Inspired by my last post that showed the geometry of pseudo-twisting, I decided to apply it to actual twisting of helices. And as I expected, I learned new things applying the logic I’d learned before.
So here is a reminder of what the pseudo-twisting image looked like:
Here the emphasis is on the green cone of refraction and not on where this cone is derived from. Looking it the image more closely, the length of the slant of the cone is twice the diameter of the dot (depicted as a translucent sphere). So, if there is twisting, the dimensions of the cone of refraction can be determined by adding a sphere of refraction to the image. As noted, the sphere has twice the radius of a dot. Also, you can introduce a ring of refraction to the intersection of the cone with the sphere. This also means that when there is twisting, the two rings of refraction of neighboring dots no longer the same but are separated by a distance determined by the degree of twisting. In this case it’s okay to replace the cone of refraction with just the sphere and ring of refraction to avoid cluttering the image.
So, this is how it looks like:
And the same image from the front:
And directly from the side:
Which of course looks almost exactly like the image at a slight angle.
Now that I have all the necessary geometrical components to describe this twisting, the new/corrected equations shouldn’t be too difficult to determine. Except I already know the next problem I must tackle. But that will be the subject of another post.
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