The mihrab and the arch.

A mihrab is the niche in the wall of a mosque that faces Mecca, and its arch is a piece of geometry in its own right. The horseshoe of Cordoba and the two-centre point of Cairo are each drawn from a compass, and the studio now derives the niche the way it derives the pattern inside it.

What a mihrab is

A mihrab is the niche set into the qibla wall of a mosque, the wall a congregation faces to pray, marking the direction of Mecca. It is usually the most worked surface in the building: an arch carried on two slender colonnettes over a recessed head, filled with geometry, inscription or both. Where the rest of a wall may run as an even field, the mihrab gathers that ornament into a single frame and gives it a centre. To draw a mihrab is to draw two things at once, the arch and the field it holds.

Two arches, two compasses

The two arches this set draws are the two the tradition leans on most. The horseshoe, the arch of Cordoba and al-Andalus, is a circular arc carried past the half-circle, so the opening is widest below the line it springs from and draws in again at the foot; its belly overhangs its jambs, the profile you read across the Great Mosque. The pointed arch, the two-centre arch of Mamluk Cairo and the wider east, is struck from two centres set apart on the springline, each arc drawing the far half, so the two meet at a point overhead. Both are compass work. A horseshoe is one radius and a chosen overhang; a two-centre arch is two radii and the gap between their centres, and from those few numbers the height of the apex follows. The studio computes each from its own construction, so the curve is exact and the band that frames it holds an even width the whole way round.

THE MIHRAB, IN ONE SENTENCE - the prayer niche of the qibla wall, framed by a horseshoe or a two-centre pointed arch drawn from a compass, holding a field of geometry or, left open, a screen that filters light and air.

A niche is not a repeat

A tiled field has translational symmetry: slide it by one cell and it lands on itself, which is exactly what lets it be cut as a seamless repeat. A niche has none. It is a bounded figure with a top, a foot and a centre, and no slide carries the arch onto itself. The studio keeps that distinction honest. Ask a tiled field for a seamless tile and it gives you one; ask an arched panel and it declines, because there is no translation that carries the niche onto itself. The pattern inside still tiles to the millimetre; the niche that frames it does not, and the software would rather say so than fake a join.

The screen in the arch

Fill the niche with a solid field and it is a mihrab; leave the field open and it becomes a screen. A pierced arch, the geometry carried as line with the ground cut away, is the mashrabiya and the jali. It lets daylight in but breaks the glare into an even pattern, lets a breeze through while the small openings speed it and cool it, and holds privacy without shutting out the world. Long before mechanical cooling, an arched screen did with cut stone and turned wood what a building now asks of glass and machinery. The same construction that frames a pattern frames the light and the air, which is why the niche belongs as much to the study of a cooler room as to the study of ornament.

Derived, not generated

The arch is not traced over a photograph. It is built from its centres and radii, the frame band offset from the same outline so it never wanders, and the field inside masked to the exact curve. Because the niche is a real construction and not a picture of one, it can be checked, drawn at any size and exported as true linework a workshop can cut, arch and pattern together. The medieval workshop set the arch with a cord and a peg; the studio sets it with the same geometry, on the way to the saw. Derived, not generated.