What is two-point perspective?

The view of a subject from its corner, looking level. Both sets of horizontal edges converge, each to its own vanishing point on the horizon at the viewer's eye level, while the verticals stay vertical because they are parallel to the picture.

Where do the two vanishing points go?

On the horizon, and for a comfortable view well outside the paper on both sides. For a box turned 45 degrees each point sits one viewing distance from the centre of the picture, so on a sheet held at 40 centimetres the points are 80 centimetres apart. About 10 centimetres beyond each edge of a Letter or A4 sheet is a moderate view.

Why does my two-point drawing look distorted?

Almost always because the points are on the paper. Points on the sheet describe a viewer nearly touching the corner of the building with an extremely wide angle of view. Move the points out onto a board, or use a tool that shows them where they really are.

Do the two points have to be the same distance from the centre?

No, and in life they rarely are. Equal distances mean the box is turned exactly 45 degrees. Turn one face towards the viewer and its point moves far out while the other comes in. Both stay on the horizon.

Are verticals vertical in two-point perspective?

Yes. As long as you look level, uprights are parallel to the picture and stay vertical. Once you tilt your view up or down they converge on a third point, and the drawing is in three-point perspective.

Do all the objects in a two-point drawing share the same points?

Only the ones aligned with each other. A building and its neighbour on the same street share two points. A car parked at an angle has its own pair, on the same horizon, because the horizon is the viewer's eye level and does not depend on the object.

Two-Point Perspective: The Corner View, and Where the Points Really Go

Two-point perspective is the view you have from the corner of a subject, looking level. Neither face of the building faces you, so both sets of horizontal edges run away from you and converge, each to its own vanishing point, and both points sit on the horizon at your eye level. The verticals stay vertical, because you are still looking level and an upright is still parallel to the picture. It is the view of almost every building photographed from the street, and the one most drawings get wrong, for a reason that has nothing to do with skill: the points are usually not on the paper.

Where You Are Standing

Walk from the middle of a room to its corner and look at the opposite corner. The far wall that was a rectangle is now a trapezoid sloping away to the left; the side wall that was foreshortened to nothing has opened out and slopes away to the right. Two families of horizontal edges, two points. The floor boards, the top of the skirting, the window sills all belong to one family or the other, and every one of them, extended, ends on the horizon at one of the two points.

The construction below has a house on two points. Drag the left point towards the sheet and watch the left wall: it foreshortens, its edges steepen, the corner sharpens. Drag it away and the wall opens out and calms down. Move both points together and the house swings round; move one up and the horizon tilts, which is a warning, because a tilted horizon means your head is tilted, not the building.

Drag a point (Left, Right) and the house follows. Arrow keys move a selected point one step; shift, ten.

The construction starts with its points where a comfortable view puts them: well outside the sheet on both sides. Pull them inside the sheet and you get the wedge-shaped corner of a beginner's drawing. Nothing was drawn badly; the viewer was simply placed too close.

How Far Out the Points Go

The distance between the two points is not a matter of taste. It is set by how far you are from the picture and how the subject is turned. For a box turned 45 degrees to you, each point sits one viewing distance from the centre of the picture, along the horizon. Hold a sheet of paper at a normal reading distance, about 40 centimetres, and the points for a box seen at 45 degrees lie 40 centimetres either side of the centre: 80 centimetres apart, on a sheet 28 centimetres wide. Turn the box so one face is more frontal and its point runs away to a great distance while the other comes in closer, but the product of the two distances stays fixed; the points move along the horizon like a see-saw.

This is why the points do not fit on the paper, and why forcing them on distorts everything. Points on the sheet describe a viewer standing almost at the corner of the building with a very wide angle of view, wider than any lens you would choose for a photograph. The printable grids below place the points about 10 centimetres (4 inches) beyond each side edge of a Letter or A4 sheet, which is a moderate view, and even that is outside the paper.

On paper the remedy is a board. Tape the sheet to a drawing board or a length of card at least 50 centimetres wide, extend the horizon onto the board, and put the points there. A long ruler or a taut thread from the point does the rest. In the browser the perspective grid tool simply zooms the view out until both points are in sight, and a point that is further out still gets a handle at the edge and the arrow keys.

The Exercise: a Block on a Board

You need a Letter or A4 sheet in landscape taped to a board at least 50 centimetres wide, a hard pencil, a long ruler, and half an hour. Or print the two-point grid below, whose points are already off the sheet, and work over it with tracing paper.

Rule the horizon 89 millimetres (3.5 inches) from the bottom edge on Letter, 85 on A4, and carry it out onto the board on both sides.
Mark the two points on the horizon, each 10 centimetres beyond the side edge of the sheet. Left point, right point. They are the only two marks you will make outside the paper.
Draw the near vertical: the corner of the block, 30 millimetres tall, standing 30 millimetres left of the centre of the sheet, with its foot 40 millimetres below the horizon. Its top is 10 millimetres below the horizon, so the block is lower than your eye and you will see its top face. It is vertical. Everything vertical in this drawing is truly vertical.
Connect its top and foot to both points. Four light lines. The two to the left point are the top and bottom edges of the left face; the two to the right point are the edges of the right face.
Close the faces with two more verticals: one 70 millimetres to the left of the corner, one 90 millimetres to the right. Each runs between the pair of lines heading to its point. Both are shorter than the near corner, and the one further from the centre is the shorter of the two.
Add the top. From the top of the left vertical, rule towards the right point; from the top of the right vertical, rule towards the left point. Where they cross is the far top corner of the block. You see the top face because the block stands below your eye; raise the block above the horizon and the top face disappears.
Check. Every horizontal edge you drew, extended, must hit one of the two points. Every vertical must be truly vertical. The three verticals must shorten as they move away from the near corner.

Then draw a door in the right face: two verticals, and a top edge ruled from the right point. Then a second block behind the first, sharing the same two points and the same horizon. Two blocks on the same points read as two buildings on the same street from the same standpoint; a second block with its own points reads as turned.

The Mistakes That Give It Away

Points on the paper. The most common error in all perspective drawing. The near corner becomes a wedge, the faces foreshorten violently, and no amount of correcting the details helps. Move the points out.
Points at different heights. Both points sit on one horizon. If they do not, the drawing has a tilted horizon, which means a tilted head, and every level edge in the picture will disagree with every other.
Verticals that lean. In a level view the uprights are vertical. A leaning vertical belongs to three-point perspective and needs a third point; a vertical that leans by accident is the line the eye catches first.
Windows spaced by eye. Equal windows along a receding wall shrink and crowd towards the point. Draw the first, find the centre of the wall by its diagonals, and halve outward; or use the diagonal method from the perspective grid drawing article.
A symmetric corner. Two points at equal distances means a box turned exactly 45 degrees, which is a coincidence in life. Most views have one near point and one far one, and the faces foreshorten unequally.
Everything on the same two points. Only objects aligned with the building share its points. A car parked at an angle, a bench turned to face the street, have their own pairs on the same horizon.

The Printable Grid

The two-point sheet has the horizon at 89 millimetres from the bottom on Letter and 85 on A4, and its two points about 10 centimetres outside each side edge, where the footer says they are. The guides from both points cross the sheet; the verticals are ruled. Print at 100 percent so the angles hold, lay tracing paper over it, and any building whose corner faces you can be drawn along the lines.

Two-point perspective grid, Letter landscapeDownload PDF
Two-point perspective grid, A4 landscapeDownload PDF

The sheet fixes one standpoint. For a photograph, whose points are wherever the camera was, use the perspective grid tool and let it read the two points out of the straight edges, then judge the reading with the how-to.

Face the building square on and one point is enough: one-point perspective. Tilt the camera up at it and the verticals converge too: three-point perspective. The line both points sit on is the subject of the horizon line, and the one rule behind every view, with all the printable grids, is on the perspective overview.

Frequently Asked Questions

What is two-point perspective?: The view of a subject from its corner, looking level. Both sets of horizontal edges converge, each to its own vanishing point on the horizon at the viewer's eye level, while the verticals stay vertical because they are parallel to the picture.
Where do the two vanishing points go?: On the horizon, and for a comfortable view well outside the paper on both sides. For a box turned 45 degrees each point sits one viewing distance from the centre of the picture, so on a sheet held at 40 centimetres the points are 80 centimetres apart. About 10 centimetres beyond each edge of a Letter or A4 sheet is a moderate view.
Why does my two-point drawing look distorted?: Almost always because the points are on the paper. Points on the sheet describe a viewer nearly touching the corner of the building with an extremely wide angle of view. Move the points out onto a board, or use a tool that shows them where they really are.
Do the two points have to be the same distance from the centre?: No, and in life they rarely are. Equal distances mean the box is turned exactly 45 degrees. Turn one face towards the viewer and its point moves far out while the other comes in. Both stay on the horizon.
Are verticals vertical in two-point perspective?: Yes. As long as you look level, uprights are parallel to the picture and stay vertical. Once you tilt your view up or down they converge on a third point, and the drawing is in three-point perspective.
Do all the objects in a two-point drawing share the same points?: Only the ones aligned with each other. A building and its neighbour on the same street share two points. A car parked at an angle has its own pair, on the same horizon, because the horizon is the viewer's eye level and does not depend on the object.

Sources

Linear perspective, Encyclopaedia Britannica. Orthogonals, horizon line and vanishing point; the system dated to about 1415 and documented by Alberti in 1435.
Vanishing point, Encyclopaedia Britannica. The point at which receding parallel lines appear to meet.
On Painting, Book One, Leon Battista Alberti, 1435, translated by John R. Spencer. The centric ray and the construction of the foreshortened floor, the first written one-point construction.
Draughtsman Making a Perspective Drawing of a Reclining Woman, The Metropolitan Museum of Art. Dürer's woodcut of the sighting frame and the fixed eye point, from the Underweysung der Messung of 1525.

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