The Application of NURBS to Acoustical Science


  • John O'Keefe O'Keefe Acoustics University of Toronto


NURBS, or Non-Uniform Rational B-Splines, are essentially a 3-D expansion of a 2-D B-spline.  The mathematical construct was developed by the Italian automotive industry in the early 1960s.  Since then they have been used to design everything from children’s’ toys to opera houses.  The ceiling of Toronto’s opera house, the Four Seasons Centre for the Performing Arts, was designed with a software package called Rhino, which is based, mathematically, on NURBS.  This package allows architects and engineers to design not just within a rectilinear confinement but with the curved surfaces that have served us so well in the past.  An element that has sadly been missing in current architecture.  Partly because acousticians force architects into rectilinear expressions.   But it does not need to be that way.   NURBS now give a freedom of design in acoustics, architecture and so many other fields. A study of existing rooms with profoundly focusing elements will be presented, a geometrical explanation of basic focusing elements will be reviewed and, finally, the design thoughts on a recently opened Canadian hall will be discussed.

Author Biography

John O'Keefe, O'Keefe Acoustics University of Toronto

Sole Prepriator of O'Keefe AcousticsAdjunct Professor Mechanical Engineering




How to Cite

O’Keefe J. The Application of NURBS to Acoustical Science. Canadian Acoustics [Internet]. 2017 Aug. 30 [cited 2022 Nov. 30];45(3):72-3. Available from:



Proceedings of the Acoustics Week in Canada