Spectral architectural geometry

Spectral geometry is a mathematical field that links geometrical properties to eigenvalues of differential operators on surfaces. Although it is a well-established tool in geometry processing and has been used in many contexts, the structural engineering and architectural geometry communities have n...

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Bibliographic Details
Published inComputer aided design Vol. 188; p. 103927
Main Authors Mesnil, Romain, Hayashi, Kazuki
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2025
Subjects
Architectural geometry
Discrete differential geometry
Shell structures
Spectral geometry
Spectral geometry
Discrete differential geometry
Shell structures
Architectural geometry
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Summary:Spectral geometry is a mathematical field that links geometrical properties to eigenvalues of differential operators on surfaces. Although it is a well-established tool in geometry processing and has been used in many contexts, the structural engineering and architectural geometry communities have not yet adopted this framework for shape modeling. This paper aims to explore spectral methods for applications in architectural geometries. A novel methodology for generating anisotropic Laplacian operators based on regions of interest defined by the user is proposed. The potential of spectral methods in structural design is illustrated through design problems expressed on meshes and graphs. [Display omitted] •Spectral geometry is proposed as a generic modeling framework for free-form structures.•Feature-aligned anisotropic Laplacian operator is introduced.•Linear and affine constraints are handled.
ISSN:0010-4485
DOI:10.1016/j.cad.2025.103927