Analysis and applications of subdivision surfaces
Loading...
Date
2023-07
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
UMT Lahore
Abstract
The subdivision surface is a convenient way to model objects with arbitrary topologies. Using non-uniformly sampled data points, we reconstruct objects using a piecewise smooth subdivision scheme that we analyze in this dissertation. Subdivision surfaces are well-defined, smooth tangent plane surfaces (G1) that result from repeated refinement of a mesh of 3D control points. A great deal of attention has been paid to the analysis of smooth surface schemes with symmetrical rules around each vertex and edge in the scheme. Surfaces with sharp features, however, can be created in a scheme that does not exhibit this symmetry. By using eigen analysis and characteristic maps for quartic triangular B-spline surfaces, a piecewise smooth subdivision scheme is analyzed for such surfaces. Objects have been reconstructed from 3D data using subdivision surfaces as optimized surface fittings. Dense and uniform samples of data have been used to create accurate representations of objects in the past. As a practical low-cost alternative to the construction of subdivision surfaces by hand, we propose an algorithm that computes subdivision surfaces from data.