Application of Lie Algebras in Computer Animation

Authors

  • Atefeh Hasan-Zadeh Fouman Faculty of Engineering, College of Engineering, University of Tehran, Iran

DOI:

https://doi.org/10.24203/ajas.v8i5.6331

Keywords:

computer graphic, 3D animation, geometric transformation, Lie algebra, covering map

Abstract

The mathematical theory behind the computer graphic enables one to develop the techniques for suitable creation of computer animation. This paper presents an application of Riemannian geometry in 3D animation via notions of in motion and deformation. By focusing on Lie algebras concepts, it provides a geometric framework for the implementation of computer animation.

References

Chaudhry E., You, L.H., Zhang, J.J., “Character skin deformation: A survey”, Proc. of the 7th International Conference on Computer Graphics, Imaging and Visualization (CGIV2010), pp. 41–48, IEEE, DOI: 10.1109/CGIV.2010.14, 2010.

Lewis, J.P., Cordner, M., Fong, N., “Pose space deformation: A unified approach to shape interpolation and skeleton-driven deformation”, SIGGRAPH Proc. of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pages 165–172, DOI:10.1145/344779.344862, 2000.

Hasan-Zade, A., “Geometric Modelling of the Thinning by Cell Complexes”, Journal of Advanced Computer Science & Technology, vol. 8, no. 2, pp. 38-39, 2019.

Alexa, M., “Linear combinations of transformations, In ACM Transactions on Graphics (TOG)”, Proc. of ACM SIGGRAPH, vol. 21, no. 3, pp. 380–387, 2002. DOI:10.1145/566654.566592.

Nieto, J.R., Susín, A., Cage based deformations: A survey, Deformation Models, M.G. Hidalgo, pp. 75-99, 2012.

Torres, A.M., Gómez, J.V., Lecture Notes in Computational Vision and Biomechanics, Springer, 7, 2013. DOI: 10.1007/978-94-007-5446-1_3.

Tournier M., Revéret, L., “Principal geodesic dynamics”, SCA Proc. of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 235–244, DOI:10.2312/SCA/SCA12/235-244, 2012.

Boothby, W.M., An introduction to differentiable manifolds and Riemannian geometry, Academic Press, 2003.

Olver, P.J., Applications of Lie groups to differential equations, Springer-Verlag, 1993.

O’Neill, B., Semi-Riemannian geometry: With applications to relativity, Academic Press, 1983.

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Published

2020-10-30

How to Cite

Application of Lie Algebras in Computer Animation. (2020). Asian Journal of Applied Sciences, 8(5). https://doi.org/10.24203/ajas.v8i5.6331

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