# How can I describe the 3D effect that is caused by rotating lines inside a circle?

I noticed an optical illusion of a 3D globe caused by rotating lines around a circle. As demonstrated by this codepen. Especially at Multiplayer time 22, 24, 27 when the number of points are increased to maximum. Here is a screenshot of it: The effect is much more pronounced when the lines are in motion.

## Is there a way I can invoke this effect intentionally?

I'm curious if this effect has ever been used strategically for visualizations or graphic design?

• It reminds me of 1970s nail and string art. See example here – Billy Kerr Feb 9 at 10:20
• The still image has essentiallf produced a cross-hatch shaded sphere. The density of the lines around the edges is high and decreases as you near the center. Add to that the consistent crossing of lines at certain angles that visually creates contours, and the 3D effect is almost inevitable. If the distribution hadn't been so centered, it may not have looked so round. – Web Head Feb 11 at 5:57

Every line can be a projection of an arc along the surface of a sphere. Those arcs are drawn for ex. from equator to equator and you watch them from far above the north pole. All arcs happen to be in planes which are seen exactly sideways.

Actually the arcs can be also deeper inside the sphere or outside it as long as they are in the planes which are parallel with the watching direction and the seen projections happen to reach from equator to equator.

The arcs can be arbitarily complex, even discontinuous curves as long as their twists are seen only sideways and the discontinuities are hidden by seen overlaps.

So, it's not the image of an unique 3D composition. There are infinitely different 3D compositions which can produce the same seen 2D projection. The composition contains the curves and the used 2D projection.

I believe the family of ALL possible 3D causes for the seen 2D result has no commonly used name. But this is only a belief.

In 2D the lines are all possible chords drawn to equally spaced directions from equally spaced points on a circle curve. In 3D one of the possiblities is the same drawing that you already have in XY plane, but the plane is watched from Z direction.

A widely used name for your 2D pattern can exist. Ancient astronomers with their earth centric sky model needed chords for their calculations and they had made chord tables to reduce the calculation effort. At least Ptolemy and Hipparkhos had them. Unfortunately my knowledge ends to these splinters. If the subject is interesting, read this for a start: https://en.wikipedia.org/wiki/Ptolemy%27s_table_of_chords

I see it's also possible that this pattern can be seen as a western misconception of some Indian graphic art style.

You may see the pattern as a shaded sphere. That's not nonsensense because one possible 3D cause of the pattern is a bunch of arcs along the surface of a sphere. Free holes between the seen lines are biggest in the middle and smallest at the edge. With some tough math or numerical analysis one could tell how well the lines approximate some generally used shading formula of a sphere.

# String Art

There's a manual art called String art which consist in an arrangement of colored thread strung between points to form geometric patterns or representational designs. Wikipedia

Though straight lines are formed by the string, the slightly different angles and metric positions at which strings intersect gives the appearance of Bézier curves (as in the mathematical concept of envelope of a family of straight lines). Quadratic Bézier curve are obtained from strings based on two intersecting segments.

I didn't find any tutorial but many examples about vector string art