How to create an internal spiral for a polygon?

Question

For any shape, how can I create a spiral inside it of a similar shape. It would be a similar idea to limit (using the Minkowski sum). Instead of creating the same form inside the form, although it would be a spiral of the same shape.

I found this - http://www.cis.upenn.edu/~cis110/13su/lectures/Spiral.java

It creates a spiral based on the parameters passed, so it can be for any regular shape.

I want the above for all shapes, for example, irregular polygons.

I am not very familiar with geometric terminology, but I searched for Involutes and the internal spiral search algorithm too, but was not useful to me.

Does anyone know where I will find an algorithm like this or at least ideas about how I came up with one of them?

Answer 1

this task is extremely difficult to do.

• you must have a boundary polygon that you want to fill with a spiral

  I think you already have

• create a new smaller polygon by moving all the lines inward to the step.

  This is like creating a dash line around a polygon. The pitch is the width of the screw, so at the beginning of the polygon it is 0 , and at the end it is d

• remove invalid rows from newly created screw

  Some lines at the corners and curvature will intersect. It is very difficult to detect / recover reliably after seeing

  • this for the basics

• repeat (make the next screw) ... until a place for the screw is found

  But now, after the first screw, the step is always d , this will not necessarily fill the entire form. For example, if you have a thinner spot on the figure, it will fill up much faster than the rest, so some holes may still remain.

  You must discover them and process, as you see, see

  • Search for holes in 2d point sets

  Know that detection, if the area is full, is also not trivial

Here's what this approach looks like:

[Note]

If you forget about the spiral and want to fill the interior with a zigzag or similar pattern, then this is not so difficult.

Spiral filling creates a lot of difficult geometric problems, and if you do not know geometry and vector math, this task can be too difficult for a beginner or even an average skilled programmer in this field to make it work correctly. This is at least my opinion (as I did before), so treat it as such.

Answer 2

I worked on something similar, using offsets from polgyon based on the medial axis of the Voronoi diagram. It is not simple. I can’t share the code, because it belongs to the company I worked for and may not meet your needs.

But here are some similar things I found by other people:

http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf

http://www.cosy.sbg.ac.at/~held/teaching/seminar/seminar_2010-11/hsm.pdf