Messy indices on the right please

In case you don’t know, indices are the plural form of index. Wait, isn’t the plural form of index, indexes? Well, indexes is the plural form, if you’re talking about database table indexes (I’m confused at first too). I’m referring to the offset of an array, the index of an array.

So what do I mean by messy indices on the right? Variable assignment. I mentioned something of this in the matrix rotation article, and I want to talk more on it here. And I will tell you why I prefer them on the right side of the assignment. First, I need to mention raytracing.

Tracing a light ray from the eye back to the scene

In 3D graphics, a scene is rendered and you need to know what colour each resulting pixel is. You can throw light rays everywhere, let them hit an object, bounce off that object, and continue bouncing and if that ray happen to shoot through to the camera, render it. That doesn’t sound very efficient, does it?

There are millions of light rays to shoot from a light source. They can bounce off objects in any number of ways. And only a small percentage of them will ever enter the camera.

Raytracing simplified

What you can do is, start from the camera. Trace a ray from the camera through the resulting pixel, back out into the scene and see what it hits. If it doesn’t hit an object, it will travel all the way into the sky or space. Render accordingly. If it does hit an object, continue to track the bounced (or reflected) ray until it hits nothing. Or hit a light source. Either way, you know how to render the colour. It’s a bit more involved than that, and I’m simplifying the explanation.

Basically you start from the end.

Rotating the square matrix

Let’s revisit that rotating-the-matrix problem.

For Y = 0 to 3
    For X = 0 to 3
        Destination(3-Y,X) = Source(X,Y)

Essentially, the author concentrated on the source, iterating through it with appropriate indices and assigning those values to the destination. See how “messy” the indices on left side are? I call it, the “throw values over” assignment:

Throwing values over

Then there’s the raytracing way, the “finding values” way:

Finding values assignment

There doesn’t seem to be any difference between the two. Until I tell you about rotating images…

Rotating an image 30 degrees clockwise

Suppose you want to rotate an image in non-right-angled degrees, say 30 degrees clockwise.

Rotated image outside rectangle

We can discuss the code to rotate the image some other time. Hmm… new article fodder…

Anyway, you can start from the source image, iterating through each pixel and “throw values” to the destination image. Or you can start iterating the destination image and “find values” from the source image. Each method requires you to check the boundaries of the image (index must be within width and height).

If both seem equivalent, what’s the problem? Image quality.

You see, with the algorithm involved, there’s the possibility that you’d throw different pixels from the source image onto the same pixel on the destination image. You’d be doing sine’s and cosine’s and rounding the calculation into an integer so you can map it to an index. This isn’t good, since you can override a previous calculation.

With the “find value” way, you have a similar problem. There’s the possibility that for different pixels on the destination image, you’d map back to the same pixel on the source image. However, you don’t have to use the exact colour of that source pixel. You can use interpolation to get a sort of “average” colour from the surrounding pixels.

You know, I should write something on the image rotation part. Alright, coming up soon, an image processing article focused on image rotation!

And that’s the reason why…

I prefer the messy indices on the right side of the assignment. Because I start from the end (or destination), the iteration indices are “clean” on the left side.

And now, homework! See if you can come up with code (or algorithm) to rotate an image any number of degrees, assuming the rotation is about the image’s centre. You can make it easier by rotating about the top-left corner. And you have to iterate through the pixels, not use some in-built function to manipulate the image. You can also make the image black and white, so you focus on grey values instead of an RGB triplet, to make the code simpler to write.

If you’re adventurous, and want to try the interpolation thingy to make the resulting image look better, you can research on linear interpolation and cubic splines.

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