| dc.description.abstract | The thesis addresses mainly two issues in geometric modeling, high-level modeling techniques and reconstruction. High-level modeling techniques essentially include boolean operations on objects with same as well as different dimensionality. The other high-level- modeling techniques explored are sweeping and Minkowski sum. The problem of reconstruction deals with the reconstruction of planar curves from dense cloud of unstructured point data. Central to both these solutions is a novel scheme representation called Slice representation. Slice representation is a type of spatial enumeration based representation initially proposed elsewhere and used for fast, accurate and robust computational requirements of generation of finite difference grids from tessellated non-manifold B-rep models of objects with considerable complexity. The slice representation of an object is one in which the slices are maintained in a direction-wise hierarchical fashion which are affected by the boundary of the object and from which the inference about the interior can be done very easily, A slice is conceptually a region between two axis oriented surfaces. The objects in the lowest level of this hierarchy can be conceptualized as boundary voxels in the conventional spatial enumeration representation. The main aim of current work is to investigate the suitability of the slice representation as a primary representation scheme for geometric modeling. To achieve this objective, the thesis has made the following contributions.
It is often imperative that a complex model be constructed from simple entities carrying out the boolean operations. For the boolean operations using slice representation, an algorithm is proposed in this thesis. Since in slice representation 3D objects are represented as an array of 2D objects, by performing boolean operations on respective 2D objects, the resultant 3D object is obtained. In case of 2D boolean operations to get the resultant object, the slices of one object are classified with respect to another and vice versa and valid slices are retained depending on the operation. The proposed algorithm can deal with closed manifolds as well as mixed dimensional objects of any topological dimension with equal ease. For example booleans between an object representing a volume (a cuboid)and other representing an area (a sheet) produced approN^I?^^M-Its with proper geometric properties. For rendering slice objects, an optimal algorithm for clustering has been developed for faster display. Results obtained demonstrated that the representation is closed under boolean operations. The proposed algorithm is conceptually simple, computationally fast and robust.
For defining a wide class of complex solids high-level modeling operators are required irrespective of the representation scheme chosen. There are many high-level modeling operators available in which it uses the low level operators such as translation and rotation etc. The present work illustrates translational and rotational sweeping and Minkowski sum. The low level operators such as translation and rotation using slice representation is also discussed and implemented. Examples are given to show suitability of the representation for geometric modeling and its robustness in modeling and processing various objects with different topological varieties. Minkowski sum has been used to model some engineering objects as illustrative examples.
Reconstruction is one of the fundamental problem in many areas of engineering. The thesis addresses reconstruction of planar curves from the given dense cloud of point data. The input data for reconstruction need not be structured. The algorithm, incremental reconstruction, is incremental in nature and is capable of handling large point data sets. It can also handle the data with noise. The input data is segmented into small clusters of points belonging to each grid cell. Each cluster is approximated with a line segment. The line segment is obtained as the diameter of the convex hull of the small cluster. This convex hull construction is incremental, hence the incremental nature of the algorithm. The line segments in each grid cell are connected to line segments in neighboring grid cells. This results in a polygonal approximation of the curve from which the data is acquired. The results are obtained to validate the algorithm. The choice of grid size plays a vital role in reconstruction, heuristics have to be used to choose a suitable grid size. The choice of grid cell also an important parameter in handling noisy data. Some of the available surface reconstruction algorithms use curve reconstruction as an intermediate step. Hence, it can be used for reconstruction of surfaces from large data of unstructured points. | |
