%0 Conference Paper %1 Muller:2016:RME:2994258.2994269 %A Müller, Matthias %A Bender, Jan %A Chentanez, Nuttapong %A Macklin, Miles %B Proceedings of the 9th International Conference on Motion in Games %C New York, NY, USA %D 2016 %I ACM %K 2016 acm graphics paper rotation siggraph %P 55--60 %R 10.1145/2994258.2994269 %T A Robust Method to Extract the Rotational Part of Deformations %U http://doi.acm.org/10.1145/2994258.2994269 %X We present a novel algorithm to extract the rotational part of an arbitrary 3 X 3 matrix. This problem lies at the core of two popular simulation methods in computer graphics, the co-rotational Finite Element Method and Shape Matching techniques. In contrast to the traditional method based on polar decomposition, degenerate configurations and inversions are handled robustly and do not have to be treated in a special way. In addition, our method can be implemented with only a few lines of code without branches which makes it particularly well suited for GPU-based applications. We demonstrate the robustness, coherence and efficiency of our method by comparing it to stabilized polar decomposition in several simulation scenarios. %@ 978-1-4503-4592-7

@inproceedings{Muller:2016:RME:2994258.2994269, abstract = {We present a novel algorithm to extract the rotational part of an arbitrary 3 X 3 matrix. This problem lies at the core of two popular simulation methods in computer graphics, the co-rotational Finite Element Method and Shape Matching techniques. In contrast to the traditional method based on polar decomposition, degenerate configurations and inversions are handled robustly and do not have to be treated in a special way. In addition, our method can be implemented with only a few lines of code without branches which makes it particularly well suited for GPU-based applications. We demonstrate the robustness, coherence and efficiency of our method by comparing it to stabilized polar decomposition in several simulation scenarios.}, acmid = {2994269}, added-at = {2019-02-19T19:22:37.000+0100}, address = {New York, NY, USA}, author = {M\"{u}ller, Matthias and Bender, Jan and Chentanez, Nuttapong and Macklin, Miles}, biburl = {https://www.bibsonomy.org/bibtex/2357872ab3ad0cddc97084de726d79351/analyst}, booktitle = {Proceedings of the 9th International Conference on Motion in Games}, description = {A robust method to extract the rotational part of deformations}, doi = {10.1145/2994258.2994269}, interhash = {6ce31f79e2bb79ffea90ae97cd2f15d4}, intrahash = {357872ab3ad0cddc97084de726d79351}, isbn = {978-1-4503-4592-7}, keywords = {2016 acm graphics paper rotation siggraph}, location = {Burlingame, California}, numpages = {6}, pages = {55--60}, publisher = {ACM}, series = {MIG '16}, timestamp = {2019-02-19T19:22:37.000+0100}, title = {A Robust Method to Extract the Rotational Part of Deformations}, url = {http://doi.acm.org/10.1145/2994258.2994269}, year = 2016 }