Abstract
The spine of an object is an entity that can characterise the object’s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations.
The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution.
This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arcelli, C., Sanniti di Baja, G.: Ridge Points in Euclidean Distance Maps. Pattern Recognision Letters 13(4), 237–243 (1992)
Bloor, M.I.G., Wilson, M.J.: Generating Blend Surfaces Using Partial Differential Equations. Computer-Aided Design 21, 165–171 (1989)
Bloor, M.I.G., Wilson, M.J.: Using Partial Differential Equations to Generate Freeform Surfaces. Computer Aided Design 22, 202–212 (1990)
Bloor, M.I.G., Wilson, M.J.: Spectral Approximations to PDE Surfaces. Computer-Aided Design 28, 145–152 (1996)
Bloor, M.I.G., Wilson, M.J.: Method for Efficient Shape Parametrization of Fluid Membranes and Vesicles. Physical Review E 61(4), 4218–4229 (2000)
Blum, H.: A transformation for Extracting New Descriptors of Shape. In: Wathen-Dunn, W. (ed.) Models for Perception of Speech and Visual Form, pp. 362–381. MIT Press, Cambridge (1976)
Boissonnat, J.D.: Geometric Surfaces for 3-Dimensional Shape Representation. ACM Transactions on Graphics 3(4), 244–265 (1984)
Du, H., Qin, H.: Direct Manipulation and Interactive Sculpting of PDE Surfaces. In: Computer Graphics Forum (Proceedings of Eurographics 2000), vol. 19(3), pp. 261–270 (2000)
Dutta, D., Hoffmann, C.M.: On the Skeleton of Simple CSG Objecs. ASME Journal of Mechanical Design 115(1), 87–94 (1992)
Leymarie, F., Levine, M.D.: Skeleton from Snakes, Progress in Image Analysis and Processing. World Scientific, Singapore (1990)
Nackman, L.R., Pizer, S.M.: Three-Dimensional Shape Description using Symmetric Axis Transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 7(2), 187–202 (1985)
Patrikalakis, N.M., Gursoy, H.N.: Shape Interrogation by Medial Axis Transform. In: Ravani, B. (ed.) Advances in Design Automation: Computer-Aided Computational Design, ASME, vol. 1, pp. 77–88 (1990)
Tsao, Y.F., Fu, K.S.: A Parallel Thinning Algorithm for 3-D Pictures. Computer Graphics Image Process 17, 315–331 (1981)
Ugail, H., Bloor, M.I.G., Wilson, M.J.: Techniques for Interactive Design Using the PDE Method. ACM Transactions on Graphics 18(2), 195–212 (1999)
Ugail, H., Bloor, M.I.G., Wilson, M.J.: Manipulations of PDE Surfaces Using an Interactively Defined Parameterisation. Computers and Graphics 24(3), 525–534 (1999)
Vida, J., Martin, R.R., Varady, T.: A Survey of Blending Methods that use Parametric Surfaces. Computer-Aided Design 26(5), 341–365 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ugail, H. (2003). On the Spine of a PDE Surface. In: Wilson, M.J., Martin, R.R. (eds) Mathematics of Surfaces. Lecture Notes in Computer Science, vol 2768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39422-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-39422-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20053-6
Online ISBN: 978-3-540-39422-8
eBook Packages: Springer Book Archive