Citation

Perumal, Logah (2026) Techniques for integration within Bezier domains and approximation of circular arcs. MethodsX, 17. p. 104076. ISSN 2215-0161

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Abstract

This work presents techniques to perform integration of arbitrary functions within Bezier domains in two dimensions. Techniques that are considered for general nth order Bezier domains are the use of Green’s theorem and method of integration over parametrized surface. Derivation and steps to implement Green’s theorem for the integrations are provided. New expressions for calculation of integration of functions within quadratic and cubic Bezier domains are then derived based on the concept of bijective mapping, with following advantages: • Comparison with alternate method (integration over parametrized surface) for integration within a quadratic Bezier domain shows that the proposed formula is simpler and easier to use. • Method proposed for the cubic Bezier domains can be used to approximate arbitrary circular arcs and subsequently perform integration of functions within the circular arc domains. The new methods are then implemented within the context of Extended Finite Element Method (X-FEM) and Strain-based Finite Element Method (SB-FEM) to solve problems with circular arc boundaries. • Simulation results show improvement in the solution accuracy.

Item Type:	Article
Uncontrolled Keywords:	Bezier domain, Bezier curve, Bezier surface, Numerical integration, Green’s theorem, Bijective mapping, Curved strain-based finite element
Subjects:	T Technology > T Technology (General)
Divisions:	Faculty of Engineering and Technology (FET)
Depositing User:	Ms Suzilawati Abu Samah
Date Deposited:	01 Oct 2026 06:03
Last Modified:	01 Oct 2026 06:03
URII:	http://shdl.mmu.edu.my/id/eprint/16782

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