Fisheye Perspective Grid

What a fisheye grid does

Point a normal camera at a long corridor and the walls converge to one vanishing point; walk into a bigger room and turn your head, and the parts of the wall far to your left and right seem to grow rather than shrink. A flat picture plane cannot show more than about 100° without that stretching, which is why every lens wider than 20 mm looks strained at the edges. A fisheye lens gives up on the flat plane: it records the world on a sphere and flattens the sphere into a disc. Nothing stretches, but every straight line becomes an arc.

This fisheye perspective grid is that projection, computed rather than photographed. The disc is 180° across by default. The dashed line through the middle is the horizon; the two dots on its rim are the left and right vanishing points, the dots at the top and bottom are the zenith and nadir, and the centre of the disc is where you are looking. Ground squares one metre on a side curve away from the centre, so a figure or a box placed on them keeps its true size at every angle.

Reading the curves

Every line in the world becomes part of a circle on the disc, and the rule for which circle is simple: a line and its vanishing point pair define an arc that passes through both points. Horizontal lines that run away from you go through the two horizon vanishing points; verticals go through zenith and nadir; lines parallel to the horizon that cross in front of you go through the left and right points too, but bow the other way. Only lines that pass through the exact centre of view stay straight, which is why a level horizon is the one straight line in the picture.

Tilt the camera down with a drag and the horizon rises and bends, the verticals fan out toward the nadir at the bottom of the disc, and the floor swells. That is the fisheye look of a skate video or a pet photograph taken from standing height: not distortion in the sense of error, just the honest record of a very wide view.

Matching a lens

The angle slider is the lens. 180° is a circular fisheye (about 8 mm on full frame), the image a round disc. A full-frame fisheye (15–16 mm) is also 180°, but only from corner to corner of a rectangular frame; the long edge sees about 150° and the short edge about 100°, so set the angle to around 140–150° and imagine the rectangle inside the disc. Action cameras are 120–150°; the widest phone lenses about 120°. Below 100° the curvature is gentle enough that many artists switch to the 3-point grid and accept a little edge stretch instead.

Drawing over it

The grid is most useful as a layer under a drawing: export a transparent PNG at the canvas size, set it to 30–50% opacity, and draw the arcs by eye against it. For anything geometric, the SVG export gives real curves you can snap to in Affinity, Illustrator or Inkscape. Comic panels that need a whole room, a cockpit, an underwater shot or a dream sequence are the usual reasons to reach for it; the curvilinear perspective lesson shows the construction step by step, and the 4-point, 5-point and 6-point pages open the same grid at the framings those names usually mean.