Explain the plausibility with an image

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Andreas Fabri 2015-04-28 16:06:32 +02:00
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@ -123,6 +123,20 @@ We define the *plausibility* grade \f$ p(t) \f$ as \f$ 1/r_t \f$, if
\f$ \beta_t < \beta \f$, and \f$ -\beta_t \f$ else. The parameter \f$
\beta \f$ can be specified by the user and is set by default to \f$ \pi/6\f$.
Let's have a look at the figure below.
\cgalFigureBegin{figAFSRplausible,wedges.png}
Plausibility. Triangle `t'` and incidident triangles sharing edge `e` seen from the side.
\cgalFigureEnd
\f$ \alpha_\mathrm{sliver}\f$ corresponds to the red wedge. The algorithm will never select triangle `t1`
even if it is the only candidate triangle.
\f$\beta\f$ corresponds to the green wedge. If there is a candidate triangle in this zone,
the one with the smallest radius is the most plausible.
If there is no candidate triangle in the green wedge, the triangle with the smallest
angle between its normal and the normal of `t'` is chosen. In the figure above
this would be triangle `t4`.
\subsection AFSR_Boundaries Dealing with Multiple Components, Boundaries and Sharp Edges
@ -152,6 +166,12 @@ such that \f$ p(t) < 0\f$, and \f$ r_t > k r_{t'}\f$ where \f$ t'\f$ is
the triangle on the surface incident on \f$ e \f$. The parameter \f$ k \f$
is specified by the user and is set by default to 5.
For the example given in \cgalFigureRef{figAFSRplausible}, we said that if there
was no triangle `t3` in the green wedge, triangle `t4` would be chosen as it has
the smallest angle between its normal and the normal of triangle `t'`.
However, in case its radius was \f$ k \f$ times larger than the radius of triangle `t'`,
triangle `t2` would be chosen, assuming that its radius is not \f$ k \f$ times larger.
Note that this heuristic implies that
where the sampling is too sparse with respect to curvature, it must

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