curve vertex move in quad mesh , in runtime ?

Hello vincent.
Ok, I’m going to explain you a bit more about the CurvedPolygonsNet object i showed you last time (for everybody else reading the question was this: https://support.mushroomslabs.com/question/curved-poly-shape-editor-runtime-support/)
But please: We are going to have a full documentation for runtime API and there are many things I can’t explain in a short message and which will be explained in depth in the docs. I shall ask you a bit of patience for more details about runtime components. Everything will be out with Curved Poly – Shape Editor v 1.2 which is on the road (there will be an article with more details soon about this).
Now your infos. Here I will show you an example based on the Quad1x primitive, which is one of the most simple.
What you Need to Know
Take this data from runtime structure (curvedPolygonsNet) i showed you last time:
Vector3[] vertices = curvedPolygonsNet.GetVertices();
short[] edges = curvedPolygonsNet.GetEdgesIndex();
short[] edgesIndex = curvedPolygonsNet.GetEdges();
Vertices will be an array of 12 positions in this case. It will have this structure: [v0, v1, v2, v3, h4, h5, h6, h7, h8, h9, h10, h11] where v0, v1, v2, v3 are main vertices and h4, h5 … h11 are handles (that is the internal curves vertices).  edges and edgesindex will have , instead this content:
edges [ 0, 4, 5, 1, 2, 6, 7, 3, 0, 8, 9, 2, 1, 10, 11, 3]     edgesIndex [ 0, 4, 8, 12, 16]
edges contains a full list of all the indices of each edge. EdgesIndex contains the limits of each edge within edges. So, in this example, edgesIndex says that the first edge goes from index 0 to index 4 (excluded), the second edge from 4 to 8 (excluded) and so on. Each edge can have 4 or 2 indices (4 for curved edges and 2 for linear edges). If you use primitives from the Primitives folders they are made only of curves, but if you use primitives from the libraries they may have lines.
So, now you can reconstruct the structure of each edge:
Edge 1 :  [0, 4, 5, 1]  meaning  [v0, h4, h5, v1]
Edge 2 :  [2, 6, 7, 3]  meaning  [v2, h6, h7, v3]
Edge 3 :  [0, 8, 9, 2]  meaning  [v0, h8, h9, v2]
Edge 4 :  [1, 10, 11, 3]  meaning  [v1, h10, h11, v3]
Ok. When you move a vertex, you also want to move it’s adjacent handles. To know which are the adjacent handles, you have to check the edges. For example we can see that, in this case, the main vertex v0 has two adjacent handles h4 and h8 (they are closed to it Edge1 and Edge3). So if you want to move v0, you probably want to move h4 and h8 of the same amount:
Vector3 delta = Vecto3.right*0.2f;
vertices[0]+=delta;
vertices[4]+=delta;
vertices[8]+=delta;
But: this depends on what you wish to accomplish, you will need to write your own code and formulas to move vertices. And for every model, you need to extract the adjacency relationships from the edges as i did first in this example.
Again: in two months or so we are going to have Shape Editor version 1.2 with runtime API  clearly exposed and documented online. If you need to know more, I shall ask you a bit of patience.