Calculating displacement maps based on reference maps

I already blogged about this, but I saw that some items could use some more explanation. Please read “Getting the displacement you need” first for the basic idea.

In short the principle is:

  • you have a reference map, say A
  • you apply a distortion effect to the reference map created a distorted version of A say A’
  • you calculate the displacement map that could transform A into A’ by calculating the difference in pixel value between A and A’

Difference process

Some important points before we start:
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Panoramic projection using displacement mapping

In this post we will be looking at the creation of a distorted panorama using a displacement map. The two examples below show the difference between a panorama without and with distortion (notice how in the distorted version the grid bends):

Panorama without distortion ( NondistortedPanorama (633 downloads) )



Panorama with distortion ( Distorted Panorama (714 downloads) )



Some simple tricks to note up front: Read more

Getting the displacement you need in ActionScript 2

In my previous post I explained the basics of displacement mapping, and I promised to tell something about getting the filter to do what you want it to do. Well, in order to do so, let’s look at the picture I showed you again, written a little differently:

+ *? =

where ? is an unknown scale factor

It says that given a source image, if we apply a displacement map multiplied by some scaling factor, we will end up with a result image. If we look at the visual formula written like this:

ImgSource + DispMap*ScaleFactor = ImgResult,

we can see that with some basic math we get:

ImgResult – ImgSource = DispMap*ScaleFactor, in other words:

= *?

This tells us that if we have the source image and the result, that we can in theory calculate the displacement map, but since the displacement map is related to the scalefactor, there is not a single result.

Would this simple idea gives us the one possible displacement map that caused the transformation of ImgSource into ImgResult?

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Displacement maps basics

I was working on the Bitmap API and the Displacement map filter and although there was some info available on it, it takes some time to get it to do what you want.

Basically a Displacement map is a BitmapFilter, in other words: it moves around pixels.

If you would take a source image and apply a transform to each pixel from the viewpoint of the source image, pixels might end up all over the place and some pixels in the destination image might remain unset. This is usually the way we think about transformations though: we have a source, we apply a transform and get something new.

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