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A fast path planning method by optimization of a path graph for both efficiency and accuracy is proposed. A conventional quadtree-based path planning approach is simple, robust, and efficient. However, it has two limitations. We propose a path graph optimization technique employing a compact mesh representation. A world space is triangulated into a base mesh and the base mesh is simplified to a compact mesh. The compact mesh representation is object-dependent; the positions of vertexes of the mesh are optimized according to the curvatures of the obstacles. The compact mesh represents the obstacles as accurately as the quadtree even though using much fewer vertexes than the quadtree. The compact mesh distributes vertexes in a free space in a balanced way by ensuring that the lengths of edges are below an edge length threshold. An optimized path graph is extracted from the compact mesh. An iterative vertex pushing method is proposed to include important obstacle boundary edges in the path graph. Dijkstra's shortest path searching algorithm is used to search the shortest path in the path graph. Experimental results show that the path planning using the optimized path graph is an order of magnitude faster than the quadtree approach while the length of the path generated by the proposed method is almost the same as that of the path generated by the quadtree.