Multiple point perspective

There is some debate as to what should define perspective points above 3. There are a few possibilities.

A Facet in geometry is one line segment of a polygon or one (continuous) surface of a polyhedron.
  1. Simply adding facets to an object, so that instead of a cube which has 3 sets of parallel surfaces, we might draw a cylinder with six turning sides (see the image to the right).

    Including the possible vertical vanishing point this would create an object with 4 vanishing points. Theoretically a new point could be added for pair of sides you add to the cylinder.
  2. Some have used 4 point to describe cylindrical camera views, or images that see 360 degree around the viewer. Here, the tricky part is deciding how to draw the curves where the lines meet.
An object with multiple vanishing points. We could make similar images for other shapes like trapezoids or diamonds.
In this image, which shows all four sides of a square room, each vanishing point would be at the center of a wall (one will actually appear on both far edges where a wall is split). However, note how the vanishing point lines (on the floor and ceiling) have to curve to reach the opposite wall.
The same image, but with lines added that can help in drawing this image. First, a horizontal line (in pink) that you choose the position of can be added to denote the apex of the curves. Second, draw a curve (blue) by hand that starts at one vanishing point, touches the apex line, and then ends at another vanishing point.

Now you know that any object ending on these (blue) lines is the same distance from the viewer no matter which wall they are in front of.

Even though the image above makes use of 4 vanishing points for the walls, it is similar to the 2-point perspective method in that the vertical lines are parallel to eachother.

If you're ok with the far left and right edges not aligning (so that it is no longer a 360 degree view) then it would be possible to have the vertical lines tilt inwards to add another point of convergance.

  1. The third way of adding multiple vanishing points to a scene also involves the artist having to estimate the curvature of lines.

The above curved lines that we would have to approximate when drawing (unless you have a large set of French curves) are producing a kind of spherical distortion.

Spherical distortion in the real world is distortion caused by the rounded shape of a lens. This can be either the lens of a camera or of the human eye.

Why perspective is not just for synthetic shapes

Throughout this page I've been using basic cuboids for the example images because they are the simplest shape you can use that has distinct, parallel surfaces leading to single points. This DOES NOT mean that hard-edged shapes are the only use for the perspective process.

This section still Under construction: 2. Practice Take a 2d image, skew it into a rhombus using diagonal middles to help a. Dividing skewed cuboids. a. Lens Distortion i. Spherical distortion VS No distortion. 1. Practice Have the same line lead to two different Vanishing points.