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I saw a video on YouTube where a person uses a transparant, knotted pyramid to display "holograms" using their smartphone. (I have not been able to reproduce this yet, so I can't tell for sure if it works).

I was wondering, given a model, which transformations I should apply to get the different projections needed to produce this effect?

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    $\begingroup$ Please don't call these optical tricks "holograms". Refer to the "Things often confused with holograms" for an overview. In this case, you're talking about a classic Pepper's ghost illusion. No 3D at all, apart from having 4 different perspectives. update: I've proposed an edit to adjust the question accordingly. $\endgroup$
    – waldyrious
    Commented Aug 7, 2015 at 16:13

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Assuming your optimal viewing angle is parallel to the surface of the display and the pyramid is made from faces that are 45 degrees to its virtual (non-existant) base, it's actually just a simple non-transformed image (besides the reflection).

1:1 projection. No transformations. No scaling.

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    $\begingroup$ For more information, see Pepper's Ghost $\endgroup$
    – Mark
    Commented Aug 9, 2015 at 9:12
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    $\begingroup$ Its an interesting comment about Pepper's ghost. Notice that Pepper's ghost was originally a reflection of a 3D object so the reflection itself was 3D. In the case of these popular device based projections, the projections are only 2D so the effect is only a 2D reflection suspended in space. The most popular Youtube videos meant for doing this don't even have 4 different perspectives, just 1 repeated 4 times. $\endgroup$
    – Octopus
    Commented Aug 10, 2015 at 15:19
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I was wondering, given a model, which transformations I should apply to get the different projections needed to produce this effect?

There are at least 2 types of videos and many ways to produce them. It is technically correct to call this effect Pepper's ghost but you will obtain more relevant search results by searching for: "Smartphone 3D Hologram" (over 2 million hits).

To make the projector you'll need: graph paper, CD case, marker or pen, pair of scissors, Cellotape and/or superglue, craft knife or glass cutter, and a smartphone or computer monitor.

  1. Draw one side of a square frustum on graph paper and cut out 4 shapes from a CD case.

  2. Tape and/or glue them together and place it top down on the center of your cellphone screen.

Holographic Smartphone Projector

To make videos there are two kinds to choose from, one image rotated 90° and repeated, or four different images representing each side of the image. Whichever style is chosen each image is placed in a quadrant around the center of the screen.

Use this for a template:

Holographic Template

To make the simple rotated image use a program such as AVISynth or PowerDirector, load the video into the Timeline, add a grid, duplicate the track 3 times, rotate each track 90° and place it in one of the quadrants.

4 Videos, rotated 90°

The second type of video is produced from 4 seperate images each rotated 90°, this provides a different view from each side. It's difficult to produce a live video of this type, align everything perfectly, and not get the opposing cameras in each other's shot. It's easier to create an animation for this purpose. It should look like this:

Dancing Girl

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