/ Chris Simmonds / Places to live

We have documented previously how we adopt different geometries to resolve the complex planning of the settings of our buildings and urban plans. But do they have any pedigree and what are the underlying principles for their use?

In answer to the first question, three cities have played a distinctive role in that understanding. Our own home town Glasgow with its distinctive grid inevitably plays a powerful role in our psyche with its regular tartan drape across the topography of undulating hills descending to the river. It is hardly surprising that the Greek and Roman proportional models from Vitruvius to Alberti, and Palladio onto Le Corbusier found favour in this rigorous city setting. By way of contrast our sister city of Edinburgh, celebrates its diversity by a juxtaposed series of set pieces in an intriguing close packing of distinctive neighbourhoods. The resultant complex geometrical interrelationships between these neighbourhoods is a quality that in Paris is overcome by the powerful unifying diagonals.

Lessons learned from our city studies has enabled us to develop a geometric toolkit of possible responses.

The first is a linear response. By striking a line we reinforce the status quo of our gridded cities and towns. Through edging as at Crown Street, cornering at St Andrews Square, aligning as at Laurieston, and framing the existing quality of the city in Johnstone the original grid is supported and acknowledged.

Sometimes the linear model is less productive. Like our Edinburgh model, unusual circumstances demand a more elaborate response which the one-liner can't deliver. A sweep, to form a special series of bays as at Graham Square, a curve to reconcile an unsubtle road scheme that has left backs and fronts scattered across the urban space as in Paisley, a double curve to diminish the building scale at Fettes 6th form centre, or a more pronounced circular form used as a unifying device focused around St Francis Church and intertwining with its mirror along the road.

And then there is the Parisian 'angularity', in our case not the angularity at a city scale, but nonetheless dramatic cuts into the urban form opening up courts as at Moore Street, or creating a monumental visual slot in the building form framing views of the docks beyond at Yoker from the street beyond.

There is a danger in being trite about the broad generalities that shape our responses. But in line, sweep and cut, it is fair to say we have the beginnings of a shorthand guide to our geometric approach.

Queen Elizabeth Square focused around St Francis Church, Glasgow