Python-互补齿轮形状

Question

I'm trying to find the complementary rotary "gear" shape to any input polygon shape. For example this polygon, is rotated around so that the complementary gear becomes apparent. Both shapes would be able to rotate without interferences.

I'm having issues defining the second polygon, which is the edge of the white inner region. One method I can think of is "sampling" the input shape along its circumference, and rotating like before to generate a pointcloud. A concave hull algorithm (Alpha shape) could be used to obtain the edge.

While this would work, I feel there must be a more elegant solution to this problem.

Thanks

Polygon and its rotated image

Sampled polygon and resulting pointcloud

close up of edge

Answer 1

I figured it out. The solution is to track all vertices and a special point for each edge. Then, the inner gear shape can be extracted by doing an intersection of all obtained curves.

The contact point on the edges is the point on that edge which is closest to the instantaneous rotation center of the gear, which is the point where the two base circles touch.

I'm using shapely to do the intersections.

I tried uploading the gif but that didn't work, so here is a link:

https://photos.app.goo.gl/nuYUv03ZWTYpFJrq2

Answer 2

Thanks guys, I solved it. The solution is to track each vertex and contact point on each edge. The contact point is the point on that edge closest to the instantaneous rotation center, which is the point where the two base circles touch.

I then use shapely to find the intersection of all obtained shapes, which represents the inner gear.

I tried uploading a gif, but that's not working so here it is instead:

https://photos.app.goo.gl/nuYUv03ZWTYpFJrq2