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I am creating artwork for a screen printing application that transfers the design to a pyramid shape using a silicone pad. How can I anticipate the distortion or better yet template the distortion so it will look correct on the piece even with new artwork designs? I print to a flat surface and pad print to the pyramid shape surface.

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    Why wouldn't the side of the pyramid not be flat? – joojaa Mar 3 '18 at 21:34
  • can't you simply place the pyramid at such angle that the printing surface is flat perpendicular to the printer? – Luciano Mar 6 '18 at 14:51
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Placing artwork on a pyramid is simple, if nothing continues over the seam. The content on all sides can be placed and positioned separately.

Let's have a pyramid. It's of the common type (=the sides are equilateral triangles). Place your artwork slices A, B, C and D onto the triangles:

enter image description here

The angles of an equilateral triangle are all 60 degrees => Rotate them with 60 degrees differences and align side by side. Here are 2 possible ready-to-print arrangements:

enter image description here

If your artwork happens to be designed for placing onto a pyramid or you do not care of straightness, fitting and symmetry, you can place the artwork directly on aligned triangles.

Designing a shape which fits on a pyramid and continues over seams is discussed here:

Designing repeating pattern for top section pyramid

Things start to be tricky, if your drawing (which can also contain some texts) isn't designed for pyramid and you want to print it over a seam to have enough room. How to map the image without losing the continuity on the seam? In addition the texts must be well readable over the seam and all graphic shapes must be recognizable, preferably like there's no seam at all.

We try few different methods with a random drawing. It should be placed to cover a good part of 2 triangles The red line shows the wanted place of the seam.

enter image description here

The texts have intentionally letter spaces on the seam. This is optional, but it reduces the needed accuracy and there's no need to split individual characters.

The simplest approach is to place the drawing as is, Here it's as flat and as seen on a pyramid. The 3D view is "perpendicularly towards the seam" It's nearly the isometric projection, but seen from a little higher angle, just about to reveal the back side => 3D "renderig" is made simply by squeezing horizontally to 82% (checked in a 3D CAD program) and adding some shading

enter image description here

If the drawing is stretched horizontally to 121% before placing, the 3D view would be undistorted:

enter image description here

Unfortunately the view is perfect from that one direction. From elsewhere it seems tilted and distorted. Here are 3 different views of the same arrangement as a screenshot from a freeware 3D CAD program (the drawing is stretched to max size):

enter image description here

The texts are tilted and they have a sharp reading direction bend on the seam, when the watching direction is not the optimal one. You must radically distort the drawing to make the reading direction continuous or at least natural looking (=horizontal). Unfortunately that really means heavy distortion. There are infinitely different possiblities, but we discuss 2 of them. See the flat images:

enter image description here

In the left there are drawn (=blended in Illustrator) parallel lines which are horizontal after the triangles are bent to pyramid.If text are forced to follow these lines, their reading direction is natural altough there's an angle at the seam.

In the right there are circular arcs. Texts will continue smoothly over the seam, if they are forced to follow the arcs.

NOTE: Actually the texts must be curved only at the seam. They can be horizontal to the left from the red line and to the right from the green line. We skip the mixed version

Forcing texts along circular curves without splitting the drawing to parts is possible with Illustrator's Envelope distort. Preset warp pattern "Arc" works for this:

enter image description here

  1. the drawing is placed in and grouped with a rectangle. Its midpoint is on the wanted place of the seam.

  2. the drawing is placed on 2 adjacent triangles. The drawing is squeezed horizontally about 50% because warping will make it wider

  3. Envelope distort > Make with warp > Arc > Horizontal -66,7% is applied to generate 120 degrees arc

  4. Envelope distortion is expanded, everything is ungrouped, all extra parts are deleted. The simplest 3D view is formed by shading the triangles and squeezing all horizontally to 82%.

We see the bottom of the drawing is bloated. It would be useful to redraw it. Just in this case it would be easy, because it's a curve with a pattern brush. But that's actually like the drawing was redesigned to fit on a pyramid.

Forcing the text lines horizontal is possible by applying Illustrator's transforms. Left and right halves need opposite deformations. Most easily this is done as follows:

  • split the drawing to separate parts along the wanted seam line. Group both halves with an equal rectangle
  • apply every distortion step mirrored to both halves.

An example:

enter image description here

  1. The drawing is splitted and the halves are temporarily shifted apart.Both halves have got a grouped rectangle to make the sizes equal. Splitting is actually made by duplicating and inserting opposite clipping masks.

  2. The halves are skewed. It's Object > Transform > Shear > Vertical, angles are +30 and -30 degrees.

  3. Both halves are selected at the same time. With the free transform tool bottom corners are dragged apart and top corners are pushed closer each other

Step 3 is optional, skewing can be enough. NOTE: The free transform tool is tricky. To drag a corner you must

  • select the object or objects
  • hover the mouse over the corner until the drag arrow appears and the rotation arrow goes away
  • press and hold left mouse button without moving the mouse
  • press and hold the Ctrl key
  • drag the corner

To drag 2 adjacent corners symmetrically holding Ctrl isn't enough, you must at the same time hold Ctrl, Alt and Shift keys. If you stop dragging and want to continue, you must start from the hovering.

Here are the results as simplest 3D rednerings (= extra parts removed,shaded, squeezed horizontally to 82%):

enter image description here

If you make these as physical printed pyramids, they would not look right (tested) because there's a conflict. The drawing is printed on the tilted surface of the pyramid, but it's like a vertical folded poster. Eyes do not find the right interpretation. It can be helped by adding some detail which make the lie "they are folded vertical posters" stronger:

enter image description here

I tried this in practice (=printed a non-squeezed version, clipped the extras off and folded it to 90 degrees). Watching it only one eye open (=no stereo) the eye suddenly accepted the lie. It took about ten seconds to forget the stereo view. => When watched both eyes open, the distance must be several meters

Done.

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I do not understand what is the distortion, because I asume a pyramid has flat faces.

If you are looking for a specific projection, for example seeing the image from a top view, a cenital view, I would use a 3D program like Blender, project the image and unwrap the texture.

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The first option that you have would be to create a grid on the flat transfer surface large enough to encompass the pyramid. Use lines of sufficiently small spacing and as thin as possible, to get best resolution.

Cover your pyramid with removable printable material (paper?) and perform a transfer print.

When you unwrap the paper, you'll have a clear outline of the printable surface. That's one step accomplished for your template.

The grid pattern you've now printed will be distorted to match the contours of the pyramid. If your pyramid consists of only flat surfaces, you should have a clean grid on the paper. If there are contours/curved surfaces, the grid will be distorted an appropriate amount.

It would be necessary to scan in the paper to transfer the grid pattern to an image editor such as Photoshop or Paint Shop Pro. I use PSP and occasionally "un-distort" an image. In the case of your grid, you would use a similar method and create a template for that tool that would duplicate the distortion in the opposite direction for your art work.

Alternatively, less easily accomplished and dependent on one's skill with 3d modeling programs (Blender comes to mind), you could model the pyramid to scale, create a grid to represent the texture of the model and impose it on the model. Once placed, you would then "unwrap" the grid to create your template.

Texture in the above context refers to assigning colors, gradients and images to surfaces of a 3D model.

I see Rafael has provided for this same option in his answer, posted while I composed mine.

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I have worked with pad printing many years ago, and we did print on many irregular surfaces.

To reduce problems we always fabricated a special cradle for the object to be printed on, to make the surface as horizontal as possible (our printers had a vertical axis).

You don't need to worry about distortion due to the shape of the pad, because if the pad applies the same amount of pressure to the image plate (the one with the ink) and the printing surface the print should transfer without distortions.

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The true answer to the distortion replies is this is a square bowl that is upside down to print the out side. The bowl comes in 3 sizes. I expect that a flat screen print transferring to an upside down square bowl will distort. Other bowls will also be in the mix that are round and steep sided. All new kinds of process challenges we are not currently versed in. 3D modeling is possible. Solidworks can output in photoshop or illustrator formats but I do not know if the are still 3D when opened. Heard of Blender but not familiar with it.

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