Determine Mesh Orientation by Voxel-Based Principal Component Analysis

In this paper we propose a new method to determine the part orientation of a 3D mesh based on Principal Component Analysis (PCA). Although the idea and practice of using PCA to determine part orientation is not new, it is not without practical issues. A major drawback of PCA, when it comes to dealing with meshes comprised of nodes and elements, is that the results are tessellation-dependent because of its sensitivity to variability. Two CAE meshes derived from the same CAD model but with different mesh node distribution characteristics, for instance, can yield different principal components. This is an undesirable outcome because the primary concern in model reorientation is shape, not the representational details of the shape. In order to reduce the influence of node characteristics, weight factors were proposed in the past, but the improvement is limited. To overcome this limitation, we must eliminate the influence of mesh node distribution. We achieve this by introducing an intermediate workspace, which is subsequently voxelized. We then find the intersection of the mesh model with the voxelized workspace. We collect the intersecting voxels to form an intermediate, tessellation-independent representation of the mesh. Applying PCA to this “neutralized” representation allows us to achieve mesh-property-independent results. The voxel representation also provides an opportunity of computational efficiency. We implemented an octree data structure to store the voxels and implemented a fast intersection (between a mesh element and a voxel) check procedure utilizing the interval overlap check derived from the separating axis theorem. Practical issues concerning determination of the voxel space resolution is addressed. A two-step trial and correction approach is proposed to enhance the consistency of results. Our voxel-based PCA is robust, fast, and straightforward to implement. Application examples are shown demonstrating the effectiveness and efficiency of this approach.