Octahedral Frames for Feature-Aligned Cross Fields

Paul Zhang, Josh Vekhter, Edward Chien, David Bommes, Etienne Vouga, Justin Solomon

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the spherical harmonic basis. We provide theoretical analysis of these energies in the smooth setting, showing that they penalize deviations from surface creases while otherwise promoting intrinsically smooth fields. We demonstrate the applicability of our method to quad meshing and include an extensive benchmark comparing our fields to other automatic approaches for generating feature-aligned cross fields on triangle meshes.

Original languageEnglish
Article number25
JournalACM Transactions on Graphics
Volume39
Issue number3
DOIs
StatePublished - Jun 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Owner/Author.

Funding

P. Zhang received generous support from the Department of Energy Computer Science Graduate Fellowship. E. Vouga received generous support from Adobe, SideFX, and NSF IIS-1910274. D. Bommes received generous support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (AlgoHex, grant agreement no. 853343). J. Solomon received generous support from Army Research Office grant W911NF-12-R-0011, National Science Foundation grant IIS-1838071, Air Force Office of Scientific Research award FA9550-19-1-0319, and a gift from Adobe Systems. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these organizations. Authors’ addresses: P. Zhang, E. Chien, and J. Solomon, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; emails: [email protected], [email protected], [email protected]; J. Vekhter and E. Vouga, University of Texas at Austin, Austin, TX 78712; emails: {josh, evouga}@cs.utexas.edu; D. Bommes, University of Bern, Hochschulstrasse 6, Bern, 3012, Switzerland; email: [email protected]. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). © 2020 Copyright held by the owner/author(s). 0730-0301/2020/04-ART25 https://doi.org/10.1145/3374209 P. Zhang received generous support from the Department of Energy Computer Science Graduate Fellowship. E. Vouga received generous support from Adobe, SideFX, and NSF IIS-1910274. D. Bommes received generous support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (AlgoHex, grant agreement no. 853343). J. Solomon received generous support from Army Research Office grant W911NF-12-R-0011, National Science Foundation grant IIS-1838071, Air Force Office of Scientific Research award FA9550- 19-1-0319, and a gift from Adobe Systems. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these organizations.

FundersFunder number
Department of Energy Computer Science
European Union's Horizon 2020 research and innovation program
National Science FoundationIIS-1838071, IIS-1910274
Air Force Office of Scientific ResearchFA9550-19-1-0319
Army Research OfficeW911NF-12-R-0011
Horizon 2020 Framework Programme853343
European Research Council

    Keywords

    • Discrete differential geometry
    • feature alignment
    • geometry processing
    • singularities
    • total variation

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