## BASIC LINEAR PERSPECTIVE

To carry out these basic examples about linear perspective I have used a tool that I find very useful for learning the linear perspective. Such a
tool is just one of the many video games in three dimensions that exist today, that through a three-dimensional graphics engine has the ability to
generate complex linear perspectives in real time and in an accurate way.

Before beginning, we have to learn a couple of key concepts about linear perspective:

All lines vanishing at the same point are parallel.

We call horizontal lines those vanishing on the horizon, and vertical lines those that are perpendicular to the horizontal ones. It also can be
defined the vertical lines as those that target the center of the earth, that is, as the line that forms the string of a plumb-line.

In these images, the blue line represents the horizon and the aquamarine circle in the center, the point of view of the observer. Let's go with the
first example:

Here we look at a window in a totally front way. As we have our eyes focused on the horizon, the verticals are kept parallel, and therefore not
vanishing in any point.

Now we look a little upwards. We see that the verticals converge into the sky, towards a vanishing point located above our head - the zenith -.

And the opposite case. We look down and the verticals converge on to the ground, towards a vanishing point located beneath our feet - the nadir -.

Now an example of frontal or parallel perspective. It is characterized by having a single vanishing point, which lies on the horizon and that will
always match our view point.

Now we see an example with two vanishing points. These two vanishing points are located on the horizon. As we also have our view point on the
horizon, the verticals do not converge.

And here we have an example with three vanishing points, and now we look up above and see that the verticals have now become convergent. The
following image shows the opposite case, when looking down.

And finally, look where the sides of the staircase converge. The left wall converges on the horizon as it is horizontal, while the sides of the
staircase, being inclined, converge at a point located above the horizon. In case they were inclined downwards, they would converge towards a point
located below the horizon.

If you want to deepen in the study of linear perspective, or want information on a topic, follow the links at the top right to access the most
advanced and comprehensive tutorial.