# Linear perspective and receding lines

In the image I attached you see a cube (made by Blender). The edge 1 is smaller than edge 2 and 3. I expected that the edge 2 and 3 should be shorter than the edge 1 because as the parallel lines go away from the edge 1 they should converge and hence the edge 2 and 3 should be shorter. What am I missing?

• This is not the same kind of 2 point perspective people like to draw but rather true perspective. It is hard to say but the camera centerline is closer to the lines of the side and thus for a pinhole camera means they start out at a shalower angle Jul 9, 2020 at 17:26
• I just started learning to draw. Are there different kinds of perspective? Can I change the Blender's setting to make the perspective suitable for drawing?
– MOON
Jul 9, 2020 at 17:31
• No the 2point perspective people usually draw does not exsist in reality. Its always 3point perpective no matter what. But yes you could tiltshift the lense to a view that is close to 2 point. Or raytrace but both of those are beyond scope here. Jul 9, 2020 at 17:46

An elementary sight line drawing puts the things to their places:

O is the observing point. The red sight lines 3a and 3b show the ends of edge 3 on the green image plane. The blue sight lines 1a and 1b show the ends of edge 1 on the green image plane.

The angle between 1a and 1b is smaller than the angle between 3a and 3b. Thus the apparent length of edge 1 is smaller than the apparent length of edge 3 (or 2).

This is only the side view. If you make the same drawing but as seen from the top you will see that the ends of edge 3 (and 2) have also sideways distance, but the ends of edge 1 haven't it. That makes the apparent length difference even bigger.

What's missing: some practicing to construct a perspective drawing when the observer's point (=the station point, as they often say) the image plane and the top and side views of the whole constellation are given.

• Thanks! This indeed explain it. However, I am confused why it is stated that the parallel lines that recedes should converge. Is this rule of thumb a special case of what you described? Then, when is it fine to use the convergence of receding parallel lines?
– MOON
Jul 9, 2020 at 22:20
• Mathematicians have proven that in a perspective image a set of lines which in the 3D world are parallel should really point to the same covergence point (or vanishing point as they say). That and many other math facts are used in drawing as shortcuts to get something which looks perspective. Sight line construction and numerical transformations (in 3D software) are exact methods but artists like to use shortcuts because it's a fast way to get some consistency to a work which is based on artistical decisions. Sight line construction is tiresome and math happens easily only in a computer.
– user82991
Jul 9, 2020 at 22:33
• @MOON (continued) The convergence is easy to believe by thinking an infinitely long straight rectangular house which starts here and continues to infinity. The infinite lines of its 2D image must vanish to the same point.
– user82991
Jul 9, 2020 at 22:40