Functionality in Solids Obtained from Partial Differential Equations

Bloor, M. I. G.; Wilson, Michael J.

doi:10.1007/978-3-7091-6916-2_2

Cited by 18 publications

(17 citation statements)

References 11 publications

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“…It is noteworthy to mention that when the domain is restricted to 0 ≥ u ≥ 1 and 0 ≥ v ≥ 2π, the solution is also restricted to the use of periodic boundary conditions. The solution to Equation (8) can then be expressed in terms of a Fourier series. The full details of such a solution are presented in [10].…”

Section: The Bloor-wilson Pde Methodsmentioning

confidence: 99%

“…Notice that the method itself is not restricted to these cases since full numerical techniques such as finite differences or finite element can be employed for finding the solution to Equation (8).…”

Section: The Bloor-wilson Pde Methodsmentioning

confidence: 99%

“…The work presented in [8] portrays another application related to design analysis. The Bloor-Wilson PDE method is employed here to visualise the physical properties or functional performance of a given object.…”

Section: Design Analysismentioning

confidence: 99%

“…Again, the BloorWilson PDE method is regarded as an excellent choice to accomplish this purpose. Both morphing and characterization of movement can take advantage of mathematical properties inherent to the solution of Equation (8) restricted to the exclusive use of periodic boundary conditions where the resulting PDE surfaces are characterized by the spine. Mathematically speaking, the spine of a surface is a curve described by a polynomial function, which can be thought as the skeleton of the PDE surface [39].…”

Section: Animationmentioning

confidence: 99%

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A survey of partial differential equations in geometric design

et al. 2007

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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. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique together with some other applications to computer graphics.

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Section: The Bloor-wilson Pde Methodsmentioning

confidence: 99%

Section: The Bloor-wilson Pde Methodsmentioning

confidence: 99%

Section: Design Analysismentioning

confidence: 99%

Section: Animationmentioning

confidence: 99%

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A survey of partial differential equations in geometric design

et al. 2007

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“…The work discussed in this paper centres around the pioneering work of Bloor and Wilson on the so called PDE method [4,5,25]. The particular approach used here treats shape modelling as a boundary-value problem.…”

Section: Introductionmentioning

confidence: 99%