Research On Hole-filling Algorithm For Triangular Mesh Models

Triangular mesh is an important representation of digital geometry processing.However,because of some complicated reasons,such as the limitation of scanner technology,the geometric complexity of the model,the self-occlusion of the model and the deformity of the object,the obtained triangular mesh model contains a variety of holes.The existence of holes will increase the difficulty of subsequent mesh processing algorithms,including mesh deformation,mesh simplification,etc.In many cases,we need a complete triangular mesh structure,so the hole-filling of triangular mesh model is an important and meaningful topic in digital geometric processing.Closed three-dimensional curve can shorten to a point in a direction.Based on this theory,we propose a hole-filling method using inward normal.First of all,we extract the hole's boundary from Triangular mesh model,and store in the border side array according to the continuity.Secondly,we need calculate concave and convex and corresponding angle of each boundary point,on this basis,find the most suitable for repair of boundary point according to the principle of minimum-angle and curvature.In determining the most suitable vertex at the same time,according to corresponding angle of each boundary point,we determine whether the insertion point,if it need insert point,then we need calculate the inward normal vector by multiplication crossing the boundary point's the approximate tangent vector and the vector.Then we can obtain the insert point with the inward normal vector and relating distance to generate the triangular mesh by the rules for creating triangles.Repeat the above steps,we can get the finished triangular mesh after repairing.We realize the algorithm on the different structural holes.Compared with the traditional hole-filling algorithm,the experimental results show that this algorithm can get the better triangle structure,the model after repairing by our method is more stable.The accuracy of the computational grid vertex normal vector almost entirely depend the property of hole-filling algorithm based on inward normal vector.That is to say,if calculation error of the vertex normal vector is bigger,the cumulative error will may cause slightly raised in the middle hole repair.So based on hole-filling algorithm using inward normal vector,we propose the optimized algorithm of hole repairing using quadratic error metric.First of all,we obtain rough patch using hole-filling algorithm based on inward normal vector.Secondly,we calculate the quadratic error metric of vertex in the hole using the vertices and k-neighborhood vertex in the hole.Finally,we can get the vertex location after the optimizing using the quadratic error metric.Repeating the above steps,we can get every vertex location after the optimizing using the quadratic error metric in the hole,we complete the optimized-operation.We implement the algorithm on the different structural holes.Compared with the bilateral filter algorithm,the experimental results show that this algorithm can get the better triangular mesh,the experimental results also show the feasibility and effectiveness of the algorithm in this paper.