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