parameters: (
          self, trajectory_params: TrajectoryParameters, t: float
      )
return_statement: return x, y, yaw
docstring: Get point on the arc trajectory using the following parameterization.
  
              r(t) = <R * cos(t - pi/2) + a, R * sin(t - pi/2) + b>
  
              R = radius
              a = x offset
              b = y offset
  
          Args
          ----
          trajectory_params: TrajectoryParameters
              The parameters that describe the arc to create
          t: float
              A value between 0 - 1 that denotes where along the arc
              to calculate the point
  
          Returns
          -------
          x: float
              x coordinate of generated point
          y: float
              y coordinate of generated point
          yaw: float
              angle of tangent line to arc at point (x,y)
docstring_summary: Get point on the arc trajectory using the following parameterization.
docstring_tokens: Get point on the arc trajectory using the following parameterization .
function: def _get_arc_point(
          self, trajectory_params: TrajectoryParameters, t: float
      ) -> Tuple[float, float, float]:
          """
          Get point on the arc trajectory using the following parameterization.
  
              r(t) = <R * cos(t - pi/2) + a, R * sin(t - pi/2) + b>
  
              R = radius
              a = x offset
              b = y offset
  
          Args
          ----
          trajectory_params: TrajectoryParameters
              The parameters that describe the arc to create
          t: float
              A value between 0 - 1 that denotes where along the arc
              to calculate the point
  
          Returns
          -------
          x: float
              x coordinate of generated point
          y: float
              y coordinate of generated point
          yaw: float
              angle of tangent line to arc at point (x,y)
  
          """
          start_angle = trajectory_params.start_angle
  
          arc_dist = t * trajectory_params.arc_length
          angle_step = arc_dist / trajectory_params.turning_radius
  
          if trajectory_params.left_turn:
              # Calculate points using
              # r(t) = <R * cos(t - pi/2) + a, R * sin(t - pi/2) + b>
              t = start_angle + angle_step
              x = (
                  trajectory_params.turning_radius * np.cos(t - np.pi / 2)
                  + trajectory_params.x_offset
              )
              y = (
                  trajectory_params.turning_radius * np.sin(t - np.pi / 2)
                  + trajectory_params.y_offset
              )
  
              yaw = t
  
          else:
              # Right turns go the opposite way across the arc, so we
              # need to invert the angles and adjust the parametrization
              start_angle = -start_angle
  
              # Calculate points using
              # r(t) = <R * -cos(t + pi/2) + a, R * sin(t + pi/2) + b>
              t = start_angle + angle_step
              x = (
                  trajectory_params.turning_radius * -np.cos(t + np.pi / 2)
                  + trajectory_params.x_offset
              )
              y = (
                  trajectory_params.turning_radius * np.sin(t + np.pi / 2)
                  + trajectory_params.y_offset
              )
  
              yaw = -t
  
          return x, y, yaw
function_tokens: def _get_arc_point ( self , trajectory_params : TrajectoryParameters , t : float ) -> Tuple [ float , float , float ] : start_angle = trajectory_params . start_angle arc_dist = t * trajectory_params . arc_length angle_step = arc_dist / trajectory_params . turning_radius if trajectory_params . left_turn : # Calculate points using # r(t) = <R * cos(t - pi/2) + a, R * sin(t - pi/2) + b> t = start_angle + angle_step x = ( trajectory_params . turning_radius * np . cos ( t - np . pi / 2 ) + trajectory_params . x_offset ) y = ( trajectory_params . turning_radius * np . sin ( t - np . pi / 2 ) + trajectory_params . y_offset ) yaw = t else : # Right turns go the opposite way across the arc, so we # need to invert the angles and adjust the parametrization start_angle = - start_angle # Calculate points using # r(t) = <R * -cos(t + pi/2) + a, R * sin(t + pi/2) + b> t = start_angle + angle_step x = ( trajectory_params . turning_radius * - np . cos ( t + np . pi / 2 ) + trajectory_params . x_offset ) y = ( trajectory_params . turning_radius * np . sin ( t + np . pi / 2 ) + trajectory_params . y_offset ) yaw = - t return x , y , yaw