# Building the impossible

Another change that has impacted on all forms of computer-aided design and engineering is the move to distill the actual form of the buildings into mathematical equations. Because many of today's structures are based on organic shapes, curves have to be manipulated with great accuracy not only to perfect the design, but also to ensure that the building's components can actually be fabricated.

The curve form is known as its parametric base. The parametric equation is simply a method of defining that curve, and even a low-powered PC can handle it with ease. The impact of parametric modelling is that designers have been liberated from the limitations of the human mind, allowing them to use more organic shapes in their buildings. What was once the province of high-level programmers is now accessible as desktop applications. Coupled with 3D modelling, the PC desktop suddenly becomes a powerful tool that can move a design from initial concepts through to the actual manufacture of components.

For the architect, being able to manipulate a curve's form is the ultimate control over their design. Suddenly, complex geometrical designs become possible. For example, Zaha Hadid, whose designs seem to defy the laws of gravity and physics, uses parametric curve manipulation to make sure that these buildings are able to exist past the initial design stage and become a physical reality.

Desktop architecture

Computers have a long history in the field of architectural design. The iconic shell shape of the Sydney Opera House – which was designed in 1957 and completed in 1973 – relied on computers to calculate the angles of each pre-cast concrete component.

35 years later, computers are enabling architects to complete buildings that in theory seem almost impossible to build. Hadid has designed several extraordinary buildings, including the Rosenthal Centre for Contemporary Art, the BMW Central Building in Leipzig and the Phaeno Science Centre.

What all these buildings have in common is the use of computers to describe the shapes that the buildings are constructed from. Mathematical equations are used to refine a shape into spheres, cones or tori (doughnut shapes). Reducing a shape to its mathematical components means that it can be infinitely manipulated.

Using traditional graphics with their use of stored coordinates and defined surfaces would mean that more computations would have to be performed to manipulate the shapes. By reducing a shape to an equation, the software application simply has to draw a straight line between two points and segment this into a number of nodes in order to create shapes that can be easily manipulated to the architect's specification.

Hand in hand with this mathematical modelling of a building or structure's fundamental shapes is the rationalisation process. This takes the shapes that have been modelled on a computer and projects them into the real world. A step-by-step process is created that is able to build the shapes that are on screen. This is where the architect's computer model meets the demands of engineering.

Often a modelled shape will have to be further refined to create a number of subcomponents that can actually be cast in concrete. Today, programming is just as important as design when architects and engineers meet to create a new building.

Specialist applications, including the Autodesk NavisWorks range, enable designers and construction companies to work together to realise new buildings or structures. Systems like NavisWorks enable architects and construction companies to identify what they call clash detection. This is where the design of a building clashes with the construction processes that are available. The computer can instantly see if there will be a problem on the building site, saving time and money for the engineers.