For information on what “radii ends” are, visit the “Spiderweb Education ” page linked to at the top of this page.

These points cannot be placed too close to each other or to the hub. They can be dragged after being placed.

To delete one, click the “Delete One” button; the cursor will become a “delete” icon until pressing the Escape or Backspace key or clicking. It will revert when you click anywhere on the page, but if you click on a radius endpoint, that point will be deleted.

To delete all of them and start this step over, click the “Reset” button.

The radius points must form a convex polygon with the hub inside (that the hub is inside is tested using substack’s point-in-polygon algorithm, licensed under the MIT License). This refers to the geometric relationships between radius points.

For more on convex polygons, please consult Wolfram’s MathWorld encyclopedia article on convex polygons.

The algorithm this page uses to test for a convex polygon is to:

1. Call the hub the origin of a polar coordinate system.
2. Pick a direction to be 0°.
3. Determine the angular coordinate of each web radius point in this coordinate system.
4. Order the n web radius points ordinally by their angle, p₀ through p_n-1.
5. Let these points be indexed modulo n so that p_n = p₀, p_n+1 = p₁, and so on.
6. ∀ p_i ∈ [p₀,p_n-1], find z_i, the z-component of the cross product (p_i→p_i+1)⨯(p_i+1→p_i+2).
7. The test is to make sure the sign (positive or negative) of all z_i are the same. Credit to Jason S on StackOverflow.