Abstract
This paper proposes a discrete approximation of Laplace-Beltrami operator for quadrilateral meshes which we name as mean Laplace-Beltrami operator (MLBO). Given vertex p and its quadrilateral 1-neighborhood N(p), the MLBO of p is defined as the average of the LBOs defined on all triangulations of N(p) and ultimately expressed as a linear combination of 1-neighborhood vertices. The operator is quite simple and numerically convergent. Its weights are symmetric, and easily modified to positive. Several examples are presented to show its applications.
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Xiong, Y., Li, G., Han, G. (2011). Mean Laplace–Beltrami Operator for Quadrilateral Meshes. In: Pan, Z., Cheok, A.D., Müller, W., Yang, X. (eds) Transactions on Edutainment V. Lecture Notes in Computer Science, vol 6530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18452-9_15
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DOI: https://doi.org/10.1007/978-3-642-18452-9_15
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