Perspective Grid: One, Two, Three and Four Point

One idea, four grids

Perspective has exactly one rule behind it: lines that are parallel in the world are not parallel in a picture. They converge, and the place where they would meet is a vanishing point. Everything else, including all four grids here, follows from that.

The number in the name counts how many families of parallel lines the view lets you watch converging. It is a fact about where you are standing, not a style you choose.

Each view has a page of its own in Learn, with the construction running on the page, an exercise with measurements and a printable grid: start at the perspective overview.

One point: you are facing it square on

Stand in the middle of a corridor and look down it. The floor, the ceiling and the tops of the doors all run away from you and meet at a single point somewhere near the far end. Meanwhile the door frames stay upright and the skirting boards stay level, because those directions run across your view rather than away from it, and a direction parallel to the picture never converges.

Use it for a wall seen head on, a road running straight away, a room drawn from the doorway. If you find yourself wanting the side wall to lean, you are no longer in a one point view.

Two point: you are at the corner

Step to the corner of a building. Neither wall faces you now, so both converge, each to its own point, and both points sit on the horizon. Uprights are still upright, because you are still looking level.

Both points usually sit well outside the picture, which is why this is the grid people get wrong on paper: they cram the points onto the sheet and the building comes out looking like a wedge of cheese. Here the view zooms out to show you where they really are.

Three point: you tilt the camera

Now look up at the tower, or down into the stairwell. The uprights are no longer parallel to the picture either, so they converge as well, on a third point far above or below the frame. This is why a photograph taken from the pavement makes a tower appear to lean away from you.

The grid drops its verticals in this mode on purpose. In a three point view nothing is vertical, and a guide that pretended otherwise would be the single most misleading line on the page.

Four point: the view starts to curve

Look along a very wide view, or through a fisheye lens, and a straight edge of a room stops imaging as a straight line at all. It bows: flat at the vanishing points, bulging near the middle of the frame. Comic artists use it for a sense of vertigo, and architectural photographers spend their lives fighting it.

Where the horizon is, and where it is not

The horizon is your eye level, drawn here in blue. It is not part of the construction, it is what the construction implies: everything above it you are looking up at, everything below it you are looking down at. You do not move it directly. It follows the vanishing points, so dragging them is what decides where the viewer is standing.

There is an eye level in all four views, but it does not always appear as a straight line, and it does not always appear at all. In one and two point it is a straight line across the picture, and both horizontal vanishing points sit on it. In three point it is still straight, but the tilt that creates the third point often pushes it off the frame entirely, which is why a photograph taken steeply upwards shows no horizon: it has fallen below the bottom edge of the picture. The third point never sits on it, which is precisely what makes it the third.

In the curved view the horizon bows like everything else. It comes back straight in exactly one case, when it runs through the middle of the frame, because that is the one direction you are looking straight along and a line through the centre of vision cannot bend. Drawing it straight anywhere else would contradict the grid around it.

Reading the perspective out of a photograph

With a picture loaded, the tool can find the grid instead of you placing it. It looks for the straight edges in the image, then for the point that the largest family of them agrees on. Load a photograph of a building, choose two point, and press the button.

It then tells you two things. What share of the edges it found the whole grid accounts for, and how many edges the thinnest direction of that grid rests on. Ten edges and ten is a firmer answer than seventeen and three, and one figure cannot say both.

It also shows you the edges themselves. That is the part worth using: a percentage asks to be believed, but edges lying along the floor bands of a building can be looked at, and if they lie along a tree instead you know at once why the answer was odd. Switch them off when you have seen enough.

A third check runs behind both. Two vanishing points fix the focal length of the camera that took the picture, and so the angle of view, which the tool reports beside the reading. If that angle comes out at something no ordinary photograph is taken at, the pair is rejected however neatly the edges agreed with it. The first check asks whether edges point at a place. This one asks whether the picture could have been taken at all.

Three point is read as two measurements rather than one, because the two horizontal directions meet a little way outside the frame and the uprights of a building meet hundreds of frame heights above it. If your uprights are parallel, the tool says so and sends you to two point: that is not a fault in the photograph, it means the camera was held level.

It cannot read a curved grid, because straight edges cannot establish one, and it says that too. When nothing agrees at all, it says that rather than drawing a plausible grid over your photograph. A confident wrong answer would be the worst thing this tool could do.

Using the grid

• Start with the mode that matches where you were standing, not the one that looks most impressive.
• The horizon has no handle of its own: it runs through the vanishing points, so you set it by moving them. Put it at your eye level, and everything above it you are looking up at, everything below it you are looking down at.
• Drag the vanishing points until the guides run along the edges of your subject. On a photograph, two or three edges lining up is enough to fix the rest.
• For fine adjustment, select a point and use the arrow keys. One press moves it a pixel, and holding shift moves it ten. This is the way to set a point whose handle is pinned at the edge of the picture, because it is further out than the view can show.
• Each point's lines have their own colour, so a line on the picture can be traced back to the point it belongs to. The colours can be changed in the panel, and they are carried into every export.
• Show a box or a house to see what the grid means. It is built from the same points as the guides and follows them as you drag, which is the quickest way to feel what each point does. In the curved view there is none, because a body with straight edges would contradict the grid around it.
• Fewer guides is usually better. Enough to see the direction, few enough to see the drawing under them.
• Anything can be taken back. Reading a picture, switching mode and moving a point are each one step, and a whole drag is one step rather than one per pixel.