Semi-regular, quadrilateral-only meshes exhibit a structural regularity that facilitates subsequent geometry processing, including parameteric surface fitting, texture and displacement mapping. This method pushes simplification-based remeshing to its limit by allowing for the creation of very coarse base domains, defining a limited number of quadrilateral patches, concurrently extraordinary vertices, over the model.

A localized approach to quadrilateral mesh coarsening that introduces a novel deletion operator and weighting scheme to adjust behavior to surface attributes. The localized technique is compared to our quad-based simplification scheme, emphasizing the improved effects including better mesh structure, vector field alignment, mesh accuracy and simplification performance.

An automated technique towards quadrilateral mesh simplification that explores the effects of deletions on the dual representation. The algorithm implements multiple collapse operators and adaptively selects their application to produce and maintain hiqh quality elements at multiple levels of detail. Verification tests guarantee topological preservation, manifold constructions and maintenance of feature edges.

An extension of the previous feature curve extraction method, leveraging robust moving least squares to identify and project points to sharp features. An iterative spline fitting method is used to smooth the projection-based noise while aligning cubic curves along the feature regions.

A robust algorithm to extract features by defining polylines along the sharp edges of point-based models. Leverages the techniques of robust moving least squares to project points towards such regions.

A new approach to surface generation and curve deformations that sets up a vector field to guide a wavefront morph that sweeps well-behaved surfaces.

A novel algorithm to stitch corners formed by an odd number of spline surfaces with minimized G¹ discontinuities while interpolating input data points in the region. The algorithm is implemented as part of a triangular mesh to spline conversion system.

It is important to create visually smooth surfaces when they are intended for manufacturing. Where virtual representations can visually cheat discontinuities in the surfaces via normal smoothing, such regions are detectable on physical reconstructions. My thesis work addresses the mathematical constraints required to acheive smooth blending between adjacent spline surfaces.

Improved bandwidth utilization of Grid Computing applications over the WAN by communicating over multiple physical connections.