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some doc adjustments
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@ -769,13 +769,13 @@ The poisson sample elimination has the following parameters:
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double(*func)(const Point &p, const Point &n, double squared_distance, double r_max)
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\endcode
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The default weight is \f$\left(1 - \frac{d_{p,n}}{2r_{max}}\right)^8\f$ with \f$d_{p,n}\f$ being the distance between the point p and its neighbor n.
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- \f$r_{max}\f$: The \f$r_{max}\f$ parameter specifies the radius of the neighborhood, i.e., the neighboring points that are used to calculate the weight of a point. r_max has to be provided if a custom *weight_function* is used. Only points within a distance of \f$r_{max}\f$ is used to calculate the weight of a point. A large value can thus cause a large running time. The default is calculated based in the bounding volume \f$V\f$ of the input points, the *dimensions* parameter and the number of input points \f$N\f$:
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- \f$r_{max}\f$: The \f$r_{max}\f$ parameter specifies the radius of the neighborhood, i.e., the neighboring points that are used to calculate the weight of a point. r_max has to be provided if a custom *weight_function* is used. Only points within a distance of \f$r_{max}\f$ are used to calculate the weight of a point. A large value can thus cause a large running time. The default is calculated based in the bounding volume \f$V\f$ of the input points, the *dimensions* parameter and the number of input points \f$N\f$:
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\f$dimensions = 2:\qquad\f$ \f$r_{max} = \sqrt{\frac{V}{2\sqrt{3}N}}\f$
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\f$dimensions = 3:\qquad\f$ \f$r_{max} = \sqrt{\frac{V}{4\sqrt{2}N}}\f$
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- *progressive*: The output points of the function can be reordered to be progressive. A progressive ordering will increase the running time by at most 2 as the function is internally applied several times on increasingly smaller subsets. The default value is false.
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- *progressive*: The output points of the function can be reordered to be progressive. A progressive ordering will increase the running time by a factor of at most 2 as the function is internally applied several times on increasingly smaller subsets. The default value is false.
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\cgalFigureAnchor{Point_set_processing_3figPoisson_elimination}
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<center>
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@ -785,7 +785,7 @@ The default weight is \f$\left(1 - \frac{d_{p,n}}{2r_{max}}\right)^8\f$ with \f$
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Poisson elimination on point cloud with 21k points and results with \f$\frac{1}{2}\f$, \f$\frac{1}{4}\f$ and \f$\frac{1}{8}\f$ of the input size.
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\cgalFigureCaptionEnd
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\subsection Point_set_processing_3Example_poisson_elimination Poisson Sample Elimination Example
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\subsubsection Point_set_processing_3Example_poisson_elimination Poisson Sample Elimination Example
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The following example reads a point cloud, applies poisson elimination to reduce the point cloud to \f$\frac{1}{5}\f$ of its size and saves it into a file.
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@ -213,13 +213,13 @@ void pop_heap(std::vector<std::size_t>& heap, std::vector<std::size_t>& heap_pos
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\cgalParamNBegin{maximum_radius}
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\cgalParamDescription{radius of the poisson disk in which the neighboring points are taken into account for elimination.}
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\cgalParamType{double}
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\cgalParamDefault{the default is calculated from the `dimension`, the volume of the bounding box and the `number_of_points`. For more details, see \ref Point_set_processing_3PoissonElimination.}
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\cgalParamDefault{the default is calculated from the `dimension`, the volume of the bounding box and the `number_of_points`. For more details, see parameter section in \ref Point_set_processing_3PoissonElimination.}
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\cgalParamNEnd
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\cgalParamNBegin{weight_function}
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\cgalParamDescription{a weight function that calculates the weight of a neighbor point based on its squared distance and the `maximum_radius`.}
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\cgalParamType{an instance of `std::function<double(const Point&, const Point&, double,double)>`.}
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\cgalParamDefault{See \ref Point_set_processing_3PoissonElimination.}
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\cgalParamDefault{See parameter section in \ref Point_set_processing_3PoissonElimination.}
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\cgalParamNEnd
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\cgalParamNBegin{geom_traits}
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