Why are two “Mapping Nodes” in Sequence needed for Volumetric Tunnel?

[spikeyxxx]

Why the ‘squashed’ sphere wouldn’t rotate is because Blender (and probably 3D Graphics programs in general) use a trick to calculate a sphere: they say, a sphere is an object with a constant distance (called radius) to it’s centre. This works in 99.7% of all cases, but sometimes it fails. The advantage of calculating a sphere this way, completely outweighs the sporadic ‘failures’/bugs.

Say we take a look at point (0, 0, 1)) which lies on a sphere around the Origin with radius 1. 

Now scale this point by 7 on the X-axis. Now it is point (0, 0, 7) and it’s distance to the Origin is now 7, meaning that the sphere intersects the Z-axis at (0, 0, 1/7). (Does this still make sense?)

Rotate the point 90° (for simplicity) around the Y-axis and you get (7, 0, 0), but the distance to the Origin is still 7, so the sphere still intersects the Z-axis at (0, 0, 1/7).

In my original explanation I mixed distance to Origin of a point with length of a vector, which makes it more confusing, but it’s all the same in 3D.

I hope this helps, it’s rather difficult to explain 🙂

[Matthew Fricker]

Sorry to go off topic here but @theluthier could you explain your workflow for making those GIFs of you working in Blender? I know how to make them in Photoshop from individual animation frames but how do you go about doing it from a screen recording? Thanks! 

[spikeyxxx]

@frikkr there are web applications to make GIF’s out of anything…. ezgif is quite good. There is also a Linux app called Peek that lets you make a (partial) screen recording and saving it as a GIF…don’t know if it’s available for other platforms.

[Ingmar Franz]

@spikeyxxx Thank you for the in-depth explanation👍! I have to study it tomorrow with a rested head 😉. Good night 🛌🌛⭐😊!

[Ingmar Franz]

Say we take a look at point (0, 0, 1)) which lies on a sphere around the Origin with radius 1. 

Now scale this point by 7 on the X-axis. Now it is point (0, 0, 7) and it’s distance to the Origin is now 7, meaning that the sphere intersects the Z-axis at (0, 0, 1/7). (Does this still make sense?)

@spikeyxxx  Why doesn’t the sphere now intersect the z-axis at (0, 0, 1/7)? Isn’t it the point (0, 0, 1) that is scaled away from the x-axis?

[spikeyxxx]

@duerer good catch! That was a ‘typo’; should indeed be the X-axis.

[Ingmar Franz]

@spikeyxxx And if it’s still a sphere with one surface point at (0, 0, 7), how can this sphere intersect any axis at 1/7 ?

[spikeyxxx]

@duerer the point (1, 0, 0) is being mapped to (7, 0, 0), but it is still called (1, 0, 0). 

The  distance from the Origin to the ‘new’ point (1, 0, 0) is 7.

The distance from the Origin to the ‘new’ point (1/7, 0, 0) is 1:

That is why the sphere intersects the X-axis at (1/7, 0, 0).

When we now rotate around the Y-axis by 90°, the original point (1, 0, 0) is being mapped to (0, 0, 7), but it is still called (1, 0, 0).

So the distance from the Origin to the (scaled and rotated) point (1, 0, 0) is 7.

That is why the sphere still intersects the X-axis at (1/7, 0, 0).

It is difficult to wrap your head around, I know 😉

[spikeyxxx]

@duerer maybe this helps:

The Mapping Node (Type Point) doesn’t move points, but ‘maps’ them to other points; meaning that when point A gets mapped to point B, it stays where it is, but gets ‘all’ the properties from point B (apart from Location…).

So, in our little example, point (1/7, 0, 0) gets first mapped to point (1, 0, 0), meaning it gets, amongst others, the property ‘lies on a sphere with center (0, 0, 0) and radius 1’. Rotating it 90° around the Y-axis will map it to point (0, 0, 1), which happens to also have the property ‘lies on a sphere with center (0, 0, 0) and radius 1’.

[Ingmar Franz]

@spikeyxxx Thanks for your patience 🙂! I think I’m getting closer to what you mean 😀. Now I have to practice a little bit 😉. 

[spikeyxxx]

@duerer with things like this, that seem hard to understand, I find it helpful to read/listen to several, different explanations and think about it a few times, until you suddenly get that ‘Aha-moment’ and it all becomes sooo obvious, that it is hard to remember how it was when you didn’t ‘get’ it 🙂

You don’t have to thank me for my patience; as long as you don’t understand my explanations, that means that I haven’t  explained it well enough and maybe even that I haven’t understood it myself completely. In both cases, it’s my rersponsibility to do something about it 😉

[Ingmar Franz]

Thank you again, @spikeyxxx 😀!

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