Geometric Reasoning with Mesh-based Shape Representation in Product Development
Triangle meshes have become an increasingly popular shape representation. Given the ease of standardization it allows and the proliferation of devices (scanners, range images ) that capture and output shape information as meshes, this representation is now used in applications such as virtual reality, medical imaging, rapid prototyping, digital art and entertainment, simulation and analysis, product design and development. In product development manipulation of mesh models is required in applications such as visualization, analysis, simulation and rapid prototyping. The nature of manipulation of the mesh includes annotation, interactive viewing, slicing, re-meshing, mesh optimization, mesh segmentation, simplification and editing. Of these editing has received the least attention. Mesh model often requires editing either locally or globally based on the application. With the increased use of meshes it is desirable to have formal reasoning tools that enable manipulation of mesh models in product development. The mesh model may contain artifacts like self-intersection, overlapping triangles, inconsistent normal’s of triangles and gaps or holes with or without islands. It is necessary to repair the mesh before further processing the mesh model. An automatic algorithm is proposed to repair and fill arbitrary holes while maintaining curvature continuity across the boundaries of the hole. The algorithm uses slices across the hole to first identify curves that bridge the hole. These curves are then used to find the surface patch that would fill the hole. The proposed algorithm works for arbitrary holes in any mesh model irrespective of the type of underlying surface and is able to preserve features in the mesh model that are missing in the input information. Since editing during product development is mostly feature based, an automatic algorithm to recognize shape features by directly clustering the triangles constituting a feature in a mesh model is proposed. Shape features addressed in the thesis are volumetric features that are associated with either addition or removal of a finite volume. The algorithm involves two steps – isolating features in 2D slices followed by a 3D traversal to cluster all the triangles in the feature. Editing a mesh model mainly implies editing local volumetric features in that model. An automatic algorithm is proposed for parametric editing of volumetric features in the mesh model. The proposed algorithm eliminates the need of original CAD model while manipulating any volumetric feature in the mesh model based on feature parameters. An automatic algorithm to manipulate global shape parameters of the object using the mesh model is developed. Global shape parameters include thickness, drafts and axes of symmetry. As the mesh models do not explicitly carry this information global editing of mesh models (other than for visualization) has not been attempted thus far. This thesis proposes the use of mid-surface to identify and manipulate global shape parameters for a class of objects that are classified as thin walled objects. Mid-curves are first identified on slices of the part and then the mid-surface is obtained from these mid-curves. Results of implementation are presented and discussed along with the scope for future work.