The site was originally full of warehouses and rail yards:
They were all leveled and cleared off for Griffin Square, a large development in the 1980s that fell through.
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Those green patches are going to be areas of retail/entertainment adjacent to the hotel. Or, it could include a portal to the DART subway station. The city council wants the new DART route to serve the convention center hotel, but it will cost at least $300 million more than any other route and serve fewer passengers. The Convention Center already has a station nearby.