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Figures


Figure 1: Principal directions at point .


Figure 2: Degenerated Bezier bicubic patches: (a) octant of a sphere, (b) rectangle.


Figure 3: Evaluation of mesh control parameters at a singular point .


Figure 4: Triangulation of a surface with a collapsed side.


Figure 5: Computation of the location of the vertex .


Figure 6: Use of the ellipse in the principal axes to compute the location of the vertex .


Figure 7: Weighting factors for smoothing in the parametric space.


Figure 8: Hemisphere modeled by a single patch with two singularities.


Figure 9: Shaded mesh on the hemisphere from Fig. 8.


Figure 10: Triangulation of parametric space of the hemisphere from Fig. 8.


Figure 11: Principal directions and stretches in the parametric space of the hemisphere from Fig. 8.


Figure 12: Hemisphere modeled by a single patch without singularities.


Figure 13: Shaded mesh on the hemisphere from Fig. 12.


Figure 14: Triangulation of the parametric space of the hemisphere from Fig. 12.


Figure 15: Principal directions and stretches in the parametric space of the hemisphere from Fig. 12.


Figure 16: Hemisphere modeled by four patches with one singularity.


Figure 17: Shaded mesh on the hemisphere from Fig. 16.


Figure 18: Triangulation of the parametric space of one patch of the hemisphere from Fig. 16.


Figure 19: Principal directions and stretches in the parametric space of one patch of the hemisphere from Fig. 16.


Figure 20: Approximation of a hyperbolic paraboloid.


Figure 21: Resulting mesh on the hyperbolic paraboloid.


Figure 22: Triangulation of the parametric space of the hyperbolic paraboloid.


Figure 23: Patch representing a twisted plane with a hole.


Figure 24: Resulting mesh on the twisted plane with a hole.


Figure 25: Triangulation of the parametric space of twisted plane with a hole.



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Daniel Rypl
2005-12-03