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Andreas Fabri 2013-01-11 12:46:15 +01:00
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33
Interpolation/doc/Interpolation/CGAL/interpolation_functions.h
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@ -63,8 +63,8 @@ std::pair< Data_type, bool> operator()(const Key_type& p);
generates the interpolated function value computed by Farin's interpolant. generates the interpolated function value computed by Farin's interpolant.
\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. \pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range `[first, beyond).
\pre The range \f$ \left[\right.\f$ `first`, `beyond`\f$ \left.\right)\f$ contains either one or more than three element \pre The range `[first, beyond)` contains either one or more than three element
The function `farin_c1_interpolation()` interpolates the function values and the The function `farin_c1_interpolation()` interpolates the function values and the
gradients that are provided by functors using the method described in \cite f-sodt-90. gradients that are provided by functors using the method described in \cite f-sodt-90.
@ -89,7 +89,6 @@ to provide the square root operation.
\sa `PkgInterpolationRegularNeighborCoordinates2` \sa `PkgInterpolationRegularNeighborCoordinates2`
\sa PkgInterpolationSurfaceNeighborCoordinates3 \sa PkgInterpolationSurfaceNeighborCoordinates3
s.
*/ */
template < class RandomAccessIterator, class Functor, template < class RandomAccessIterator, class Functor,
class GradFunctor, class Traits> typename Functor::result_type class GradFunctor, class Traits> typename Functor::result_type
@ -115,8 +114,8 @@ function value and a Boolean. The Boolean indicates whether the
function value could be retrieved correctly. This function generates function value could be retrieved correctly. This function generates
the interpolated function value as the weighted sum of the values the interpolated function value as the weighted sum of the values
corresponding to each point of the point/coordinate pairs in the corresponding to each point of the point/coordinate pairs in the
range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. range `[first, beyond)`.
\pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. \pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range `[first, beyond)`.
\cgalHeading{Requirements} \cgalHeading{Requirements}
@ -155,20 +154,22 @@ norm, Functor function_values);
/*! /*!
\ingroup PkgInterpolation2Interpolation \ingroup PkgInterpolation2Interpolation
The function `quadratic_interpolation` interpolates the function values and first degree The function `quadratic_interpolation()` interpolates the function values and first degree
functions defined from the function gradients. Both, function values and functions defined from the function gradients. Both, function values and
gradients, must be provided by functors. gradients, must be provided by functors.
This function generates the This function generates the
interpolated function value as the weighted sum of the values plus a interpolated function value as the weighted sum of the values plus a
linear term in the gradient for each point of the point/coordinate linear term in the gradient for each point of the point/coordinate
pairs in the range \f$ \left[\right.\f$ `first`, pairs in the range `[first, beyond)`. See also
`beyond`\f$ \left.\right)\f$. See also `sibson_c1_interpolation()`.
`sibson_c1_interpolation`. \pre `norm` \f$ \neq0\f$ `function_value(p).second == true` for all points `p` of the point/coordinate pairs in the range \f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$.
\pre `norm` \f$ \neq0\f$ `function_value(p).second == true` for all
points `p` of the point/coordinate pairs in the range `[first, beyond)`.
\cgalHeading{Parameters} \cgalHeading{Parameters}
See `sibson_c1_interpolation`. See `sibson_c1_interpolation()`.
\cgalHeading{Requirements} \cgalHeading{Requirements}
@ -200,7 +201,7 @@ function_gradient,const Traits& traits);
/*! /*!
\ingroup PkgInterpolation2Interpolation \ingroup PkgInterpolation2Interpolation
The function `sibson_c1_interpolation` interpolates the function values and the The function `sibson_c1_interpolation()` interpolates the function values and the
gradients that are provided by functors gradients that are provided by functors
following the method described in \cite s-bdnni-81. following the method described in \cite s-bdnni-81.
@ -210,9 +211,10 @@ This function generates the interpolated function value at the point
If the functor `function_gradient` cannot supply the gradient of a If the functor `function_gradient` cannot supply the gradient of a
point, the function returns a pair where the Boolean is set to point, the function returns a pair where the Boolean is set to
`false`. If the interpolation was successful, the pair contains the `false`. If the interpolation was successful, the pair contains the
interpolated function value as first and `true` as second value. \pre interpolated function value as first and `true` as second value.
`norm` \f$ \neq0\f$. `function_value(p).second == true` for all points
`p` of the point/coordinate pairs in the range \f$\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. \pre `norm` \f$ \neq0\f$. `function_value(p).second == true` for all points
`p` of the point/coordinate pairs in the range `[first, beyond)`.
\cgalHeading{Parameters} \cgalHeading{Parameters}
@ -221,8 +223,7 @@ The template parameter `Traits` is to be
instantiated with a model of `InterpolationTraits`. instantiated with a model of `InterpolationTraits`.
The value type of `ForwardIterator` is a pair associating a point to a The value type of `ForwardIterator` is a pair associating a point to a
(non-normalized) barycentric coordinate. `norm` is the (non-normalized) barycentric coordinate. `norm` is the
normalization factor. The range \f$ \left[\right.\f$ normalization factor. The range `[first, beyond)` contains the barycentric
`first`,`beyond`\f$ \left.\right)\f$ contains the barycentric
coordinates for the query point `p`. The functor coordinates for the query point `p`. The functor
`function_value` allows to access the value of the interpolated `function_value` allows to access the value of the interpolated
function given a point. `function_gradient` allows to access the function given a point. `function_gradient` allows to access the

3
Interpolation/doc/Interpolation/CGAL/sibson_gradient_fitting.h
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@ -50,8 +50,7 @@ estimation method based on natural neighbor coordinates
/*! /*!
estimates the estimates the
gradient of a function at the point `p` given natural neighbor gradient of a function at the point `p` given natural neighbor
coordinates of `p` in the range \f$ \left[\right.\f$ `first`, coordinates of `p` in the range `[first, beyond)` and the function values of the neighbors
`beyond`\f$ \left.\right)\f$ and the function values of the neighbors
provided by the functor `f`. `norm` is the normalization provided by the functor `f`. `norm` is the normalization
factor of the barycentric coordinates. factor of the barycentric coordinates.
*/ */

14
Interpolation/doc/Interpolation/CGAL/surface_neighbors_3.h
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@ -19,9 +19,8 @@ The functions \c surface_neighbors_certified_3 also return, in
addition, a Boolean value that certifies whether or not, the Voronoi addition, a Boolean value that certifies whether or not, the Voronoi
cell of `p` can be affected by points that lie outside the input cell of `p` can be affected by points that lie outside the input
range, i.e. outside the ball centered on `p` passing through the range, i.e. outside the ball centered on `p` passing through the
furthest sample point from `p` in the range \f$ furthest sample point from `p` in the range `[first, beyond)`. If the sample
\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. If the sample points are collected by a k-nearest neighbor or a range search
points are collected by a \f$ k\f$-nearest neighbor or a range search
query, this permits to verify that a large enough neighborhood has query, this permits to verify that a large enough neighborhood has
been considered. been considered.
@ -51,7 +50,7 @@ of the cell of `p` in this diagram.
/*! /*!
The sample points \f$ \mathcal{P}\f$ are provided in the range The sample points \f$ \mathcal{P}\f$ are provided in the range
\f$\left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$. `[first, beyond)`.
`InputIterator::value_type` is the point type `Kernel::Point_3`. The `InputIterator::value_type` is the point type `Kernel::Point_3`. The
tangent plane is defined by the point `p` and the vector `normal`. The tangent plane is defined by the point `p` and the vector `normal`. The
parameter `K` determines the kernel type that will instantiate the parameter `K` determines the kernel type that will instantiate the
@ -59,7 +58,7 @@ template parameter of `Voronoi_intersection_2_traits_3<K>`.
The surface neighbors of `p` are computed which are the The surface neighbors of `p` are computed which are the
neighbors of `p` in the regular triangulation that is dual to neighbors of `p` in the regular triangulation that is dual to
the intersection of the \f$ 3D\f$ Voronoi diagram of \f$ \mathcal{P}\f$ with the intersection of the 3D Voronoi diagram of \f$ \mathcal{P}\f$ with
the tangent plane. The point sequence that is computed by the the tangent plane. The point sequence that is computed by the
function is placed starting at `out`. The function returns an function is placed starting at `out`. The function returns an
iterator that is placed past-the-end of the resulting point iterator that is placed past-the-end of the resulting point
@ -85,7 +84,7 @@ const ITraits& traits);
/*! /*!
Similar to the first function. The additional third return Similar to the first function. The additional third return
value is `true` if the furthest point in the range value is `true` if the furthest point in the range
\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$ is further `[first, beyond)` is further
away from `p` than twice the distance from `p` to the away from `p` than twice the distance from `p` to the
furthest vertex of the intersection of the Voronoi cell of `p` furthest vertex of the intersection of the Voronoi cell of `p`
with the tangent plane defined be `(p,normal)`. It is with the tangent plane defined be `(p,normal)`. It is
@ -101,8 +100,7 @@ K);
/*! /*!
The same as above except that this function The same as above except that this function
takes the maximal distance from `p` to the points in the range takes the maximal distance from `p` to the points in the range
\f$ \left[\right.\f$`first`, `beyond`\f$ \left.\right)\f$ as additional `[first, beyond)` as additional parameter.
parameter.
*/ */
template <class OutputIterator, class InputIterator, class template <class OutputIterator, class InputIterator, class
Kernel> std::pair< OutputIterator, bool > Kernel> std::pair< OutputIterator, bool >