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Triangle Subdivide


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I am trying to make a subdivided square but essentially keep all triangular topology. I can start with an X division, but then each subsequent subdiv level would like each polygon face or each "tri" to divide.  This should be done in a very specific way, such that the hypotenuse is bisected and then a new edge connects between that midpoint of the hypotenuse and the origin of the triangle. The picture describes it all better than words. Notice that each new edge alternates between 90* and 45* (red lines are the new cut lines) with every other subdivision.  

 

For some reason I am having trouble executing this simply... I can imagine all kinds of crazy VEX code that will find the length of all the sides of the triangle on "neighbors" and compare them to find the hypotenuse, then find the midpoint, add a vertex, then add a connecting edge.  It seems like this can be done with some extensive programming which I am about to embark on, but please tell me there must be a simple way and I am just overlooking an easy SOP node here?

post-5696-0-75067100-1452641200_thumb.jp

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Is this an H15 file?  The poly Extrude does not load.

 

I think the example is close to what I had.. but the problem is when you start with a grid it and then subdivide first THEN triangulate it doesn't quite replicate the pattern above. 

 

I'll try to make another image example to show the pattern of subdivision.  

 

 

post-5696-0-95473000-1452700859_thumb.jp

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