THE City Art Centre is Edinburgh City Council’s three storey venue for art in Edinburgh. Its capacious galleries have room for multiple exhibitions at once, and this year’s winter offerings are a diverse selection from contemporary applied art to historical architectural drawings. There is also the Hidden Gems exhibition in the basement, a gallery of just that from the council’s collections.

On the third floor, artists Angie Lewin and Lizzie Farey, both of whom have exhibited at the Scottish Gallery over in the New Town in the last month or so, come together in an exhibition that plays with both the idea of the “fine line”, of drawing, in art, and also of that “fine line” with which artists working in media traditionally seen as craft grapple with in the perception of their work.

It’s a tricky one, at least for traditionalists, for craft cannot be separated from art purely by function, and how does one define function in any case? To explore further, Lewin and Farey, in collaboration with City Art Centre curator Maeve Toal, have invited two other artists whose work is based in detailed observation and drawing in an exhibition which displays some innovative and experimental approaches to their respective forms.

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Frances Priest’s ceramic objects function, if you will, as sculptures. Intricate, finely delineated, brightly coloured, with tessellations of colour and geometry referencing cultural forms from Islamic tiles to Indian architecture, Priest was approached by Farey to take part in the exhibition, while Lewin approached Bronwen Sleigh, whose own geometrical experimentation with the etched and free-standing line stands in counterpoint to Farey and Lewin’s own fluid works.

It’s a fine exploration of the workings of line, from Lewin’s offcuts of Japanese paper, re-used to decorate driftwood or formica in small-scale renditions of her still life works in mixed media, a refreshing reworking of her form. Farey’s woven willow, made by drawing in string on the floor of her studio, then bending and cutting the wet harvested willow – from her own field – to fit, has an ethereal nature that seems to inhabit the space in front of the wall, despite being created as ostensibly flat objects. The CAC have also brought Farey’s stunning large-scale work, Aerie (2011), out of storage for the occasion, dominating the stair well.

Further down the building, there's a joint exhibition between husband and wife Charles Poulsen and Pauline Burbidge. Songs for Winter is a meeting of the two artists’ work, created at their home in the Borders, which is in itself a work of art, having been renovated by their own hands over the past 25 or so years. If Poulsen’s sculptural work in wood is frequently in the buildings and the gardens of his home, his exhibits here are large and intricate abstract drawings, a rendering of the landscape in only its most infinitesimal detail and essence, a fragile foil to his chunky, heavy sculptures.

They mingle well with Burbidge’s ever-evolving textiles, her large scale quilts flecked with little grains of hand stitching over cyanotype prints of corns, grasses and other natural forms. She hand-draws stitches with a specially designed machine, allowing her to evolve her work into ever more fluid form. Burbidge will hold a cyanotype workshop in January, part of a series of events accompanying both contemporary art exhibitions which are detailed on the City Art Centre’s website alongside academic essays in the excellent pamphlets produced for both.

On the second floor, the innovations of the past are explored in Playfair and the City, a fascinating delve not only through the 19th century architect’s iconic classical architecture, including the observatory on Calton Hill, currently being renovated for the city’s Collective art gallery, but also his neo-Gothic work, which includes Heriot's and Donaldson's Hospitals and New College on the Mound.

Equally fascinating are those projects which were not built – or not fully – from the arcade lining the Mound to the plans for the further extension of the New Town. Amongst Edinburgh’s notoriously hilly topography, Playfair had a skill for judging the place of his buildings on the city’s skyline. David Robert’s wonderful landscape view of Edinburgh from the West, The Donaldson Hospital, highlights the value of this skyline and Edinburgh’s rural roots. Amidst the rampant development currently going on in Edinburgh, and the apparent lack of thought given to the character and importance of the city’s historic and contemporary skyline, Playfair’s understanding of all aspects of a building’s place in its urban environment is salutary.

A Fine Line/Songs for Winter/Playfair, The City Art Centre, 2 Market Street, Edinburgh, 0131 529 3393, www.edinburghmuseums.org.uk, until Spring 2018, Wed-Sat, 10am-5pm; Sun 12pm-5pm