Geometric trimming of a surface involves removal of unwanted portions of the surface and providing a new mathematical description for the trimmed patch. This entails creating a new geometry for the trimmed patch, which closely approximates the corresponding portion on the original patch. The procedure is shown to involve obtaining data points on the B-spline surface that lie within the region specified by the parameter values for the trimming curve and describing a new surface which interpolates this new set of data points. This research looks at optimizing the procedure described above by basing the choice of parameter values for the trimming curve, at points where curvature optima occur over the surface. A visualization tool kit has been developed using OpenGL, as a means to discern the difference between the two surfaces. In order to quantify and aid in minimizing the error (difference) in approximating the original surface with the trimmed patch, an error measurement tool developed in MATLAB has been employed. / Master of Science

Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information. / Master of Science

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Ongoing developments in the field of medical imaging modalities have pushed the frontiers of modern medicine and biomedical engineering, prompting the need for new applications to improve diagnosis, treatment and prevention of diseases. Biomedical data visualization and modeling rely predominately on manual processing and utilization of voxel and facet based homogeneous models. Biological structures are naturally heterogeneous and in order to accurately design and biomimic biological structures, properties such as chemical composition, size and shape of biological constituents need to be incorporated in the computational biological models. Our proposed approach involves generating a density point cloud based on the intensity variations in a medical image slice, to capture tissue density variations through point cloud densities. The density point cloud is ordered and approximated with a set of cross-sectional least-squares B-Spline curves, based on which a skinned B-Spline surface is generated. The aim of this method is to capture and accurately represent density variations within the medical image data with a lofted surface function. The fitted B-Spline surface is sampled at uniformly distributed parameters, and our preliminary results indicate that the bio-CAD model preserves the density variations of the original image based point cloud. The resultant surface can thus be visualized by mapping the density in the parametric domain into color in pixel domain. The B-Spline function produced from each image slice can be used for medical visualization and heterogeneous tissue modeling. The process can be repeated for each slice in the medical dataset to produce heterogeneous B-Spline volumes. The emphasis of this research is placed on accuracy and shape fidelity needed for medical operations.