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Can someone explain to me why a cylinder with this node tree becomes a double-sided cone?

I have tried to check it and to calculate it by hand using a vector $(3,0,0)$ but can't figure it out. The green dotted line is supposed to represent the side of the cylinder befor the math operation. Somehow the vector $(3,0,0)$ must become the vector $(0,0,0)$.

In the node tree, the separate xyz node takes the $z$ value and makes it the $x$ and $y$ value of the new vector, while $z$ is defined as $1$.

Then the vectors are multiplied with each other. I am not a mathematician but according to chatGPT the cross product can be used to calculate this. obviously $(-3,-3,3)$ is the result. But it must be $(0,0,0)$.

SCreenshot

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    $\begingroup$ That position node is a field node, and will not reference the object location, but instead the position of each point as it is processed through the tree. $\endgroup$ Feb 2, 2023 at 21:45
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    $\begingroup$ Oh I misunderstood your test case $\endgroup$ Feb 2, 2023 at 21:50
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    $\begingroup$ Cross product is different, vector multiply is multiplication straight across, so the result here is 0,0,0 $\endgroup$ Feb 2, 2023 at 21:53
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    $\begingroup$ You're multiplying the position vectors of all your points by 1 on the Z, so their height does not change. But you're multiplying their horizontal placement (X and Y values) by their heights. The ones on the upper part just get bigger since they're being multiplied by a positive number, but the ones on the lower part "flip" (all the while getting bigger) since they're being multiplied by a negative number (their Z is below 0). Since the bottom "flips" but the top stays fixed, it twists, creating this cone shape. $\endgroup$
    – Kuboå
    Feb 2, 2023 at 21:57
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    $\begingroup$ Here's a demonstration of what's happening: i.imgur.com/Ewp7DX6.mp4 $\endgroup$
    – Kuboå
    Feb 2, 2023 at 22:12

1 Answer 1

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First - I would strongly recommend against using ChatGPT as a general knowledge engine. It has frequently been shown to provide confident, totally incorrect answers. For instance, the cross product of $(3,0,0)$ and $(0,0,1)$ is $(0,-3,0)$, not $(-3,-3,3)$

Second, you're using element-wise multiplication: for vertices on the center circle of your cylinder $(z=0)$ and your current node setup, you're performing

$(x,y,z) * (z, z, 1) = (xz, yz, z) = (0, 0, 0)$

Change your vector math node to "Cross Product" and you should be in business.

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  • $\begingroup$ @quellenform Careful, ChatGPT will come for you one day :) $\endgroup$
    – Neil
    Mar 17, 2023 at 13:45
  • $\begingroup$ @Neil Seriously, I prefer to learn and know things myself rather than depend on an AI. Therefore: Rather no, because the day will come when real knowledge counts, completely independent of an assisting mechanism ;-) $\endgroup$
    – quellenform
    Mar 17, 2023 at 13:49
  • $\begingroup$ @quellenform I agree with you, we definitely need to avoid reliance on AI, but I'm certain it's going to be a valuable tool for us in many ways. $\endgroup$
    – Neil
    Mar 17, 2023 at 13:57

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