Building a roof like your neighbors curved one requires three engineers, an architect and possibly and act of congress if the roof is going to be "approved" by local clueless building inspectors. Plus the local zoning office will need to approve the color and shape to make sure it suits them well. That was just the permit attempt for the township planning board to approve your idea. If you use timber and not some engineered prefab system it could literally take years for approval. They have lost their minds in NJ.