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**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