Readit NewsInteresting to note that the parametric equations of the spiral are linear in spherical coordinates. https://en.wikipedia.org/wiki/List_of_common_coordinate_tran...
* I wrote a similar article around making "blobs" a while back: https://www.hailpixel.com/articles/generative-art-simple-mat...
thanks for sharing! definitely an inspiration, I might use it for next project :D
The equation used creates a visually appealing result but I’m wondering what a good goal would be in terms of consistency in the distance between the spirals, or evenness in area divided, or something like that.
How was this particular function selected? Was it derived in some way or simply hand-selected to look pleasing?
that was also my first intuition when making this, but turned out making the z function linear won't make it a sphere.
to make a sphere, you have to configure it in a way so that it forms a circle with the other axes. In this vis, its the sin(0.02 * πt) and cos(0.02 * πt) part that do this.
someone makes an interactive version here: https://www.desmos.com/3d/t66etxi1y8 (thanks!) so you can try changing the z function for yourself.
thanks for the feedback!
The part that I was expecting to see but didn't: how can you move at a constant speed? For the original purpose of positioning objects along a path, it doesn't matter. But when moving, you can see it's moving much more slowly at the beginning and end (mostly determined by the radius). What if I want it to travel at a constant rate? Or even apply an easing function to the speed?
I'm sure there's some fancy mathematical trick that would just do it. If I were only more comfortable with math... my handwavy sketch would be to compute the speed function by differentiating the formulas to get dx, dy, and dz and passing them through the Pythagorean equation, then reparameterize on a t' variable using the inverse of the speed function? Maybe? I feel like I'm speaking using words I don't understand.
currently the path is expressed as function of (t), and it's the t that progressed at the constant speed.
so the cube will finished one loop at the same duration, and thats why it moves much slowly at the beginning and end, where distance of one loop is smaller.
I have to admit I made it that way because it's simpler to implement:D. Making it move at constant speed require some more works, but others have provided some solutions here so I think I'll try
If you want really great further consideration of creating geometric figures with parametric equations, Joseph Choma's book "Morphing" is an all-timer.
https://www.quercusbooks.co.uk/titles/joseph-choma/morphing/...