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Figures


Figure 1: STL mesh of a simple object.


Figure 2: Identification of topological and geometrical bg edges: a) topological bg edges, b) geometrical bg edges bounding planes, c) geometrical bg edges between bg faces at large angle, d) geometrical bg edges between bg faces of significantly different aspect ratio.


Figure 3: Identification of topological and geometrical bg nodes: a) topological bg nodes, b) geometrical bg nodes.


Figure 4: Identification of model curves: a) vertex curves, b) loop curves.


Figure 5: Identification of model surfaces (individual surfaces are distinguished by different levels of gray).


Figure 6: Two levels of hierarchical refinement of a bg face.


Figure 7: Two stages of refinement -- splitting and averaging.


Figure 8: Averaging masks: a) surface mask (n=7), b) 4-point curve mask, c) 3-point curve mask.


Figure 9: Application of the modified Butterfly scheme to a simple domain: original control grid (top left), four refinement levels (top right, middle row, and bottom left), and the limit surface (bottom right).


Figure 10: Comparison of subdivision schemes: a) STL mesh, b) limit surface of the original subdivision scheme, c) limit surface of the modified (rule I) subdivision scheme.


Figure 11: Comparison of subdivision schemes: a) STL mesh, b) limit surface of the original subdivision scheme, c) limit surface of the modified (rule II) subdivision scheme.


Figure 12: Application of the subdivision scheme to a cylindrical surface: a) STL mesh, b) limit surface of the original subdivision scheme, c) limit surface of the modified (rule II) subdivision scheme.


Figure 13: Application of the subdivision scheme to a cylindrical surface: a) modified STL mesh, b) limit surface of the subdivision scheme applied to the modified STL mesh.


Figure 14: Uniform mesh of a simple object.


Figure 15: Graded mesh of a simple object.


Figure 16: STL mesh of a propeller.


Figure 17: Boundary representation of a propeller.


Figure 18: Graded mesh of a propeller.



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Daniel Rypl
2005-11-05