Three-Point Perspective: Looking Up, Looking Down, and Nothing Stays Vertical

Three-point perspective is the view you have at the corner of a subject when you tilt your gaze up or down: at a tower from the pavement, into a stairwell from the landing, down at a street from a window. The two horizontal families of edges still converge on two points on the horizon, as they do in two-point perspective. But the verticals are no longer parallel to the picture, because the picture itself is tilted with your gaze, so they converge as well, on a third point far above the frame when you look up and far below it when you look down. In a three-point view nothing in the picture is vertical.

Where You Are Standing

The thing that changes between two-point and three-point is not the building and not where you stand. It is where you look. Stand at the corner of a tall building and look level at its base: two-point, the walls vertical. Now raise your head to the roof. Your picture plane, the imaginary window you are drawing on, has tilted back with your face, and the walls, which are still parallel to each other in the world, now run away from that window. Parallel lines that run away from the picture converge. So the walls converge, upward, to a point somewhere above the roof, and the building looks as though it leans away from you.

Every photograph of a tall building taken from the street is a three-point picture, which is why they lean. Architectural photographers avoid it by keeping the camera level and shifting the lens upward instead of tilting the body, which keeps the picture plane vertical and the walls parallel. Drawing has the same choice: draw the tower level from a distance and it is two-point; stand under it and look up and it is three-point, with the third point where the walls would meet.

The construction below has its third point below the sheet: you are looking down at the house, from a hill or an upper window. Drag the third point closer to the sheet and the look steepens, the walls taper harder, and the roof opens out towards you. Drag it far away and the view flattens back towards two-point. Drag it above the sheet and you are looking up from the ground.

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

The grid draws no verticals in this view, on purpose. A vertical guide would be the single most misleading line on the page, because it would say that something in the picture is upright, and nothing is.

Where the Third Point Goes

The third point lies on a vertical line through the centre of vision, the spot you are looking straight at, and it is far away: much further than the two horizontal points are from the centre. How far depends only on how steeply you tilt. A gentle look up, ten or fifteen degrees, puts the point several picture heights above the frame, and the walls taper so little that a viewer barely notices. A steep look up a skyscraper puts it within a picture height of the top edge, and the taper is the subject of the picture.

The horizon moves too. It is still your eye level, still the line the two horizontal points sit on, but as the picture plane tilts upward the horizon slides down in the frame, and in a steep view it falls off the bottom edge entirely. That is why a photograph taken steeply upwards shows no horizon: it is there, below the picture, and the two side points are on it. The third point never sits on the horizon; that is precisely what makes it the third.

Looking down mirrors all of this. The third point is below, the horizon slides up in the frame and may leave through the top edge, and the verticals taper downward, so a street seen from a high window narrows towards the pavement. The horizon line page follows the horizon through all of these positions.

The Exercise: a Tower From Below

You need a Letter or A4 sheet in portrait this time, taped to a board with at least 15 centimetres of room above and below, a hard pencil, a long ruler, and half an hour. The printable three-point grid below is a landscape sheet looking down; for the tower, rule your own.

  1. Rule the horizon 40 millimetres from the bottom edge of the sheet and carry it onto the board on both sides. It is low because you are looking up: the picture plane has tilted back and your eye level has slid down the frame.
  2. Mark the two side points on the horizon, each 12 centimetres beyond the side edges of the sheet.
  3. Mark the third point on the board 15 centimetres above the top edge of the sheet, on the vertical centre line. All three points are off the paper.
  4. Draw the near corner of the tower: from a foot 10 millimetres below the horizon and 20 millimetres left of centre, rule a line towards the third point, 150 millimetres long. It leans in towards the centre of the sheet. That lean is the whole subject.
  5. Connect the foot of the corner to both side points, and the top of the corner to both side points. Four lines, two for each face.
  6. Close the faces with two more edges ruled towards the third point, one 50 millimetres left of the corner at its foot, one 60 millimetres right. Both lean towards the centre line; the further from the centre, the more they lean.
  7. Check. Extend any "vertical" edge and it must reach the third point. Extend any horizontal edge and it must reach one of the two side points. Not one line in the tower is truly vertical or horizontal.

Then add three rows of windows on the left face. Their sills run to the left point; their sides run to the third point; and the rows crowd together towards the top of the tower, because the top is further from you than the base. If the rows come out evenly spaced, the tower has stopped receding.

The Mistakes That Give It Away

  • A vertical somewhere. The door frame drawn upright out of habit, or the near corner ruled with the T-square. In a three-point view every upright runs to the third point, the near ones as much as the far ones.
  • The third point too close. A point just above the frame describes a view tilted almost straight up, which is a stunt rather than a standpoint. For most subjects it belongs several picture heights away, and the taper is gentle.
  • The horizon in the middle of the picture. Looking up pushes the horizon down the frame; looking down pushes it up. A horizon at mid-height with a third point above it describes a viewer who is both looking up and looking level, which no one is.
  • Windows spaced evenly up the tower. Storeys of equal height shrink towards the third point, and so do the gaps between them. Find the middle of the face by its diagonals and halve upward.
  • Three-point used for a low building at eye level. A house seen from across the street is two-point; there is no tilt worth drawing. Use the third point when the view asks for it, not for effect.

The Printable Grid

The three-point sheet looks down: its two side points are about 10 centimetres beyond the side edges on the horizon, and its third point lies about 10 centimetres below the bottom edge, on the centre line. It carries the guides from all three points and no verticals, like the construction above and the perspective grid tool. Print at 100 percent and turn the sheet upside down for a view that looks up.

A photograph of a tower already has its three points fixed by the camera. Load it into the tool, choose three point, and let it read them from the straight edges; the how-to shows how to tell a good reading from a poor one.

Next

Lower your gaze to level and the third point goes to infinity: two-point perspective. Widen the view until even straight edges bow: curvilinear perspective. Face the subject square on and one point does it all: one-point perspective. The one rule behind every view, and the grids for all of them, are on the perspective overview.

Frequently Asked Questions

What is three-point perspective?
The view from the corner of a subject with the gaze tilted up or down. The two horizontal families of edges converge on two points on the horizon, and the verticals, no longer parallel to the tilted picture plane, converge on a third point far above or below the picture. Nothing in the picture is vertical.
Where is the third vanishing point?
On a vertical line through the centre of vision, above the picture when you look up and below it when you look down, and usually far away: several picture heights for a gentle tilt, within a picture height only for a steep one. It never sits on the horizon.
Why do buildings lean in photographs?
Because the camera was tilted up. Tilting the camera tilts the picture plane, the walls run away from it and converge, and the building appears to lean backwards. Architectural photographers keep the camera level and shift the lens instead, which keeps the verticals parallel.
Where is the horizon in three-point perspective?
Still at the viewer's eye level, but low in the frame when looking up and high when looking down. In a steep view it leaves the picture altogether, which is why a photograph taken steeply upwards shows no horizon.
When should I use three-point instead of two-point perspective?
When the view is tilted enough that the taper of the verticals is part of what you see: a tower from its base, a street from a high window, a stairwell from the landing. A house across the street seen at eye level is two-point.
Why does the perspective grid draw no verticals in three-point mode?
Because in a three-point view there are none. A vertical guide would claim that something in the picture is upright, and every upright in the scene converges on the third point.

Sources

  1. Linear perspective, Encyclopaedia Britannica. Orthogonals, horizon line and vanishing point; the system dated to about 1415 and documented by Alberti in 1435.
  2. Vanishing point, Encyclopaedia Britannica. The point at which receding parallel lines appear to meet.
  3. Linear Perspective: Brunelleschi's Experiment, Smarthistory. The demonstration panel of the Florence Baptistery, dated by Manetti to around 1420.
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