In the design of buildings, structural analysis is traditionally performed after the aesthetic design has been determined and has little influence on the overall form. In contrast, this paper presents an approach to guide the form towards a shape that is more structurally sound. Our work is centered on the study of how variations of the geometry might improve structural stability. We define a new measure of structural soundness for masonry buildings as well as cables, and derive its closed-form derivative with respect to the displacement of all the vertices describing the geometry. We start with a gradient descent tool which displaces each vertex along the gradient. We then introduce displacement operators, imposing constraints such as the preservation of orientation or thickness; or setting additional objectives such as volume minimization.


Paper PDF (8.4 MB)
Supplemental PDF (0.4 MB)
Slides PowerPoint (460 MB)



Thanks to Sylvain Paris and reviewers of the MIT pre-deadline for helpful discussions, and Adriana Schulz for renderings. This work was partially supported by Shell. E. Whiting acknowledges the NSERC Canada PGS program. H. Shin acknowledges the Samsung Scholarship Foundation.


  author    = {Emily Whiting and Hijung Shin and Robert Wang and John Ochsendorf and Fr{\'e}do Durand},
  title     = {Structural Optimization of 3D Masonry Buildings},
  journal   = {ACM Transactions on Graphics},
  volume    = {31},
  number    = {6},
  year      = {2012},
  pages     = {159:1--159:11},

Emily Whiting
Last modified: Fri Jan 25 2013