Parameterization and reconstruction from unstructured mesh is one of the most important ways of improving numerical modeling and calculation. Upon triangular mesh, gradient field via harmonic equation is created, integral flow is tracked and parameterized mesh is reconstructed. First, gradient field construction theory based on discrete Laplace equation, its data structure model and solution scheme of sparse matrix are constructed. Then, one uniform algorithm for solving flow line node by integration of local coordinate transformation and parameterized equation is advanced. And schemes like gradient convergence, shortest distance and extreme parameter are optimally occupied upon special cases of no intersection or multiple intersections when tracing flow line. Finally, harmonic theory and its application in mesh reconstruction are verified via case studies, which also indicate algorithm robustness and uniqueness for mesh reconstruction representation.