online 3D Scanning Point Cloud Data Oriented toward 3D Printing

Controllable C1 continuous blending of time-dependent parametric surfaces

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