Transformation of a closed 3D triangular mesh to a quadrilateral mesh based on feature edges

In this paper, we propose a method of applying the Q-Morph to the closed three-dimensional triangular mesh. The Q-Morph is the method in order to transform the triangular mesh to the quadrilateral mesh. The Q-morph begins quadrilateral transformation from the initial front edges which are usually the boundary of the 2D domain. Also, the Q-Morph can be applied to the 3D domain. But, the closed 3D triangular mesh does not contain any boundary edges which can be the initial front edges. Because of this reason, the Q-Morph cannot be applied directly to the closed 3D triangular mesh. The initial front edges must be the path of the line segments of which each line segment appears as the edge of the mesh. Furthermore, the shape of converted quadrilateral heavily depends on the initial front edges. So, the initial front edge should be generated by taking the change of the shape into account for effective quadrilateral transformation. Our proposal is to extract feature edges from input triangular mesh based on the semantic mesh partitioning. And, we modify extracted feature edges so that the extracted edges may adapt to the initial front. We use existing mesh partitioning algorithm for feature edge extraction. In general, extracted feature edges may be jaggy. We smooth extracted jaggy feature edges and modify the triangular mesh so that the smoothed feature edges may appear as the mesh edge in order to create the initial front of the Q-Morph.