# Two-Point Perspective

Two-point perspective is used when only the vertical edges of rectangular objects are parallel to the picture plane, as opposed to one-point perspective, in which whole sides of an object-and therefore horizontal and vertical edges-are parallel to the picture plane. In two-point perspective, only the verticals are truly parallel to each other. All lines of edges parallel to the flat earth will appear to point to locations on the horizon. Each set of receding parallel lines has its own vanishing point. Sets of parallel lines that are parallel to one another share a vanishing point. We will now apply two-point perspective to drawing a specific subject, a square shed with a peaked roof. The shed is seen from a corner. The room is a perfect cube, meaning that its height, width, and depth are the same. The steps we follow here apply no matter what the dimensions are of the object you are drawing.

This is an example of a subject drawn in two-point perspective. The horizon is very high in this picture, indicating that we are looking down at the books.

Top and Side Views, Station Point, and Picture Plane

We start with a top view of the shed, represented by a square with a line drawn from the middle of one side 10 the middle of the opposite side. This middle line is the ridge of the roar. The square is placed at the top of the page at an angle.

Draw a horizontal line that touches the lower comer of the shed's roof seen in the top view. This line represents the top view of the picture plane (like the paper seen from its edge). Off to one side of the page, draw a side view of the shed using the same scale as you did for the top view. It will look like a square with a rectangle on top for the roof.

Now choose a station point, the imaginary place from which the subject will be seen. (It is also the artist's location.) Place it at a location near the bottom of the page, directly below the near comer of the shed. If you place the station point close to the top view of the shed, your drawing will give viewers the impression of standing close to the shed. Placing the station point far from the top view gives the impression of seeing the shed from a distance.

To achieve accurate measurements in two point perspective, start by placing a correctly proportioned top view of your subject at the top of the page at an angle. (In this demonstration, the subject is a square shed with a peaked roof.) Draw a side view of the subject, in the same proportions as the top view, to the right of the page. Then place a station point below the top view where you imagine yourself standing to see the subject. Place the picture plane next to the top view. Because we are looking down at this part of the drawing, we see the picture plane edgewise, so it is only a horizontal line.

Vanishing Points and Horizon Line

Next, locate the vanishing points. From the station point draw two lines, one parallel to the left side of the shed and one parallel to the right side. Mark where these lines touch the line of the picture plane. These are the picture plane vanishing points.

Now choose where you want the horizon line. If an ant's-eye view is desired, you would place the horizon line very near the bottom of the shed's side view. If an elevated view is desired, you would place the horizon line high above the shed's side view. The horizon line is parallel to the edge view of the picture plane.

From the marks you made indicating the picture plane vanishing points, draw vertical lines down to the chosen horizon line. Make marks on the horizon line where these vertical lines meet it. These are the horizon line vanishing points.

We next find the picture plane vanishing points by drawing diagonal lines from the station point parallel to the side walls of the top view. Make two marks where these lines touch the picture plane line; these are the picture plane vanishing points.

We now choose a horizon line. The higher the horizon line the more elevated our view will be; the lower the horizon line the lower our view. Bring the picture plane vanishing points straight down to the horizon line and make marks. These marks are the horizon line vanishing points.

Wall Height and Width

Now draw a ground line from the bottom of the shed's side view to the middle of the page, parallel to the horizon line. Next, draw a line from the lower corner of the top view to the station point, perpendicular to the ground line. This line represents the closest corner of the shed. On this tine all true measurements are made. To determine the height of the shed wall, draw a line parallel to the ground line from the top of the wall in the side view. The distance between this line and the ground line represents the height of the wall.

To determine the width of the shed's walls, draw one line from the station point to the left-hand corner of the top view drawing, and another line [rom the station point to the right -hand corner of the top view. Where each of these lines intersects the line of the picture plane, make a mark. From each of these marks, draw a line downward from and perpendicular to the picture plane line. These lines establish where the left and right walls end in perspective. You have now established the back corners for the left and right walls.

From the top and bottom of the front shed corner, draw lines to the left and right horizon line vanishing points. These lines define the top and bottom edges of the side walls.

Draw a ground line from the bottom of the side view to the middle of the page. The ground line is parallel to the horizon line. Now draw a fine from the lower corner of the top view to the station point. This will form the near corner of our shed drawn in perspective. Find the height of the shed's wall by drawing a line from the top of the side view wall, parallel to the ground line, to this corner line.

To find the width of the shed, draw lines from the station point to the left and right corners of the top view. Make marks where these fines cross the picture plane fine.

From these new marks, draw lines perpendicular to the picture plane. These lines place the side corners of the shed in perspective.

Draw lines from the top and bottom of the shed's near corner to the horizon line vanishing points to establish the left and right walls of the structure.

Roof

To establish the roof, draw a horizontal line from the top of the side view roof to the corner line of the perspective view. Where this line crosses the corner line of the perspective view, make a mark. From this mark, draw a line to the left-hand vanishing point on the horizon line. This is the perspective line of the roof.

Next, draw a line from the station point to the left peak of the roof in the top view. Where this line crosses the picture plane, make a mark. From this mark, draw a line straight down to the perspective roof line. This locates the peak of the roof. Draw in the front of the roof.

The next line to establish is the ridge of the roof. From the front peak of the roof, draw a line to the horizon line's right vanishing point.

To find the back peak of the roof, draw a line from the station point to the back peak of the roof in the top view. Where this line crosses the picture plane, make a mark. From this mark draw a vertical line down to the perspective ridge line of the shed. This establishes the back corner of the roof; your drawing is now complete.

To establish the height of the peaked roof in perspective, draw a fine parallel to the ground line from the top of the side view roof to the shed's corner line and make a mark. From this mark, draw a line to the left vanishing point on the horizon line. This is the perspective roof line.

Now draw a line from the station point to the front peak of the roof in the top view. Make a mark where this line crosses the picture plane.

From this new mark, draw a line straight down to the perspective roof line. Where these lines meet is the peak of the roof.

Draw the pitched roof lines to the point you have just established.

To find the back peak of the roof draw a line from the station point to the back peak of the roof in the top view. Make a mark where this line crosses the picture plane.

Draw a line from the front peak of the roof to the right horizon line vanishing point. This will be the roof's ridge. Then draw a vertical line down to the roof's ridge. This establishes the back peak of the roof and the length of the ridge.

Our shed is now correctly drawn in two-point perspective.

Working with More Complex Subjects

The same principles we have just covered apply to more complex subjects as well. If you have overhead and side views (as you might find in a set of blueprints) of a subject, you can follow the steps described above to get very accurate perspective drawings. This is done by drawing lines from the station point through a picture plane to the actual locations on the overhead view and then marking the places where these lines intersect the picture plane. Lines drawn perpendicular from the marks on the picture plane will locate all of the width measurements in the perspective drawing.

All height measurements are transferred from the side view to the near comer of the perspective drawing. If a height measurement is needed for the back of a wall, you must find it first on the near corner. Then draw a line from that point to the horizon line vanishing point on that side. The heights and widths of objects appear to diminish as the objects recede in perspective; this is a way of calculating exactly how much they will be reduced. Heights and widths remain consistent between two perspective lines sharing the same vanishing point.

Horizontal measurements are calculated from the object's near corner. If you want to locate a door or window that is not symmetrically placed on a wall, or locate chimneys, dormers, signs, brickwork, and so on, follow these steps:

1. Start with the proportionally accurate horizontal measurements, as though the wall were parallel to the picture plane instead of receding in space.

2. Place these measurements on a horizontal ground line drawn from the lower front comer of the wall to either side.

3. Translate these measurements to the edge of the wall nearest the picture plane using parallel lines.

4. Draw perspective lines from each point of the translated measurements to the wall's vanishing point on the horizon.

5. Draw a diagonal line on the wall from one corner to another. (If you use the alternative diagonal, the measurements are reversed.)

6. Where the diagonal line and the perspective lines cross marks the placement of horizontal measurements in perspective. (You may have to use vertical lines up or down from the crossings to place window and door edges.)