In this paper, we propose a novel and coherent framework for fast footstep planning for legged robots on a flat ground with 3D obstacle avoidance. We use swept volume approximations computed offline in order to considerably reduce the time spent in collision checking during the online planning phase, in which an RRT variant is used to find collision-free sequences of half-steps (produced by a specific walking pattern generator). Then, an original homotopy is used to smooth the sequences into natural motions avoiding gently the obstacles. The results are experimentally validated on the robot HRP-2.