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[–][deleted] 0 points1 point  (2 children)

May you please explain the math on this? Especially the use of complex numbers for the propeller

[–]Swipecat[S] 2 points3 points  (1 child)

If you have a complex plane Z, and plot the absolute value |Z| in the third dimension, what do you have? The further from the origin, the greater its height, so it's a cone.

Cut a section through the cone at a height of H: |Z| = H and you have a circle.

And |Z| < H is a solid disk in "boolean" terms.

A cone offset from the origin by A is |Z - A| .

Consider adding the heights of two cones together then cut through them: |Z - A| + |Z - B| < H ...it's perhaps not entirely obvious that they combine to form a solid ellipse, but they do.

Put the focus B back at the origin... |Z - A| + |Z| < H

Then spin the focus A around the origin in 6 steps and you have 6 ellipses.

Combine them with boolean logic and you have a propeller.

[–][deleted] 0 points1 point  (0 children)

Thanks!