How do I create a 3D perspective floor graphic effect in Illustrator for print?

Question

I am looking to create a 3D effect 2D printed floor vinyl like the attached picture in Adobe Illustrator. Any help would be appreciated.

Answer 1

In case you don't want actual 3D....

This can be done by merely drawing a flat shape, then using the Free Transform Tool to add perspective distortion and skewing to get to something similar.

This is all flat Illustrator objects so it won't change, doesn't have any "dynamic lighting", and is not any sort of "live" 3D.

Answer 2

An image search for camera carpet vendor advertisements revealed one thing: television cameras at sport stadiums are so far away from the carpets that the television view is close to a perspectiveless parallel projection. That simplifies so much the making of the ready to print file for a carpet that elementary 3D vector geometry calculations could tell how to distort the art design for certain apparent placement on a vertical or a tilted plane (like in your example).

As already said by others, the placement of the TV-camera affect very much which is the right distortion. The "no perspective" -simplification drops out the need to take the camera distance into the account, one needs only the direction from the carpet to the camera lens.

For a short distance camera the "no perspective"-simplification would, of course, be fatal; the carpet would look totally wrong in that case.

One might think if the focal length of the camera has some effect? Answer: It's not needed, the camera operator couldn't destroy the effect by zooming. That's true as well for long and short distance cameras. But for short distances the distance and direction from carpet to camera would both be as important in constructing the right looking camera carpet.

Making 3D vector geometry calculations and applying matrix formulas for projection transforms is too much for most of us. But parallel projections are so simple that the solution is possible with very elementary calculations and by using Illustrator, Inkscape or other vector program as a drawing tool. It's shown in the 2nd half of the answer. But it's useful to read at first how a 3D program can be used in a simple way, because it helps understanding the 2D drawing method.

No calculations are needed, if one has a 3D CAD program (Fusion 360 etc...) or a pro quality 3D art modelling program. It makes the needed 3D transformations. We try to distort only the edges in 3D and stretch the actual artwork into that shape in Illustrator.

This is a rendered simple 3D model what a camera could see, when there's no carpet, but an actual stand which carries a fake airline logo:

The projection is parallel. The green rectangle is the piece of stadium ground which should get the equivalent camera carpet.

The logo and the invisible surfaces of the stand are removed, the two remaining stand surfaces are half transparent (unwanted automatic transparency for separate surfaces in the elementary 3D program)

The bright green dot is actually an inserted line which points straight towards the camera. The line is easiest to define as 2 separate planar projections. Here's the first one:

And this is the second one ( the top view, the highlight is removed to show that the line punches the ground surface):

The line shows only the direction to the camera, not the distance nor the actual place. It's enough, because we assumed a parallel projection.

Unfortunately we do not have any practical way to project the colored logo along the line to the ground plane. I use too simple program, the logo can be there only a screen resolution raster image. But we can "project" the visible stand surfaces by making an extrusion along the line. The result:

Splitting the solids along the ground surface and removing all above the ground level shows the right edges of the projected surfaces on the carpet (the projection line is still there, it's needed later in checking the result in 3D):

This image could be exported as a vector to Illustrator for perfect snapping, but I take only a screenshot. In Illustrator I stretch and shear my logo design to fit into the projected edges:

The triangle cap of the stand image is also needed. I made it grey with black edge to show later it's taken from Illustrator:

This is a rectangular screenshot of the carpet. I skipped cutting the edges and pasted screenshot back to the 3D model, but this time on the ground plane:

It's the same view as the original 3D model. If you watch carefully, the highlighted viewing direction line can be seen as a bright green point.

You may wonder if Illustrator's 3D effects could be used somehow like I used a CAD program to find the right outline of the distorted artwork and stand?

Forget it. They distort a planar image for apparent 3D view. You want the exact opposite, you want to create a planar image which should be distorted.

How to construct it without using a 3D program As said above, the parallel projection case is easy. The artwork rectangle should be stretched to bigger size and sheared (=skewed in Inkscape). It can be made in a vector drawing program by drawing only. Smart guides and snaps make all fit exactly. The next image has the legacy engineering style top and side view drawings which contain the known facts:

The blue presents the artwork. Calculations are needed to find the dimensions for the drawing if it must be scaled down for some reasons. The other possible reason to make elementary calculations is to find for the stand profile the side view height height T-U and the top view height A-B for easy drawing in case only the dimensions of the artwork and the tilting angles of the planes are given.

Both views have the known direction (=the sight line) to the camera as green lines. The lines are in both views drawn via the top corner T of the artwork. The side view shows only the elevation angle of the sight line and the top view shows the projection of the sight line on the ground.

The point G1 in the side view is important. The sight line meets the ground in G1. Point G2, the place, where the top view sight line meets the ground, can be found by drawing a horizontal line. G2 is the projected place of the top corner T in the distorted image.

Now we have all what's needed to draw the outline of the distorted artwork and the visible triangle of the stand profile. Corners A, B and C are there as is, because they are on the ground. The wanted outlines are drawn as magenta:

Side G2-G3 is a duplicate of side B-C. Side C-G3 is a duplicate of side B-G2. The artwork must be sheared and scaled into parallelogram G2-B-C-G3-G2. The visible triangle is A-B-G2-A. The next image shows how it could be made surely right:

The artwork is a group which has a rectangle and outlined text. In the left the artwork and the wanted outline are aligned.

In the middle the artwork is scaled vertically.

In the right there's the ready to print camera carpet. The artwork is selected and a top corner is dragged with the shear tool. The side face triangle image A-B-G2-A is copied, filled with solid grey and placed to the left edge of the parallelogram.

Why did I scale and shear? Why I didn't use free distort and drag the corners of the artwork? Because I have a dodgy ancient version of Illustrator where such function do not work as wanted. The corners and edges would be OK, but straight lines inside become curved.

What, if perspective is needed?

Watching carefully your example reveals that the far end of the fake Turkish Airlines advertisement stand is about 15% lower than the near end. That's substantial. If we assume the far end is 2 meters further from the camera than the near end we can easily believe that the distance from the carpet to the camera is only about 13 meters. A no-perspective camera carpet for a camera this close would look distorted. The only fix is to have a method to take into the account also the distance between the carper and the camera.

The 2D method "how to draw the outline of the camera carpet" can easily be expanded to handle also perspective imaging. The parallelogram will be replaced by a less regular 4-gon and the artwork must be distorted into it.

Here's the same artwork on the same stand, but the camera distance is short:

The camera has elevation in the side view and both top corners of the artwork need own sight lines to the camera. In the next image the magenta lines are the outlines of the visible triangle and the distorted artwork on the carpet. The undistorted artwork is shown in the left:

Distorting the artwork right to the 4-gon G2-B-C-G3-G2 needs some investigations. Dragging the corners doesn't make it. I haven't tested how current Illustrator CC works. I inserted to the artwork some straight lines just for testing. The perspective is not steep enough and the inserted straight lines get curved:

The inserted lines should be placed in the same way as they are in the next construction where a new sight line is inserted to the half height of the artwork in the side view and the exact half height line is drawn inside the 4-gon. The diagonals of the 4-gon and the half-height line meet in the midpoint of the forthcoming properly distorted artwork:

Inkscape makes it right. In the recent version path effect Perspective Envelope accepts groups of paths which makes possible to use it in practice:

Only insert the effect to the grouped artwork and drag the corners with the node tool. Reducing the transparency shows that the extra lines in the distorted artwork are the same as the theoretical ones in the construction image.

Inkscape unfortunately doesn't distort bitmap images. There's Inkscape plugin InkRasterPerspective which claims it can do it. I don't have it. But at least Photoshop's Edit > Transform > Distort makes it right for this (tested).

Done, except I cannot say if the free transform tool in Illustrator CC creates the distortion right or not.

Answer 3

As posted earlier by @Billy Kerr, this is a highly-specific product and technique - however it is absolutely something you can do readily in Adobe Illustrator, Affinity Designer etc.

You need to know the exact angle relative to the camcarpet you expect the have the illustration look correct - the place where the camera's POV line of vision will be. Ideally, it's best to also have camera details like focal length, aperture, etc, so you can choose4 the correct set of perspective parameters.

Absent all the higher-level technical details, you will take a basic design (just as with @Scott's answer) and apply a perspective warp to reach the desired effect.

Here's the quick, dirty and incorrect to show you the general idea:

Unwarped

Warped

The old-school art school description for this and other related techniques is anamorphic perspective (it was once very in-vogue for painters to do this with a chromed cylinder placed at the centre of a painting, especially portraits) and in essence you are distorting your design or image such that it will appear correctly for exactly one single viewing angle only. It's actually far more complex than I'm presenting here - you need to do the relevant perspective calcs to determine the amount of foreshortening you should expect, and therefore pre-compensate for - here's what happens when you don't do that (as I didn't in my earlier example):

Warped image applied to a plane with nearby camera visible at correct perspective POV location:

View through camera - note the ludicrous foreshortening - this is why the perspective calculation is important:

Now a quick eyeballed near-correction (still avoiding the graphical perspective calcs for now) involving linear stretch along the axis of foreshortening, and roughly matching the camera's angle of view to that of the perspective distortion I applied:

stretched to minimise false foreshortening

Image on a plane w visible camera

View through camera

I think you can see the general approach - you need to know lens details of the camera (FOV, Focal length, position relative to the cam-carpet) to help match these to get a correct final result.

Here's a high-relevance external link to some folks who do this sort of thing as their bread and butter - and whose site i think explains via photos and so on perhaps better than I've tried to do so quickly here.

Cam-Carpet Vendor Link

As information: I used Affinity Designer for my vector art for this answer; you can do this in almost exactly the same manner in Adobe Illustrator. Similarly, Blender (mentioned by Billy Kerr in a comment earlier) would work for what I did; I used Modo as that's my personal preference for such tools.