Abstract A constrained Delaunay triangle mesh method is presented to recover the surface from the three-dimensional unstructured boundary point cloud. The surfaces of different three-dimensional object models are recovered by this triangle mesh method. The radius of the tested cylinder model can be accurately estimated from the derived maximum principle curvature. The derived minimum principle curvature of the tested cylinder model displays a zero value, which is the analytical value of a standard cylinder model’s minimum principle curvature.