Tetrahedral Mesh Reduction Technique

Mesh simplification (decimation) refers to reducing the number of vertices and elements in an initial mesh while preserving the appearance of the dataset. In either case, some degree of simplification may be required for various reasons, for example, reducing visualization and calculation times or reducing storage requirements. The goal of the algorithm discussed in the paper is to reduce the total number of tetrahedral elements in the volume meshes for acceleration of calculation processes and to test the feasibility of proposed solution. One of the decimation criterions proposed in this approach is a bending energy as a decimation metrics to select tetrahedral elements as the candidates for collapsing. The final step of our algorithm is improving a quality of the simplified mesh. For improving we apply interpolation approach based on radial basis functions. To interpolate the overall displacement, we use a volume spline and employ an approach that uses displacement of N control points as a difference between the original and deformed geometric forms of tetrahedral mesh elements