Following this post

Basically the logic is the same as previous post.

what is different compared to the post for kites and darts? 

the substitution rules that I used expand the surface of the pattern (Cf 3DStory at the bottom). so, the rhombs overlap.

I added a logic to get rid of duplicate rhombs within the loop.

I started to use a lot the function indicated by the arrow above. You can sort on a given item which makes sense for you or easy to calculate for CATIA. Then, you can structure another item, more difficult the same way as before. Here, I sorted/grouped the rhomb centers, because I can cluster points only. then I apply these groupings to the rhombs list and to take 1 only. really useful feature option that can be found in other features like "sort"

Also, I added the part to drive curves from the pattern of rhombs.

Basically, it is the same logic as for a Truchet tilings. you draw curves on top of rhombs. as far as the curves' extremities have the same ratios (or 1-ratios) on the rhombs, they connect. then you can add a constraint of orientation, like perpendicular curves to the rhomb edge to have tangencies. my curves are concatenation of circles. it can be extended to any other kind like Bezier curves

I enjoyed 3DStory app a lot for lean presentation. hoping it makes clearer my explanation above.

3dxml