A spline generator is used which produces curves based on discrete control points which you place; examples of curve generation functions that use control points are Catmull-Rom or Bezier. x is known, y is unknown; so use the spline function to get the y position of the curve for that x, then place your character at that x,y position.

A spline function is used which produces curves based on discrete control points which you place; examples of curve generation functions that use control points are Catmull-Rom or Bezier. x is known, y is unknown; so use the spline function to get the y position of the curve for that x, then place your character at that x,y position.