## 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.

### LINEAR PERSPECTIVE TUTORIAL

:: Basic linear perspective

Theory of linear perspective, explained in a simple way: vanishing points, vanishing lines, view point and horizon.

:: Introduction to linear perspective

Fundamental theory of linear perspective: points, lines, planes and horizon.

:: Perspective of the square

Representation of the perspective of the square, with one and with two vanishing points, and study of the distortion produced in the squares that are beyond the vision limits.

:: The inclined board

Representation of the inclined board, a surface that vanishes under the feet of the observer.

:: Perspective of the cube

Representation of the perspective of the cube with one, two and three vanishing points.

:: Inclined planes

Representation of planes that do not vanish in the horizon, due to their inclination.

:: Encasing

How to use simple figures represented in perspective to obtain the representation in perspective of more complex figures.

:: Subdivisions

How to divide a surface into parts following the laws of perspective.

:: Equidistance

How to represent stretches of equal distance following the laws of perspective.

:: Measurable perspective

Methods for representing objects in perspective, endowing them with concrete dimensions.

:: Spherical perspective

Study about spherical perspective and its differences regarding conventional perspective.