Freeing Up Architecture: Part 1

Many of today.s most striking buildings are nontraditional freeform
shapes. A new field of mathematics, discrete differential geometry,
makes it possible to construct these complex shapes that begin as
designers. digital creations. Since it.s impossible to fashion a
large structure out of a single piece of glass or metal, the design
is realized using smaller pieces that best fit the original smooth
surface. Triangles would appear to be a natural choice to represent
a shape, but it turns out that using quadrilaterals.which would
seem to be more difficult.saves material and money and makes the
structure easier to build. One of the primary goals of researchers
is to create an efficient, streamlined process that integrates
design and construction parameters so that early on architects can
assess the feasibility of a given idea. Currently, implementing a
plan involves extensive (and often expensive) interplay on
computers between subdivision.breaking up the entire structure into
manageable manufacturable pieces.and optimization.solving nonlinear
equations in high-dimensional spaces to get as close as possible to
the desired shape. Designers and engineers are seeking new
mathematics to improve that process. Thus, in what might be
characterized as a spiral with each field enriching the other,
their needs will lead to new mathematics, which makes the shapes
possible in the first place. For More Information: .Geometric
computing for freeform architecture,. J. Wallner and H. Pottmann.
Journal of Mathematics in Industry, Vol. 1, No. 4, 2011.