This paper presents a method for biped gait generation along a predefined curve with fully stretched knees. First, we design a spatial gait pattern as a function of the traveled distance on the path without considering dynamics. Then, a consistent dynamic walking motion is obtained by optimization that minimizes the zero-moment point and the speed errors while considering the trade-off between kinematics and dynamics. This method generalizes the spatially quantized dynamics-based gait generation, which is our former method restricted to straight paths, to walk on arbitrary curves. The generated gaits are validated by dynamic simulation.