## Archived - How To Draw Floor Tiles In One Point Perspective

#### 10 April 2021

This post was originally published on Wordpress by Tarren Stroud (pixelglade's other alias) on 10 April 2021. It has been reposted for archival purposes. All images have been converted to clickable thumbnails at 100px height. Click to load the fullsize image.

An important skill that landscape or cityscape artists need to know is how to draw perspective grids, and how to project them to scale. Additionally, these techniques can be used to draw floor tiles or pavement tiles in perspective. This allow the artist to render a beautiful interior or background, creating the illusion of depth.

By using this perspective technique, you can convert the image depicted on flat 2-dimensional paper to a 3-dimensional image – or at least an optical illusion of one. With this skill, you will be able to sketch the ground when it is covered in a grid or checker pattern.

This technique is helpful for the beginner artist who is tackling the challenging subject of perspective drawing. With one point perspective skills, you can depict a cityscape, some ancient ruins, or the floor of a gothic church or cathedral. You can have confidence you are drawing accurately as this projection technique involves a reliance on keeping objects to scale relative to one another, this is a great skill to develop if you have difficulty eyeballing or guessing proportions as objects recede into the distance.

## About perspective projection

If you are new to this projection technique of perspective, I recommend checking out the preceding blog post on projecting squares in perspective, which also explains some definitions such as spectator point, line of the plan (or ground line), horizon line, diagonal vanishing point (or point of distance), and vanishing point. Parallel projection is an advanced form of perspective used by architecture students and artists. You can do these exercises in pencil in your sketchbook or in a digital drawing program.

In this blog post, I will cover the following topics:

- Historical drawings of fantasy architecture
- Paintings of floor tiles and church interiors
- How to draw tiles in perspective
- How to draw diagonal tiles in perspective
- How to draw a perspective grid with varying sized squares

The exercises featured in this blog post are sourced from the public domain book Elements de Perspective by Armand Cassagne (originally published 1874) available on the Internet Archive. I have translated the instructions from French to English because I wanted more artists to be able to benefit from this valuable drawing resource.

## Historical drawings of fantasy architecture

Some example of perspective floor tiles in illustrations include the following lithographs. We can see in these drawings, examples of the tiles we will be drawing in this blog post – plain squares, diagonals or diamond style, and irregularly sized. I also included a few more complicated patterns for interest.

These classical architecture drawings from 1551 were listed under the title: Vues d’optique (optical perspectives or viewpoints). They are by Geymüller, H. de. Les Du Cerceau and these images were digitized thanks to the Getty Research Institute, with many more example images available to view from the Internet Archive.

This style is termed capriccio and is a depiction of **fantasy architecture** popular in the Renaissance and Baroque periods. Capriccio involves the juxtaposition of familiar buildings or architecture elements in unfamiliar or unconventional ways.

Architecture illustrations of this period were sometimes based on imagination, relying on the drawer’s complex and detailed knowledge of the subject or of their resourcefulness. You can tell they are in one point perspective as the lines of the walls facing the viewer are transverse which means they are horizontal or perpendicular to the horizon line. I personally find these capriccio illustrations slightly eerie, both in terms of how empty they are and how magnificent they are. They remind me a lot of the abandoned city of gods, Anor Londo, in the game Dark Souls.

## Paintings of floor tiles and church interiors

If you prefer paintings, one artist who specialized in gothic, church, or palace interiors was Dirck van Delen, who produced beautiful paintings which feature floor tiling as part of the environment. If you draw a horizon line then place a ruler along the receding lines of the buildings, you can see the lines disappearing to a single vanishing point. The checkerboard pattern alternates with yellow and blue and all recede to a single vanishing point.

A dutch Baroque painter you may be more familiar with but also drew a lot of interiors including floor tiles is Johannes Vermeer. Vermeer specialized in drawing domestic interiors. Both of these artists paintings were made during the Dutch Golden Age of Painting during the 17th Century.

Now you have some familiarity with the subject material (the floor tiles!) and seen a few different ways they can be portrayed in artwork, let us move on to the exercises.

## How to draw tiles in perspective

The size of the tiles can be any scale you choose, one square could be 1 foot, 1 meter, or 2 feet, it is really up to you. It may depend on the blueprint you are trying to draw. In the end, the projection method relies on the same principles. If we consider a single square, the way it is replicated in perspective, which underlies all the following exercises, is the following rule:

In Figure 61, given any square, if you find the intersection of the diagonals, you will have found the center of the square. By then drawing a line through the center (horizontal in the example, but it could be vertical – depends on the orientation), and then crossing one corner through the center, you can replicate the square and can make a checkerboard by repeating this rule over and over.

This rule applies in perspective as well, and when drawing floor tiles or grids, it is on a greater scale. The below exercise is a shortcut to projecting a large grid.

**Operation:** The geometric square ABCD (fig. 62) is divided by the largest of its number up to infinity into equal parts, let it be 8 here, by the vertical lines a”H-b”L-c”M, etc. We observe that if we draw one of the diagonals, say AC, that the intersections a, b, c, d, etc., produce the horizontal lines H’L”, M’N”, etc., on dividing the square by its height into eight equal parts, form with the previous divisions regularly sized squares, such that it offers the squares of a checkerboard.

## How to draw diagonal tiles in perspective

Trace the same diagonal checkerboard below the ground line, then follow the below instructions to project it in perspective.

**Operation:** Given the receding square ABC’D’, make the receding lines a”P-b”P-c”P, etc., and the diagonals AC’; plus, the intersections a’, b’, c’, d’, etc., draw the horizontals which determine the squares of the checkerboard in perspective, equal among them.

Let a tiled floor arranged like in a geometrical plan ABCD (fig. 63): the side of the stones will recede at a distance, like in the angled square in figure 53.

The angles of the stones, at the points e, f, g, produce the receding lines eX’-fX’-gX’ and the receding lines eX-fX-gX. Let the intersections of these receding lines between them give the far angles* of each of the stones at the first row to the points M’, L’, R’, S’, a’, corresponding to the points M, L, R, S, a of the geometric plan. These receding lines, prolonged, determine successively the other squares at the far end of the drawing area.

We see that the diagonal of each square is given on the line of the plan, at the points e, f, g, the receding diagonal lines opposite suffice to determine the squares; we prove in producing the receding lines eP-fP-gP, which touch equally the angles L’, R’, S’, etc.

## How to draw a perspective grid with varying sized squares

Below is a checkerboard formed by squares of different shapes and sizes, viewed from the front. Follow the instructions to draw it.

**Operation:** Consider the layout of the checkerboard determined by the plan A’FAG (fig. 64).

Draw the receding lines A’P-B’P-C’P-EP-FP and the receding diagonals A’X’-C’X’-EX’, which determine on the side FA” the points E”, D”, C”, B”, A”.

From each of these points, construct the horizontals touching the side A’G’ at the corresponding points N, M, L, H, G’: these horizontals finish the checkerboard in perspective following the layout given by the geometric plan A’FAG.

## Summary and additional resources

In this blog post, you will have learned how to project a grid of squares, a grid of diamonds, and varying sized tiles into perspective. In the next blog post I will discuss projecting 3d objects into perspective, and then apply that knowledge to drawing a room interior.

If you want to jump ahead to something more complicated, I have written in another blog post about a classical architecture treatise, Perspectiva Pictorum by Andrea Pozzo. Alternatively, if the projection method for grids is still a bit complicated for you, you can take a step back and learn how to project squares into perspective using the same technique.

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