Question How does this flow shader work?

So, I'm trying to follow this CatLikeCoding's tutorial. And I got the results similar to the tutorial but I don't understand how it works. I know, the shader adds/subtracts time value from the UV coordinates to make the texture slide, But I don't understand How they came up with these values to make the flow curved?
Are these values just interpolations across the edges? What If I wanted to make a different 'shape' with the flow?

How do these values work? Can anyone explain?
This is the tutorial - https://catlikecoding.com/unity/tutorials/hex-map/part-8/#7.6
This is how they make the shader - https://catlikecoding.com/unity/tutorials/hex-map/part-6/#8

 

they've added two quads to a triangle, that triangle occupies U1--0 and V.8--.1

the dimensions are the UVs for the new quads to bend for the estuary

Code (CSharp):

1.       estuaries.AddQuadUV2(
2.             new Vector2(1.5f, 1f), new Vector2(0.7f, 1.15f),
3.             new Vector2(1f, 0.8f), new Vector2(0.5f, 1.1f)
4.         );
5.         estuaries.AddTriangleUV2(
6.             new Vector2(0.5f, 1.1f),
7.             new Vector2(1f, 0.8f),
8.             new Vector2(0f, 0.8f)
9.         );
10.         estuaries.AddQuadUV2(
11.             new Vector2(0.5f, 1.1f), new Vector2(0.3f, 1.15f),
12.             new Vector2(0f, 0.8f), new Vector2(-0.5f, 1f)
13.         );

does this image help?

 

Yes, I get it now.
The outer vert UVs are 'pulled back' to give the appearance of curved texture.
I tried visualizing it in Blender and it works.

Thank you for the help!