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Last update: Oct. 23, 2003
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Two planes attached on one side to create a V-shaped gutter, here
forming right (90deg.) angle : 800 pts.
The points are randomly distributed on the 2 planar surfaces
The "surface scaffold" (i.e., the less significant part of the shock scaffold) gives us back a meshing of the input data. Thus, we can re-build connectivity on the input samples automatically.
Here we use a notion of scale as a ratio as follows. Consider a triplet of point generators. We take for numerator of the scale ratio the length of the longest side of the triangle through the triplet. Then, we take for denominator the (minimum) length of a shock curve from its source to one of its endpoint (at a shock vertex). Shock curves (and associated triangles) are then rank-ordered from smallest to largest scale. This measure favors, on one hand and for equivalent length of a shock curve, smaller triangles. On the other hand, it favors, for triangles of similar size, longer shock curves.
In the following animations, we show different increasing thresholds on scale. We also illustrate the values of scale, by coloring triangles associated to selected shock curves, where warmer (red) colors correspond to the smaller scales, while colder (blue) colors correspond to the larger scales.
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Two planes attached on one side to create a V-shaped gutter, here
forming right (90deg.) angle : 800 pts.
The points are randomly distributed on the 2 planar surfaces as well as
perpendicularly to these planes.
