Harmonic Functions for Rotational Symmetry Vector Fields
| dc.contributor.author | Shen, Zhongwei | en_US |
| dc.contributor.author | Fang, Xianzhong | en_US |
| dc.contributor.author | Liu, Xinguo | en_US |
| dc.contributor.author | Bao, Hujun | en_US |
| dc.contributor.author | Huang, Jin | en_US |
| dc.contributor.editor | Eitan Grinspun and Bernd Bickel and Yoshinori Dobashi | en_US |
| dc.date.accessioned | 2016-10-11T05:21:08Z | |
| dc.date.available | 2016-10-11T05:21:08Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v(x) on a 3D domain W, we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron-symmetry, cube-symmetry and dodecahedron-symmetry groups. | en_US |
| dc.description.number | 7 | |
| dc.description.sectionheaders | Geometry | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 35 | |
| dc.identifier.doi | 10.1111/cgf.13047 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 507-516 | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.13047 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.1111/cgf13047 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.subject | I.3.5 [Computer Graphics] | |
| dc.subject | Computational Geometry and Object Modeling | |
| dc.subject | Geometric algorithms | |
| dc.title | Harmonic Functions for Rotational Symmetry Vector Fields | en_US |