Sains Malaysiana 38(6)(2009): 835–840

Gambaran Inovatif terhadap Permukaan Persamaan Pembezaan Separa

(Innovative Representation of Partial Differential Equations Surface)

Shahrul Nizam Ishak & Jamaludin Md Ali*

Pusat Pengajian Sains Matematik

Universiti Sains Malaysia, 11800 Penang, Malaysia

Received: 18 November 2008 / Accepted: 4 February 2009

ABSTRAK

Makalah ini menunjukkan dua jenis peringkat Persamaan Pembezaan Separa(PPS) dalam versi teritlak daripada kaedahPPS Bloor-Wilson. Modifikasi terhadap parameter a(u, v) dalam persamaan tersebut diilustrasikan melalui beberapa contoh. Kelebihan dan kekurangan terhadap aplikasinya juga dibincangkan.

Kata kunci: Gambaran permukaan bentuk bebas; lengkung berkelopak bunga; tembikar; peringkatPPS

ABSTRACT

This paper presents two types of orders of Partial Differential Equations (PDE) in a generalized version from the Bloor-Wilson PDE method. The modification of the parameter a(u, v) in the equation is illustrated with some examples. The advantage and disadvantage on the application are also been discussed.

Keywords: Free-form surface representation; petaloid curve; earthenware jar; orders of PDE

REFERENCES

Bloor, M.I.G. & Wilson, M.J. 1989. Generating blend surfaces using partial differential equation. Computer Aided Design 21(3): 165-171.

Bloor, M.I.G. & Wilson, M.J. 1990. Using partial differential equations to generate free-form Surfaces. Computer Aided Design 22(4): 200-212.

Bloor, M.I.G. & Wilson, M.J. 1995. The efficient parameterization of generic aircraft geometry. Journal of Aircraft 32(6): 1269-1275.

Bloor, M.I.G. & Wilson, M.J. 1996. Spectral approximations to PDE surfaces. Computer Aided Design 28(2): 145-152.

Dekanski, C.W., Bloor, M.I.G. & Wilson, M.J. 1995. The generation of propeller blade geometries using the PDE method. Journal of Ship Research 39(2): 108-116.

Du, H. & Qin, H. 2005. Dynamic PDE-based surface design using geometric and physical constraints. Graphical Models 67(1): 43-71.

Elyan, E. & Ugail, H. 2007. Reconstruction of 3D Human Facial Images Using Partial Differential Equations. ACM Trans. Journal of Computers 2(8): 1-8.

Gonz‡lez, G., Ugail, H., Willis, P. & Sheng, Y. 2008. Parametric Representation of Facial Expressions on PDE-based Surfaces. Eighth IASTED International Conference on Visualization, Imaging and Image Processing (VIIP 2008): Palma de Mallorca, Spain: 402-407.

Shahrul, N.I, Yahya, Z.R. & Jamaludin, M.A. 2008. Moulding Vase-Design Interactively using GUI. Proceedings of International Conference on Science & Technology: Applications in Industry & Education: Penang, Malaysia: 2598-2603.

Shahrul, N.I. & Jamaludin, M.A. 2008. Parametric surface generation using partial differential equations (PDE) based approach. MATEMATIKA 24(2): 149-158.

Lowe, T.W., Bloor, M.I.G. & Wilson, M.J. 1990. Functionality in Blend Design. Computer Aided Design 22(10): 655-665.

Ugail, H., Bloor, M.I.G. & Wilson, M.J. 1999. Techniques for Interactive Design using the PDE Method. ACM Trans. On Graph. Des. 18(2): 195-212.

Ugail, H. 2003. On the Spine of a PDE Surface. In Springer-Verlag, edited by MJ Wilson, RR Martin. Proceedings of Mathematics of Surfaces X. Berlin: pp. 366-376.

Ugail, H. & Kirmani, S. 2006. Techniques for interactive design using the PDE method. WSEAS Transactions on Computers 10(5): 2156-2161.

Ugail, H. & Sourin, A. 2008. Partial Differential Equations for Function based Geometry Modeling within Visual Cyberworlds. Cyberworlds 2008. IEEE Computer Society pp. 224-231.

You, L.H., Zhang, J.J. & Comninos, P. 2004. Blending surface generation using a fast and accurate analytical solution of a fourth-order PDE with three shape control parameters. The Visual Computer 20(2-3): 199-214.

Zhang, J.J. & You, L.H. 2001. Surface Representation using Second, Fourth and Mixed Order Partial Differential Equations. Proceeding of the International Conference on Shape Modeling and Applications. Genova: IEEE Computer Society. pp. 250-256.

*Corresponding author; email: jamaluma@cs.usm.my