The horizon line is your eye level

On an upright picture the horizon is always drawn at the height of your eye: raise your eye from 1.6 m to 3 m and the horizon climbs the back wall with it.

Where the sky meets the sea

Look out over a calm sea and you see a sharp line where the water meets the sky. That line is the horizon. Climb a cliff and the line rises with you; sit on the beach and it sinks. It never sits above or below your eyes, it always sits at eye level. Artists use the word horizon line, or eye level, for exactly this line in a drawing, whether or not a sea is visible. In a room you cannot see it, because walls are in the way, but it is still there: it is the height in the picture that matches the height of your eye.

The model makes this exact. The picture plane stands upright, and its centre is straight ahead of the eye. A sight line aimed at anything as high as your eye is level, so it crosses the glass at eye height. A sight line aimed at a point very far away along the floor is almost level too, so the floor, however big, never climbs above that height in the picture. That is why the horizon is the line where all the floor tiles end up and where every horizontal line that runs away from you vanishes. Drag the Eye height slider from 0.2 m to 3.6 m and the red horizon on the glass follows your eye step by step.

Above, at and below the eye

The horizon sorts everything in the picture. Anything below your eye, such as a table top or the floor, is seen from above, so you see its top surface. Anything above your eye, such as a ceiling or a shelf high on the wall, is seen from below. A surface exactly at eye level is seen edge on and shrinks to a line. Set the eye to 0.8 m in the model: the low blue box is below the horizon and shows its top, while the tall green box rises through it. Raise the eye to 3 m and you look down on all three boxes, as a bird would.

The historians of mathematics J J O'Connor and E F Robertson point out that Giotto, painting about a century before the rules were written down, already followed a version of this: lines above eye level tilt downwards as they go away from the viewer, and lines below eye level tilt upwards. Linear perspective turns that habit into a rule with a definite line. Every horizontal edge that runs away from you slopes towards the horizon, from above if it is higher than your eye and from below if it is lower.

A rule for things on the same floor

Here is a useful consequence. On an upright picture plane the horizon is at eye height, h, above the floor. So the horizon crosses every upright object standing on the floor at the height h, however far away the object is. If your eye is 1.6 m above the floor, the horizon passes through the top of every 1.6 m fence post in a long row, near or far. If your eye is 1.5 m up and a building is 6 m tall, the horizon cuts the building one quarter of the way up, at 1.5 ÷ 6 = 0.25 of its height, and it cuts a second 6 m building further down the street at the same quarter. Artists use this to check that objects of the same height are drawn consistently across a scene.

Where you put the horizon also changes how a picture feels. A low horizon, near the bottom of the picture, gives a view from close to the ground, often called a worm's eye view, with buildings towering overhead. A high horizon gives a bird's eye view where you look down on rooftops and floor plans. A horizon through the middle gives the ordinary view of someone standing.

1. Draw a light horizontal line across your paper: that is your eye level.
2. Draw one box clearly below it and show its top face.
3. Draw one box that the line passes through: no top or bottom face shows.
4. Draw one box above it and show its underside.
5. Mark one point on the line and join the back corners of each box to it.