One-point perspective

Face the back wall square on and every depth edge in the room, from the floor tiles to the tops of the walls, runs to one point straight ahead of your eye.

Three families of edges

A box has edges in only three directions: width, depth and height. Put the box square to the picture plane, with its front face parallel to the glass, and look at what happens to each family. The width edges run left to right, parallel to the glass, so in the drawing they stay horizontal and parallel. The upright edges are also parallel to the glass and stay vertical and parallel. Only the depth edges, which run straight away from you, cut through the glass at an angle. They are the ones that converge, and they all converge to one point. This is one-point perspective. Alberti called that point the centric point; today it is called the vanishing point.

Where exactly is that point? The English mathematician Brook Taylor gave the cleanest answer in 1719: the vanishing point of a family of parallel lines is where a line through the eye, parallel to them, meets the picture plane. The depth edges point straight ahead, so the line through the eye parallel to them is the line of sight straight ahead. It meets the glass at its centre, right on the horizon. In the model the readout calls this point V2 and gives its position as (0.00, 0.00) m: the centre of the picture.

Drawing a box step by step

1. Draw the horizon line and mark the vanishing point V on it.
2. Draw the front face of the box as an ordinary rectangle with horizontal and vertical sides.
3. Join each corner of the rectangle to V with light lines.
4. Choose how deep the box is and draw the back edge as a horizontal line between two of those lines.
5. Drop and raise verticals from the ends of that edge to finish the back face, then darken the visible edges.

The step that needs judgement is the depth of the box in step four. One-point perspective makes it easy to draw something that looks too long or too short, because the depth lines shorten very quickly. The tile floor gives you a way to measure it, and it was Alberti's favourite example. On a floor of square tiles, the lines across the floor are horizontal, the lines into the floor run to the vanishing point, and the rows of tiles get closer together as they go back. The spacing follows the drawn-height rule from unit one: a floor line D metres ahead of the eye is drawn d × h ÷ D below the horizon. With the eye 1.6 m up and the glass 1.5 m away, a floor line 4 m ahead lands 0.6 m below the horizon, and one 8 m ahead lands only 0.3 m below.

The distance point

Alberti also gave a check that the floor is right. Draw the diagonals of the tiles. A diagonal of a square tile runs at 45° to the depth lines, so it is a horizontal line in a different direction, and like every horizontal direction its vanishing point lies on the horizon. Taylor's rule puts it exactly: the line through the eye at 45° meets the glass a distance d to the side of the centre, the same as the distance from the eye to the glass. If all the tile diagonals in your drawing meet at one point on the horizon, the floor is consistent, and the gap from that point to the centre tells you how far from the picture the viewer should stand. Switch on Tile diagonals in the model and the blue lines meet at two distance points, 1.5 m left and right of V2.

One-point perspective suits scenes you face square on: a corridor, a road running straight away, a room seen from its doorway, a stage set. It goes wrong when an object is turned, because its edges are then no longer parallel or perpendicular to the glass. That is the subject of the next unit.