Title of Thesis

Geometric Modeling Using Subdivision Techniques

Author(s)

Nadeem Ahmad

Abstract
Subdivision techniques are being appreciated in geometric modelling. Curves being the basic ingredient of the surfaces, have their own importance. Since no single scheme can be fit for every situation so, there is always a room to introduce new schemes. In this dissertation the interpolating curve subdivision scheme developed by Weissman [50], has been analyzed, using Laurent polynomial method. More- over, four approximating curve subdivision schemes have been developed. These schemes have also been analyzed, using Laurent polynomial method. The local supports of these schemes are determined as well. Regarding surface generation, a mathematical model of a three dimensional object using cross sectional data has been constructed. An algorithm for generating quadrilateral net is presented. The contours have been generated interpolating the data at each section, using a linear subdivision scheme introduced by Dyn et al. [17]. The contours have been, then, blended using the non-linear subdivision scheme developed Aspert [2]. The implementation of the schemes developed have also been depicted through different examples.

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1.1 Surface Schemes
1.2 Surface Subdivision Schemes
1.3 Curve Schemes
1.4 Curve Subdivision Schemes (Basic Notions)
1.5 Literature Survey

2.1 Curve Subdivision Schemes
2.2 Surface Subdivision Schemes

3.1 6-point Interpolatory Subdivision Scheme
3.2 3-point Approximating Subdivision Scheme
3.3 4-point Approximating Subdivision Scheme
3.4 5-point Approximating Subdivision Scheme
3.5 6-point Approximating Subdivision Scheme
3.6 Reconstruction of Objects From 3D Cross Sectional Data

4.1 3-point subdivision schem
4.2 4-point subdivision scheme
4.3 5-point subdivision scheme
4.4 6-point subdivision scheme
4.5 Reconstruction of Objects From 3D Cross Sectional Data

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