Help with understanding UV's in script created mesh

First off this is what I am trying to do. I have a mesh that is made up of vertices for two concentric circles with alternating triangles i.e. one with base towards inner circle and one with base towards outer circle and so on. The texture that I would like to use is essentially an unlit transparent shader where the bottom is opaque and it fades to transparent towards the top. I wan't the textures to be arranged such that the opaque side of the texture always faces in towards the inner circle and fades towards the outer circle. The only methods of assigning UV I have basically amount to treating each triangle in the mesh like it is a cookie cutter that takes a piece out of the texture which of course will not yield the effect I want in this case. Whenever I have tried to make it so that the triangle that the uv defines is not in the same rotation as it appears in the mesh the texture gets garbled. My question is this something I can correct for or do I need to design my texture in such a way that I use my other method to assign the uv's.