Abstract: This paper proposes an approaching method to compute the straightest path between two vertices on meshes. An initial cutting plane is first constructed using the normal information of the source and destination vertices. Then an optimal cutting plane is iteratively created by comparing with previous path distance. Our study shows that the final straightest path based on this optimal cutting plane is more accurate and insensitive to the mesh boundary. Furthermore, we apply the straightest path result to compute the measured boundary in the parameter domain for mesh parameterization, and we obtain a new computing formula for vertex stretch in the planar parameterization. Experimental results show that our parameterization method can effectively reduce distortions.