In this paper, we incorporate the concept of differentiability into Voronoi diagrams. We consider the influence area diagrams consisting of areas with differentiable boundaries. The diagram is called a curved Voronoi diagram. Any level of differentiability can be used in the definition of the curved Voronoi diagram depending on its applications. One of the applications is path planning for car-like robots in an area with obstacles. Car-like robots can easily drive along a path consisting of clothoid curve segments, circular arcs, and line segments. Therefore, we discuss a method for constructing a clothoid curve, circle, and line (CCL) diagram.