0

We know that equation of a helix that propagates along z axis is - X = Rcost, Y=R Sint, Z = at. If we vary the t and plot points, entire helix will be created.

However imagine one wants to assemble tiny lines one after another such a way that they put together, creates the helix approximately. We thought of an approach here - 1) Take two points in helix carve - a. (X,Y,Z) on above equation for time = t, b. (X,Y,Z) on above equation for time = (t + t1).

2) Try to figure out the (angle, axis) pair between two lines using this link.

3) Rotate small lines in 3D space along this (angle,axis) pair and create an series of lines for the helix.

However, this approach isn't working right - we tried checking the equations, but they seem right.

Is there a better approach to find the alignment of these lines along a Helix curve.

Any help is much appreciated!...

Regards.

Ahant
  • 1
  • Why not just use segments $[f(t_k),f(t_{k+1})]$ where $f=(X,Y,Z)$? – MPW Oct 27 '19 at 18:24
  • Sorry, I didn't get you. Can you please elucidate a bit. – Ahant Oct 27 '19 at 20:27
  • MPW was saying : there is an evident answer to your question : you select points, say at times $t_k$ on your existing helix and join them by a straight line... Why do you need a more complicated solution ? – Jean Marie Oct 27 '19 at 23:46
  • Pick a few points on the helix. Draw the line segment between successive points. This makes a chain of line segments approximating the helix. Why would you do anything else? – MPW Oct 28 '19 at 02:01
  • Okay I see. So I could draw the points. But I want to crate it with a set of elements. For example a series of alternating tubes and torus. Or a series of triangles.

    So then I have an element which is upright (along the y axis). I calculate the point where it's base should be - that is the last point tk. Then I calculate (angle,axis) to move to tk + 1 and align the element along that angle, axis and I proceed.

     – Ahant Oct 28 '19 at 12:03
  • (This will be used for creating some structure in game etc. Of course we can create it in Blender and loop it. But doing through Math is more flexible and more fun. It also challenges us to more things that way. We need to calculate how much GPU/CPU horsepower these rotations burn though.

    These lines within bracket may be of the topic of math.stackexchange . Just to clarity the background...)

     – Ahant Oct 28 '19 at 12:07
  • "for example alternating tubes and torii" : OK, this is very precise, but you use "for example". Be precise, in order to get precise answers. What you have asked at first is too general. – Jean Marie Oct 28 '19 at 17:21
  • Let us say that you want to build a swimming pool slide having an approximate helix form by assembling pieces of cylinders and pieces of torii ? – Jean Marie Oct 28 '19 at 17:25
  • Yes - that can be a perfect use case. I mentioned as example simply because there are many potential use-cases and I wasn't thinking only one. – Ahant Oct 28 '19 at 19:16
  • I also thought about creating a quaternion to represent orientation of this small line but I guess they are mutually exchangeable format.

    The option than calculating two points and finding orientation of a line connecting two points - I could think of - is simply add find a derivative of the equation. So for a simple sin(x), dy/dx provides the cos(x) curve and that cos(x) value represent orientation angle at that point.

    Would doing a derivative of individual equations and collecting the angle to three axises will give the Euler Angle orientation of the curve at that point...?

     – Ahant Oct 28 '19 at 19:23
  • Thanks a bunch for sharing your thoughts!.. – Ahant Oct 28 '19 at 19:27

0 Answers0