Mesh reconstruction algorithm based on Laplace harmonic equation

Abstract

Upon the problem of transforming triangular mesh into quadrilateral mesh, gradient field via harmonic equation is created, integral flow is tracked, and parameterized mesh is reconstructed. First, gradient field construction theory, 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, the algorithm is verified via case studies. The result shows that flow lines are characterized as iso-parameterized and closed, mesh reconstruction of complicate models has no bifurcation, and mesh quality is increased with its density. The result proves that mathematical method has robustness and uniqueness for mesh reconstruction representation compared with traditional geometry method, and it will have more application scenarios.

Keywords

• theory of algorithms
• mesh reconstruction
• parameterized mesh
• harmonic equation
• integral flow tracking