Abstract
Due to intrinsic differences between surfaces and higher dimensional objects, some important results regarding surfaces can not be extended to volumetric domains. Most significantly, there exist no conformal volumetric maps apart from Mobius transformations. Although it is sometime stated explicitly, it is often overlooked that existing methods of volume parameterization produce only quasi-conformal maps, which may be âfar from conformalityâ. We therefore introduce methods for assessing the extent of the local and global volumetric deformation by means of the amount of conformal distortion produced. To this end we first illustrate basic three-dimensional quasi-conformal deformations that are produced by parameterization techniques, and highlight theoretical issues associated with spatial quasi-conformal mappings, and the relation that exists between the geometry of the domain and conformal distortion.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
