Exploring Reverse Perspective Art

Really interesting, mind-bending art can be created by messing around with linear perspective. In this Instructable I’ll show you how to bring a vanishing point out in front, between the viewer and the artwork, instead of having it in the same plane as the artwork. This is usually referred to as reverse perspective, because objects nearer the viewer are depicted as smaller than those further away, reversing the normal situation. But to do this we must work in three dimensions instead of on a flat canvas. Fortunately, that’s easy to do using 3D modelling software such as Autodesk Fusion. You can choose whether to explore the effects virtually, using Fusion’s animation capability (which was used to create the animated image above), or to create your own real-life reverse perspective artwork to hang on a wall.

In case you’re thinking, “Well, this sounds interesting, but I have no artistic ability whatsoever so this is going to be beyond my skills”, don’t worry, I have no artistic ability whatsoever either. If you do, great, you can create something using your own artwork. But if not, I’ll show you how to get the reverse perspective effect using AI or a camera to produce the initial images. All the software I used is free, including Fusion for non-commercial use.

You will be using 3D design sotware such as Fusion and image editing software such as Photoshop or the GIMP for this project, so you will need a computer. If you plan to base your artwork on photographs you take yourself then you'll also need a mobile phone or other digital camera.

To create a piece of physical artwork you'll need in addition:

1. cardboard
2. pencil and ruler
3. gaffer tape and glue
4. a knife or scissors
5. access to a colour printer

Imagine a square pyramid (a square base with 4 identical triangular sides that meet at a point) stuck onto a wall at eye level with the top and bottom edges of the square base horizontal and the point sticking into the room, towards the viewer. The point is the vanishing point for a one-point perspective artwork. Now, imagine that the square pyramid has been truncated by slicing off its tip vertically, to create a new square face that’s much smaller than the base, like the red one in the image above. The 5 visible faces (this new small square and the 4 faces surrounding it which are now trapeziums) will be our canvas for depicting the internal view of anything that is cuboid in shape – like a shoebox diorama viewed through a peephole in one end, as in the AI-generated room view above. In effect, we’ll be turning a diorama inside out.

Alternatively, reverse perspective can be used to depict the outside of a cuboid object by placing images on the inside faces of a concave truncated square pyramid. So imagine the pyramid now hollow, made of cardboard and without its large square base, and spin it around so that the small square face is the one against the wall and the large square open end is towards you, like the blue one above. This would be the canvas to create an artwork of the outside view of, say, a building. A concave pyramid like this would be harder to attach to the wall and more vulnerable to damage than the convex version which can be reinforced inside, but it might be possible to place it in an alcove where it could be supported to sit on a shelf with its axis horizontal. But both types of reverse perspective can be explored readily in Fusion.

Actually, the pyramid doesn’t need to be square, it could have a rectangular base instead – and it will need to have if the object you want to depict doesn’t have square ends. I’m guessing it would be possible to use pyramids with other base shapes (eg triangular, hexagonal) to depict something of that shape too, but there aren't too many real-life objects like that.

The process to follow will involve:

1. choosing or creating suitable images for 5 out of the 6 faces of a cuboid object
2. creating a 3D model of a truncated square/rectangular pyramid in Fusion of proportions to suit the dimensions of the selected object
3. distorting the images to make them fit the pyramid’s faces
4. applying the images to the faces as decals to create a 3D model of a reverse perspective artwork
5. viewing the artwork from different angles in Fusion to explore the discombobulating effect, and perhaps making tweaks to the model, eg to bring the vanishing point nearer or further from the viewer, with the option of creating an animation
6. if a physical artwork is wanted, using the 3D design to build a truncated square pyramid from cardboard or plywood and printing off images to stick onto it

For a concave artwork you'll need good images of the top, 3 sides and base of an object with nice square lines. Alternatively, for a convex artwork you’ll need images of, say, the ceiling, 3 walls and floor of a room. In either case, the “missing” side/wall should be one of the two smaller ones, and the images on adjacent faces/walls should tile together seamlessly. The possibilities are:

1. Open a cardboard box out flat and draw or paint on 5 of its faces. Then photograph the image on each face and digitally distort them.
2. Photograph an existing object square-on to 5 of its faces – although getting a bird’s-eye view of the top will be difficult for anything very big.
3. Find suitable images online.
4. Get a free AI tool to create suitable images – my favourite.

Another option is to cut out the photography and digital distortion stage by drawing or painting artwork that is already distorted, which is possible if you stick to simple shapes like pictures on the walls of a room. Search on YouTube for "reverse perspective room" and you'll find several tutorials.

For this ‘Ible I’ve used methods 2 and 4 for the teabag box and Georgian room interior, respectively. Step 4 goes into more detail on how to do it.

As outlined in the Step 1, our canvas will be a truncated square pyramid. We'll make a parametric one that can easily be resized to suit the images we place on it. The instructions that follow are for Fusion and assume a basic knowledge of modelling solids in the Design workspace. The screenshots above show the process.

First, a warning. Working in reverse perspective (RP) can be very confusing, the eye is constantly being deceived and after a while you won't know whether you're looking at a concave object or a convex one. Up/down and left/right can get confusing too. It helps to set the Visual Style (it's in Display Settings) as shaded rather than wireframe, and to be clear about the designations of the various surfaces - I use North for the small square top of the truncated pyramid, West for the surface on its left, East for the surface on its right, Top and Bottom. North will be facing the viewer when the viewer is directly in front of the artwork, and will be the nearest surface for a convex canvas and the furthest for a concave one. The South face is the large square base of the pyramid which doesn't have an image on it, and is open in the case of a concave canvas.

In a new Fusion design, start by creating user parameters (Modify, Change Parameters, highlight User Parameters then click the + sign at the top) as follows:

S_width - width of the South surface 410mm d1

S_height - height of the South surface 361mm d2

Vanishing_point - distance of vanishing point from South face 450mm d3

(The dimensions are those I used with the Georgian room images shown in Step 4, and can easily be changed later to suit your own graphics. I simply looked at the image sizes I had in pixels and made a 3D canvas using the same numbers in millimetres to make it easy to get canvas surfaces with the right aspect ratio to match the North image. The South face has the same aspect ratio.)

Create a new component (always a good first step) and call it Convex. In that component, create a sketch in the XZ plane and draw a rectangle, centred on the origin, of width S_width and height S_height. Finish the sketch and rename it South.

Then create a second sketch in the YZ plane and make sure there's a tick in the 3D Sketch box. Draw a construction line of length Vanishing_point from the origin towards the front and constrain it to be perpendicular to both diagonals of the rectangle in the South sketch. Now draw in the four lines from the free end of the vanishing point line (this is the vanishing point) to the four corners of the rectangle, again as construction lines. Finish the sketch and call it Pyramid. Check that both sketches have the red padlock symbol in the browser to show they are fully constrained.

Next, loft from the square base (South face) to the vanishing point to create a solid pyramid. Construct an offset plane that's 4/5 of the Vanishing_point distance in front of the South face by entering -(4*Vanishing_point/5) in the Distance box. Use Modify, Split Body to split the pyramid with that new plane and finish by Removing the unwanted tip.

That's it, virtual canvas created. Now we need to work on images that can be applied to the surfaces as decals.

Step 2 listed four ways to get suitable images: draw/paint your own; photography; searching online; or using AI. The outcome of all of them will be 5 digital images, one for each of the Top, Bottom, West, North and East faces. Don't worry about the dimensions of these images at this stage, we'll be adjusting and distorting them in the next step. But do aim for quality in terms of high resolution and good, even lighting with no shadows.

Draw/paint

You could just draw out a box net - a cross-shaped, flattened out box like in the first image above - on a piece of paper to use as a canvas, but it saves a lot of measuring and drawing of rectangles if you start with an actual box. You are basically going to recreate either the inside of a hollow rectangular space (such as a room) or the outside of a cuboid object (such as a building or packaging box). For the outside version (which will become a concave RP artwork), paint on the box without disassembling it. For the inside version, it's easier to cut it down its 4 vertical edges so you can fold it flat into a box net.

Mark a big cross on any surfaces you aren't going to decorate, like the South face and any assembly tabs, and then get to work. Avoid illustrating anything too 3D, just stick to things that are on the surfaces and reasonably flat. So, rugs on the floor and windows in the wall of a room are fine, but not furniture. Make at least some of the decoration continue around the corners from one surface to the adjacent one. If you're working on a flat box net, fold the cardboard back into a 3D structure every now and again to make sure the images flow properly across the joins.

When you've finished, photograph each of the 5 surfaces as square-on as possible, and edit them to make the surfaces into perfect rectangles before cropping away all the background. Both long sides (West and East) should have the same aspect ratio, as should Top and Bottom.

Photography

This is only going to work for smallish items as you need to be able to photograph the top and bottom surfaces as well as the two long sides and one of the short ends. As above, edit your photos to end up with rectangular images that fill the frame.

Online search

I didn't have a lot of success finding suitable box nets online, which is why I resorted to photography and using AI, but you may have better luck.

AI

I used Gemini, Copilot and ChatGPT to create images of the Georgian room I used in the next step. It was a bit of a struggle, I admit, but them I'm very much a beginner when it comes to getting the best from AI tools. I started by giving Gemini this prompt:

Create a box net showing the walls, floor and ceiling of a rectangular Georgian room with no furniture in it. One long wall should have a window with shutters. The wall opposite should have an oil painting of a racehorse in the style of Stubbs, with wall lights on either side of it. One of the short walls should have an internal door. The floor should have mahogany floorboards running lengthwise with a large oriental rug also running lengthwise and covering about 60% of the floor area. The ceiling should have coffered plasterwork. Each view of a wall, floor or ceiling must be orthogonal.

It took me a lot of further interactions to get the box net shown in the first image above, which has West and East walls that are too narrow as well as being in the wrong orientation. I tried using Copilot and ChatGPT, but they fared little better than Gemini (see 2nd image above). All 3 AI tools had problems when I attempted to get them to edit the images they produced to make them work as a box. In the end I used the GIMP to split the Gemini box net into 5 individual images and then edited the West and East walls to make them the same length as the floor. I also added in a better horse painting produced by ChatGPT. It was quite a frustrating experience, with two steps backwards for every one forwards, but it's certainly possible to produce usable images with AI if you persevere.

We need to resize the images created in the previous step and also distort those for the four surfaces (Top, Bottom, East and West) that are trapeziums rather than rectangles.

Start by making a list of the 5 surfaces with their dimensions. For the trapeziums, I used the Measure tool in Fusion to measure the height, that is the distance between the two parallel edges.

Top and Bottom: short side 82mm, long side 410mm, height 387.9mm

West and East: short side 72.2mm, long side 361mm, height 395.6mm

North: short side (height) 72.2mm, long side (width) 82mm

Also make a list of the dimensions of the 5 images you created. These are mine:

Top (ceiling) 410px x 410px

Bottom (floor) 410px x 410px

West wall 411px x 363px

East wall 410px x 360px

North wall 410px x 361px

I then asked Copilot, in relation to the West wall:

How can I use the GIMP to transform a rectangular 411 x 363 pixel image to a trapezium-shaped image with one of the parallel sides 72mm long, the other 361mm long and the distance between them 396mm? The non-parallel sides are of equal length.

And I got a really useful (but lengthy) step-by-step answer, which I will summarise as:

1. Convert mm to pixels, which at 300 dpi is 11.81 px/mm. This gives a target size for the walls trapezium of 851px × 4267px × 4678px height, ie aspect ratio of 4267 / 4678 = 0.91.
2. Aspect ratio of image is 411 / 363 = 1.13, which is wider than the trapezium. So image needs to be scaled up proportionally until its height matches the trapezium’s height. Scale factor = 4678 / 363 = 12.88. Scaled image width = 411 x 12.88 = 5295 px.
3. Open the image file, use Image → Scale Image and set the resolution to 300 dpi, then scale to 5295 × 4678 px keeping the aspect ratio locked. Resize the canvas to fit.
4. Create a new trapezium-shaped path with its corners at coordinates (1708, 0), (2559, 0), (0, 4678) and (4267, 4678).
5. Enable snapping by using View → Snap to Active Path. Then select the image layer and use the Perspective tool, dragging each corner of the image until it snaps to the trapezium path nodes.

That will give a distorted image that should fit the relevant surface of the truncated pyramid canvas in Fusion. Use an AI tool yourself to ask for more explicit instructions if needed.

All that remains is to export the image for use. Right-click the image layer in the layers dialogue and select Add Alpha Channel to enable transparency and create a transparent background. Use Tools, Paths and then Selection, Selection from Paths to select the trapezium shape, then invert the selection and hit the delete key to remove everything else. From the Layer menu, Crop to Content. De-select then export as a PNG file. (JPEG doesn’t support transparency.)

For the matching surface (ie the one that's the same size, the East wall in this case) you can re-use the path by copying it across to the new image, then you'll need to edit the nodes before using it for the other pair of trapezium-shaped surfaces (floor and ceiling in this case).

Getting the trapezium path the right way up can be confusing - remember, things nearer to the viewer must end up smaller than things further away - but it's easy enough to rotate the path through 180° if needed before doing the Perspective transformation. The North wall is much simpler, it just needs to be resized to a rectangle of the correct dimensions.

Now we need to apply the distorted images to our 3D canvas. Switch back to Fusion and from the Insert menu choose Decal and navigate to wherever you have stored the images. Select one of them and then select the face of the truncated pyramid it will go on. In the dialogue box, make sure Keep Aspect Ratio is ticked and Chain Faces is not ticked, then set the width to either S_height (for West or East) or S_width (for Top or Bottom). Rotate it by a multiple of 90° if needed, then move it into position.

Apply the other three trapezium-shaped decals in the same way, and then add the rectangular decal to the North face to complete the RP artwork.

In Fusion, try moving the viewpoint around the Georgian room artwork and note how odd it feels. Click on the orbit tool and drag it from right to left, which moves the viewpoint to the right. Normally, you'd expect that to give a better view of the left (West) wall with the door in it, but instead you see more of the right (East) wall with the oil painting on it. Similarly, tilting the artwork upwards gives a better view of the floor instead of seeing more of the ceiling. You'll probably lose orientation after a while, in which case spinning the whole object around to reveal its plain square back should help (see first image above).

Now try changing the Visual Style in Display Settings from shaded to wireframe. Spinning the artwork around to view it from the back (see second image above) now allows it to be seen with ordinary perspective, as a concave object with distant things smaller than near things. Moving the viewpoint around has the expected effects: tilting the artwork upwards gives a better view of the ceiling, for example.

You can create videos of these movements by switching to the Animation workspace, which is how I made the animated GIFs in this 'Ible. You can find instructions on how to create animations in Autodesk's Animating a design tutorial.

Referring back to Step 1, the alternative type of RP artwork involves using a concave canvas to represent the outside of a cuboid object. To create one, start by going back into the Fusion project and creating a new top-level component called Concave. Turn off the visibility of the bodies and decals in the Convex component but leave its sketches and constructed plane visible. In the Surface environment, loft the four sides of the base rectangle up to the vanishing point to create a pyramidal surface body. Split the body using the constructed plane then remove the unwanted tip and patch the resulting square hole. Stitch the patch to the rest of the pyramid. The end result is a hollow truncated cone surface body, as shown in the 3rd image above.

You can't add decals to the inside of a surface body which means it's necessary to thicken the surface body to turn it into a solid body first. Just thicken it by a small amount, say 0.1mm. When applying the decals, it helps to switch to wireframe view so you can see through the opposite surface to do the placement.

The animated GIF attached to this step shows photos of a box of Yorkshire teabags (an essential beverage in this part of the world) on the inside of such a concave canvas. It's less succesful than the convex Georgian room, I suspect because the proportions are wrong. It would perhaps have been better to have one of the long sides, the front of the box, as the North face instead of an end. It may also be that the pyramid needs to be truncated further away from the vanishing point than the 1/5 distance I used. These are things that can be investigated by experiment, likewise finding out what the best angle is for the pyramid (ie the angle between one of the triangular faces and the square base), given that the human cone of vision is about 60°.

Unfortunately, I haven't found a way to size decals parametrically, because the decals dialogue box only allows width and height to be specified and we need in addition the length of the short side to define the trapezium. Every change that's made to the 3D canvas will need the decals to be resized and reshaped in image editing software then re-applied to the surfaces and manually positioned.

You'll need to print out the 5 images to go onto a physical 3D canvas, so think about the size of printer you have available and work back from that. For a convex canvas, I suggest making it from cardboard and giving it a base (the South face), both for rigidity and to make it easy to attach to a wall.

Print the images first then stick them onto the cardboard in a cross shape (assuming the card is large enough), like the drawing above for the Georgian room, which is also attached as a PDF. If the net won't fit on a single sheet then some of the fold lines will need to become additional joints. Draw in an assembly tab on one of each pair of edges that will be joined, then cut the whole thing out.

Stick it together using glue on the assembly tabs reinforced with gaffer tape on the inside (for a convex canvas) or outside (for a concave one).