We present here a detailed description of the walking algorithm that was designed for 3D simulation of locomotion and path planning of humanoid robots. The walking patterns described were implemented on NAO humanoid models that are used in the 3D simulation league of RoboCup to play soccer. The locomotion algorithm is based on the well known 3D-LIP model that consists of defining walking primitives of the center of mass, keeping its height constant and assuming no torque at the support foot. This paper proposes to detail how to connect the walking primitives, especially at the start of the walk. The second added value of this work resides in the rotation walking primitives that are generated differently from the linear translation walking primitives. This enables the robot to achieve fast rotation on the spot or about a center located on the longitudinal axis. The paper also addresses the issue of re-entrance, i.e. how to take into account a new walking request in real time without waiting for the end of the current walk.