How to measure the distance to horizon line one-point perspective?

Question

I am drawing a room, which is 10m x 10m (or whatever units).

I am drawing it in one point perspective.

How do I determine exactly where to draw the back wall? As in, how far back.

Answer 1

This solution will work any shape of room you have. Cubic, rectangular (as I demonstrate), and even rooms you aren't looking at from straight on (in which case you rotate the top elevation, a common perspective technique).

Click on any image for a larger view.

1. Layout the general lines.

   • a) You need three horizontal lines: your horizon line, a ground line (somewhere below the horizon), and a vantage line. In this example, my vantage line is below the ground line. The vantage line represents the distance of the viewer from the horizon.
   • b) You also need to choose a vanishing point somewhere on the horizon line.
   • c) You can pick a vantage point, but in this case its only purpose is to establish where to put vantage line
   • d) Draw the front elevation of your room, with the scale dimensions. The front elevation needs to rest its bottom-most line (or point, if rotated for 2-point perspective) on the Ground Line
   • e) Draw the top elevation of your room, with the scale dimensions. The top elevation needs to be under the Vantage Line, with its top-most line (or point, if rotated for 2-point perspective) on the Vantage Line.
   • f) Draw the front view of your room, aligned with both the front and top elevations

2. The real trick to this technique is mapping the angles between corners to the Measuring Points on the Horizon Line.

   • a) From a bottom corner of your top elevation, draw a line going through the opposite corner (such as bottom-left to top-right) and continue that line all the way to the Horizon Line
   • b) Where those lines intersect, mark that point as a Measuring Point
   • c) Repeat for the other bottom corner
     

3. Draw your normal perspective lines on your room

   • a) Don't worry about the back wall quite yet, just make sure your perspective lines go either all the way to the vanishing point, or far enough that you can be reasonably sure you have room for your back wall
     

4. Now the technique comes into play. You'll use the Measuring Points to map a projection to tell you where the back wall begins

   • a) From a bottom corner of your perspective room, draw a line to the matching Measuring Point. So, if you pick the bottom-right corner, draw a line towards the Measuring Point that connects to the bottom-right corner of your top elevation.
   • b) Where this new line intersects your normal floor perspective lines represents the corner of your back wall.
   • c) You don't need to map the other bottom corner, unless you're drawing a room/shape that doesn't have parallel front and back walls
   • d) Draw a horizontal line from the back corner you measured to the other side of the floor
     

5. Standard perspective techniques will give you the top of the back wall.

   • a) Draw vertical lines from the bottom corners, and the points where they intercept are your ceiling's back corners
     

6. Go over your final guidelines and clean it up!

   • a) You're done!
     

Answer 2

In the following explanation I had to make some assumptions:

1. Room is 10 x 10 x 10
2. I had to assume a distance (station point) for the observer a fixed distance from the object. Need to know how far the observer is from the object being viewed.
3. You are looking for a one point perspective solution for where to place the back wall.

This is modified from the book "Anatomy, Perspective and Composition for the Artist" by Stan Smith, Dover Publications Inc., 2014.

Answer 3

Since this technique is different enough from my other answer, I felt it warranted a separate answer. This technique allows for more accurate control over distances from the object, making it easier to get a feel for the space you'll be creating.

1. Lay down your horizon line and pick a point on it to be the vanishing point.
2. Lightly draw the center of vision by marking a vertical line from your vanishing point down to the bottom of the page
3. Lightly draw your horizontal ground line at some point below the horizon
   • Everything on this ground line is at the scale you decide, and determines the measurements of all other lengths at different distances
   • Deciding where to put this line is up to you composition, so if you want a room 20 feet wide and 15 feet high to take up half the width of the page, and with the ceiling above the horizon, position the line accordingly
4. Draw your horizontal picture plane somewhere below your ground line
   • This can be drawn at any arbitrary distance from the ground line, even on another sheet of paper temporarily attached to the bottom of your drawing proper
   • As long as you're able to align the center of vision across your workspace, it doesn't matter how far off from the main drawing surface that you work
5. Draw a scaled-down top elevation view of your room below the measuring point
   • The top elevation is scaled based on the distance you want the observer to be from the object
   • Essentially, base this scale on the amount of space you have to work with
6. Mark a point for your vantage point/station point below the picture plane, below your top elevation, and on the center of vision
   • The distance of the vantage point to the picture plane determines the observer's distance from the object in perspective
   • In the example, I measured at a distance of two scaled room lengths from the picture plane, to demonstrate that the distances below the picture plane are all at a separate scale from those above the picture plane
7. Draw lines connection opposing corners of your top elevation, in order to determine their angles for your projection
8. Draw lines parallel to the lines you just drew, but start from the vantage point and end where they intercept the picture plane, and mark these points as your measuring points
   • For a perfect cube, you simply draw 45° angles from the vantage point, but for other shapes you need to use the actual angle found by connecting opposite corners
   • In the example, a room twice as long as it is wide has an angle of 63.435°, but you don’t need to know the angle, as long as your measuring line from the vantage point is parallel to line you can draw between corners.
   • Since the only thing that matters is that angle, you this means you can draw your top elevation anywhere below the picture plane where it's convenient to get the parallel lines (I happened to position mine centered along the center of vision, on top of the vantage point, but it's not necessary)
     9. Lightly draw a vertical guideline from each measuring point to the horizon line to determine your angular vanishing points
   • Of note, all similar angles in your drawing will have these same measuring lines, so you only need to determine the points once per unique angle (all objects twice as long as wide will use the same points)
9. Draw as much of your perspective object as you can, which at this point is the face and the vanishing lines
10. From one corner of your object, draw a line connecting it to the matching vanishing point you just determined to mark your angular vanishing line
11. Where this angular vanishing line intersects the vanishing line for the face of the opposite side is where your back wall will begin
    • You only need to determine one such point, if your back wall is similar and parallel to your front, since you can derive all other corners from it