Java: Math line design

Question

Have anyone seen this mathematic line design before and perhaps have some pointers on how to generate it? Preferably using Java.

enter image description here

It looks very similar to a problem where 4 dogs, on vertexes of a square.. starts running towards each other at equal speed. Each line here is a tangent, denoting current direction of dog at time t. — Nishant, Sep 04 '12 at 09:21
See http://mathtourist.blogspot.co.uk/2010/06/square-pursuit.html which also points to an algorithm for drawing the figure. — High Performance Mark, Sep 04 '12 at 09:29
It's just scaled and rotated squares drawn upon one another. — Alexey Frunze, Sep 04 '12 at 09:50

score 1 · Accepted Answer · answered Sep 04 '12 at 11:03

You start with the outer square (rectangle, quad).

1) Draw it.
2) Move each vertex 10 percent of the way towards its neighbor.
3) repeat starting at #1.

The slightly tricky part is in step 2. If you move vertex 1 toward vertex 2, then 2 toward 3, 3 toward 4, the last thing is to move vertex 4 toward where vertex 1 WAS - not where you moved it to. The simplest way is to make a copy of vertex 1 first - call it vertex 5 - and move each vertex toward the next one in the list.

10 percent is an adjustable parameter. Now, to move some percent of the way you can use a weighted average:

x1 = x1 + (x2-x1)*p
y1 = y1 + (y2-y1)*p

where p is 0.1 for 10 percent.

This ensures that the new vertex lies on the line drawn between the 2 old verticies in each case. It works with all quads, not just squares. This is also the beginning of understanding splines.

Java: Math line design

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