/usr/include/BALL/MATHS/cubicSpline2D.h is in libball1.4-dev 1.4.3~beta1-4.
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#define BALL_MATHS_CUBICSPLINE2D_H
#include <set>
#include <map>
#ifndef BALL_MATHS_CUBICSPLINE1D_H
# include <BALL/MATHS/cubicSpline1D.h>
#endif
#ifndef BALL_COMMON_EXCEPTION_H
#include <BALL/COMMON/exception.h>
#endif
namespace BALL
{
class BALL_EXPORT CubicSpline2D
{
public:
static const int VERBOSITY_LEVEL_DEBUG;
static const int VERBOSITY_LEVEL_CRITICAL;
BALL_CREATE(CubicSpline2D)
//@}
/** @name Constructors and Destructors.
*/
//@{
/** Default constructor.
*/
CubicSpline2D();
/** Detailed constructor
Given the increasingly sorted sample positions {\tt sample_positions_y_} in y direction,
increasingly sorted sample positions {\tt sample_positions_x_} in x direction and the
corresponding sample values {\tt sample_values}
a 2D spline is created by storing for each y sample position the corresponding
1d spline in x direction.
By default, we assume the first and the last values to be the lower and upper bounds.
If the {\tt return_average_} flag is set to true, the default return values are set to the
spline average.
If the {\tt is_natural} flag is set to true, all 1D splines and the 1D spline in y direction used in the
{\tt operator() } will be natural.
Otherwise {\tt x_lower_derivatives} and {\tt x_upper_derivatives} are taken as
first derivatives of the first/last sample positions in x direction
and {\tt y_lower_derivative} and {\tt y_upper_derivative} are taken as the first derivatives
of the first/last derivative in y direction. By default, the derivatives are set to zero.
*/
CubicSpline2D(const std::vector<std::vector<float> >& sample_positions_x,
const std::vector<float>& sample_positions_y,
const std::vector<std::vector<float> >& sample_values,
bool return_average = false,
bool is_natural = true,
const std::vector<float>& x_lower_derivatives = std::vector<float>(),
const std::vector<float>& x_upper_derivatives = std::vector<float>(),
float y_lower_derivative = 0.,
float y_upper_derivative = 0.,
int verbosity = VERBOSITY_LEVEL_DEBUG);
/** Detailed constructor
Given the increasingly sorted sample positions {\tt sample_positions_y_} in y direction,
increasingly sorted sample positions {\tt sample_positions_x_} in x direction and the
corresponding sample values {\tt sample_values}
a 2D spline is created by storing for each y sample position the corresponding
1d spline in x direction.
The {\tt return_average} flag is set to false and the default values {\tt x_default_values_}
and {\tt y_default_value_} is set to the given values.
The lower and upper bounds in x and y direction are set to the given values.
If the {\tt is_natural} flag is set to true, all 1D splines and the 1D spline in y direction used in the
{\tt operator() } will be natural.
Otherwise {\tt x_lower_derivatives} and {\tt x_upper_derivatives} are taken as
first derivatives of the first/last sample positions in x direction
and {\tt y_lower_derivative} and {\tt y_upper_derivative} are taken as the first derivatives
of the first/last derivative in y direction. By default, the derivatives are set to zero.
*/
CubicSpline2D(const std::vector<std::vector<float> >& sample_positions_x,
const std::vector<float>& sample_positions_y,
const std::vector<std::vector<float> >& sample_values,
const std::vector<float>& x_default_values,
float y_default_value,
const std::vector<float>& x_lower_bounds,
const std::vector<float>& x_upper_bounds,
float y_lower_bound,
float y_upper_bound,
bool is_natural = true,
const std::vector<float>& x_lower_derivatives = std::vector<float>(),
const std::vector<float>& x_upper_derivatives = std::vector<float>(),
float y_lower_derivative = 0.0,
float y_upper_derivative = 0.0,
int verbosity = VERBOSITY_LEVEL_DEBUG);
//-------------------------- Constructors with equal x sample positions for all y ------------------------
//Assumes that all rows have the same x-positions.
/** Detailed constructor
Given the increasingly sorted sample positions {\tt sample_positions_y_} in y direction,
increasingly sorted sample positions {\tt sample_positions_x_} in x direction (same for all splines in x direction! )
and the corresponding sample values {\tt sample_values}
a 2D spline is created by storing for each y sample position the corresponding
1d spline in x direction.
By default, we assume the first and the last values to be the lower and upper bounds.
If the {\tt return_average_} flag is set to true, the default return values are set to the
spline average.
If the {\tt is_natural} flag is set to true, all 1D splines and the 1D spline in y direction used in the
{\tt operator() } will be natural.
Otherwise {\tt x_lower_derivatives} and {\tt x_upper_derivatives} are taken as
first derivatives of the first/last sample positions in x direction
and {\tt y_lower_derivative} and {\tt y_upper_derivative} are taken as the first derivatives
of the first/last derivative in y direction. By default, the derivatives are set to zero.
*/
CubicSpline2D(const std::vector<float>& sample_positions_x,
const std::vector<float>& sample_positions_y,
const std::vector<std::vector<float> >& sample_values,
bool return_average = false,
bool is_natural = true,
const std::vector<float>& x_lower_derivatives = std::vector<float>(),
const std::vector<float>& x_upper_derivatives = std::vector<float>(),
float y_lower_derivative = 0.,
float y_upper_derivative = 0.,
int verbosity = VERBOSITY_LEVEL_DEBUG);
/** Detailed constructor
Given the increasingly sorted sample positions {\tt sample_positions_y_} in y direction,
increasingly sorted sample positions {\tt sample_positions_x_} in x direction and the
corresponding sample values {\tt sample_values}
a 2D spline is created by storing for each y sample position the corresponding
1d spline in x direction.
The {\tt return_average} flag is set to false and the default values {\tt x_default_values_}
and {\tt y_default_value_} is set to the given values.
The lower and upper bounds in x and y direction are set to the given values.
If the {\tt is_natural} flag is set to true, all 1D splines and the 1D spline in y direction used in the
{\tt operator() } will be natural.
Otherwise {\tt x_lower_derivatives} and {\tt x_upper_derivatives} are taken as
first derivatives of the first/last sample positions in x direction
and {\tt y_lower_derivative} and {\tt y_upper_derivative} are taken as the first derivatives
of the first/last derivative in y direction. By default, the derivatives are set to zero.
*/
CubicSpline2D(const std::vector<float>& sample_positions_x,
const std::vector<float>& sample_positions_y,
const std::vector<std::vector<float> >& sample_values,
const std::vector<float>& x_default_values,
float y_default_value,
const std::vector<float>& x_lower_bounds,
const std::vector<float>& x_upper_bounds,
float y_lower_bound,
float y_upper_bound,
bool is_natural = true,
const std::vector<float>& x_lower_derivatives = std::vector<float>(),
const std::vector<float>& x_upper_derivatives = std::vector<float>(),
float y_lower_derivative = 0.0,
float y_upper_derivative = 0.0,
int verbosity = VERBOSITY_LEVEL_DEBUG);
/** Copy constructor.
*/
CubicSpline2D(const CubicSpline2D& cs2D);
/** Destructor.
*/
virtual ~CubicSpline2D();
/// Set the verbosity of the spline computation and evaluation.
void setVerbosity(int verbosity);
/** A method to evaluate the 2Dspline at the access values x | y.
* First all spline in y-direction are evaluated at x.
* Based on these values a temporary 1D spline is created,
* which will be evaluated at y.
* If the access values are out of bound
* or if we have too less points given for a spline
* the {\tt default_value} is returned.
* If the spacing is zero, <tt> std::numeric_limits<float>::min() </tt>
* is returned.
*/
float operator () (float x, float y);
/** Returns the x-th default value in x direction.
* @throw Exception::OutOfRange if x >= number_of_default_values
*/
float getXDefaultValue(Index x) const;
/** Returns the y-th default value in x direction.
*/
float getYDefaultValue() const {return y_default_value_;}
// Set the default values in x direction.
void setXDefaultValues(vector<float> x_default_values) {x_default_values_ = x_default_values;}
// Set the default values in y direction.
void setYDefaultValue(float y_default_value) {y_default_value_ = y_default_value;}
// Set the lower/upper bound in y direction
void setYLowerBound(float lb) {y_lower_bound_ = lb;}
void setYUpperBound(float ub) {y_upper_bound_ = ub;}
// Get the lower/upper bound in y direction
float getYLowerBound() {return y_lower_bound_;}
float getYUpperBound() {return y_upper_bound_;}
// Set the lower/upper bounds in x direction
void setXLowerBounds(vector<float> lb) {x_lower_bounds_ = lb;}
void setXUpperBounds(vector<float> ub) {x_upper_bounds_ = ub;}
/** Returns all lower bounds in x direction.
*/
const vector<float>& getXLowerBounds() const {return x_lower_bounds_ ;}
/** Returns all upper bounds in x direction.
*/
const vector<float>& getXUpperBounds() const {return x_upper_bounds_;}
/** Get the lower bounds in x direction
* @throw Exception::OutOfRange if x >= x_lower_bounds_.size()
*/
float getXLowerBounds(Index x) const;
/** Get the upper bounds in x direction
* @throw Exception::OutOfRange if x >= x_upper_bounds_.size()
*/
float getXUpperBounds(Index x) const;
/** Returns true if the x-th spline in x direction is natural.
* If x is out of bound, <tt> std::numeric_limits<float>::min() </tt> is returned.*/
bool isXNatural(Index x);
vector<bool> isXNatural() const {return x_is_natural_;}
/** Sets the flag {\tt is_natural_} for the x-th spline to true.
* By default the method recomputes the spline.
* If the argument is false, no recomputation is done.*/
void makeXNatural(Index x, bool recompute = true);
/** Sets the flag {\tt is_natural_} for all x-th splines to true.
* By default the method recomputes all splines.
* If the argument is false, no recomputation is done.*/
void makeAllXNatural(bool recompute = true);
/** Sets the flag {\tt y_is_natural_} to true.
* Since the spline in y direction is created
* for each call of {\tt operator ()} new,
* recomputation is not necessary.*/
void makeYNatural(bool y_is_natural, bool recompute = true);
/** Returns true if the spline in y direction for each call in {\tt operator ()} is natural.
*/
bool isYNatural() {return y_is_natural_;}
// Set the lower/upper derivatives in x direction
void setXLowerDerivatives(vector<float> ld, bool recompute = true);
void setXUpperDerivatives(vector<float> ud, bool recompute = true);
/** Get the lower derivatives in x direction
* @throw Exception::OutOfRange if x >= x_lower_derivatives_.size()
*/
float getXLowerDerivatives(Index x);
/** Get the upper derivatives in x direction
* @throw Exception::OutOfRange if x >= x_upper_derivatives_.size()
*/
float getXUpperDerivatives(Index x);
vector<float>& getXLowerDerivatives() {return x_lower_derivatives_;}
vector<float>& getXUpperDerivatives() {return x_upper_derivatives_;}
// Set the lower/upper derivative in y direction
void setYLowerDerivative (float ld, bool recompute = true);
void setYUpperDerivative (float ud, bool recompute = true);
// Get the lower/upper derivative in y direction
float getYLowerDerivative() {return y_lower_derivative_;}
float getYUpperDerivative() {return y_upper_derivative_;}
/** Return the i-th spline
* @throw Exception::OutOfRange if i >= getNumberOfSplines()
*/
CubicSpline1D& getSpline(Position i);
/** Return the i-th spline
* @throw Exception::OutOfRange if i >= getNumberOfSplines()
*/
const CubicSpline1D& getSpline(Position i) const;
Size getNumberOfSplines() const {return splines_.size();}
private :
/** Method to create a 2D cubic spline relying to be given _increasingly ordered_ sample positions in y direction,
* for each y position _increasingly ordered_ sample positions in x direction, and
* the corresponding sample values.
* If the {\tt return_average_} flag is set to true, the {\tt default_value_} is the average
* of the 1D spline averages, otherwise it is set to <tt> std::numeric_limits<float>::min() </tt>.
* By default the boundaries in y direction are set to the lower and the upper y sample position.
* The {\tt operator ()} returns the 2D interpolation for given x and y values.
*/
void createBiCubicSpline();
// Sample x positions of the spline.
// Note: we allow for each y value different x positions.
std::vector< std::vector<float> > sample_positions_x_;
// Sample y positions of the spline.
std::vector<float> sample_positions_y_;
// For each y position a 1D cubic spline is stored.
std::vector<CubicSpline1D> splines_;
// Sample values of the spline.
std::vector<std::vector<float> > sample_values_;
//
// Parameters
//
// Flag to denote, if the default values should be set to the average of the spline averages.
bool return_average_;
/** The default values of the splines in x direction.
In case the access-value of the x-th spline in x direction is out of bounds
or if too less points are given,
the corresponding {\tt default_value_(x)} is returned.
*/
std::vector<float> x_default_values_;
/** The default value of the splines in y direction.
In case the access-value of the y-th spline in y direction is out of bounds or if
too less points for this spline are given,
the corresponding {\tt default_value_(y)} is returned.
*/
float y_default_value_;
/** The default value of splines in general. If the return_average_ flag is set
* to true, the averall average of the splines is computed. Otherwise it is set
* to <tt> std::numeric_limits<float>::min() </tt>. */
float default_value_;
// Lower bounds of the spline in x direction.
vector<float> x_lower_bounds_;
// Upper bounds of the spline in x direction.
vector<float> x_upper_bounds_;
// Lower bound of the splines in y direction.
float y_lower_bound_;
// Upper bound of the splines in y direction.
float y_upper_bound_;
// Flag to denote, if the splines in x direction is natural.
vector<bool> x_is_natural_;
// Flag to denote, if the splines in y direction are natural.
bool y_is_natural_;
// Values of the first derivatives of the lower x sample position
vector<float> x_lower_derivatives_;
// Values of the first derivatives of the upper x sample position
vector<float> x_upper_derivatives_;
// Value of the first derivatives of the lower y sample position
float y_lower_derivative_;
// Value of the first derivatives of the upper y sample position
float y_upper_derivative_;
///
int verbosity_;
};
}
#endif
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