A Statistical Shape Model (SSM) serves as a compact characterization of the shape variation pattern in a group of shapes (training set). Building SSM reduces to searching for correspondence across the entire training set shape instances. The population-based approach formulates the search as an optimization problem that minimizes a measure of resultant SSM, and during optimization, the correspondence updates are achieved by reparameterizing shapes in the parameter space. Previously, the reparameterization function is modeled by concatenating a large number of local warps, leading to extremely inefficient iterations and huge time cost. We propose a direct representation of the reparameterization function by B-splines, develop associated diffeomorphism conditions and derive fast gradient formula by adjoint method. Both synthetic examples and real medical applications have confirmed the effectiveness of proposed algorithm and the efficiency advantages.

Isogeometric analysis (IGA) uses the same basis functions that represent geometry for approximating physical fields in analysis. This closer integration of CAD and FEA greatly alleviates the burden of converting CAD geometry to analysis-ready models. As the standard geometric form in CAD systems, basis functions generated from NURBS, are employed to construct an exact geometric model. Convergence study on plenty of examples shows that NURBS basis function based FEA exhibits superior computational advantage to its traditional counterpart --- Lagrange polynomials based FEA. Despite the performance improvements due to choosing NURBS basis functions over Lagrange polynomials, analysis framework using Finite Element Method (FEM) is unable to avoid the expensive domain parameterization. We explore the Boundary Integral Equation Method (BIEM) based isogeometric analysis, which requires only the NURBS boundary. Analysis examples show further computational advantage of BIEM-IGA to FEM-IGA, and the proposed tech

As 3D scanning devices and technologies become more and more popular, algorithms are widely needed for the geometric processing on scan data in product design/analysis/manufacturing. Traditional approach typically involves an intermediate conversion to triangle mesh. Our proposed algorithm utilizes the promising Moving Least Square definition for point-set surfaces representation; it works directly on point data and circumvents the mesh conversion step, significantly improving the efficiency of the entire product development life cycle. We have focused on the additive manufacturing (3D printing) capabilities of proposed technique, and developed a smart slicing algorithm with both geometric and topological awareness. The algorithm has been tested on digital models and we have also demonstrated its ability in transmitting 3D geometric manufacturing data in a tele-fabrication practice.

In the broad field of Product Development, Product Lifecycle Management (PLM) is of great importance to the design and manufacturing part throughout the whole process. The development of ontological assembly representation was initiated from several considerations concerning assembly representation for PLM. Ontological representation, due to its inherent advantages, can help achieve high interoperability level that enables efficient implementation of PLM and identify a common data structure to allow data exchange between platforms. There are several kinds of software that is able to perform ontology-based modeling and analysis, and Protégé is a commonly used and powerful tool in this area. To make this idea more clear, this report will choose a typical assembly case, namely a reduction gearbox, build the corresponding ontology and explore the ontology assembly model by using related plug-ins.