My triangle needs more nodes
CJam (22 bytes)

{):X),3m*{:+X=},Xdff/}


This is an anonymous block (function) which takes N on the stack and leaves an array of arrays of doubles on the stack. Online demo

Dissection

{         e# Define a block
  ):X     e# Let X=N+1 be the number of segments per edge
  ),3m*   e# Generate all triplets of integers in [0, X] (inclusive)
  {:+X=}, e# Filter to those triplets which sum to X
  Xdff/   e# Normalise
}