Muqarnas are designed in plan

Classify arches by the geometry of the intrados: the number and position of the centres (one for round and segmental, two for pointed, three or four for basket and Tudor arches), or a single continuous curve (ellipse, parabola, catenary), and distinguish true arches, with voussoirs, from corbelled “arches” of oversailing courses.

Make the prayer hall of identical bays of columns and arcades, so that it can be enlarged by adding aisles or bays without changing its character.

hall = n aisles × m bays of one module

Carry the curve of the arch beyond the semicircle, so that the opening at the springing is narrower than its greatest width.

springing width = 2R cos β, where the arc continues β below the centre line

To draw a star pattern, cover the surface with a tiling of polygons, draw two lines through the midpoint of every edge at the same angle to it, continue each line until it meets another, and erase the tiling.

pattern = tiling + contact angle θ at every edge midpoint

Keep the grid and vary the angle at which the lines cross the edges: a small angle gives broad, blunt stars; a large one gives slender, sharp stars.

Choose the symmetry of the principal star (six-, eight-, ten- or twelve-fold) and build the field from a repeat unit that tiles the plane; stars that cannot tile by themselves are completed by secondary shapes in the gaps.