PchipInterpolatorHelper Class Reference

A helper class to perform Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation. More...

#include </home/runner/work/OrcaSlicer/OrcaSlicer/src/libslic3r/GCode/PchipInterpolatorHelper.hpp>

Collaboration diagram for PchipInterpolatorHelper:

Public Member Functions
	PchipInterpolatorHelper ()=default
	Default constructor.
	PchipInterpolatorHelper (const std::vector< double > &x, const std::vector< double > &y)
	Constructs the PCHIP interpolator with given data points.
void	setData (const std::vector< double > &x, const std::vector< double > &y)
	Sets the data points for the interpolator.
double	interpolate (double xi) const
	Interpolates the value at a given point.

Private Member Functions
void	computePCHIP ()
	Computes the PCHIP coefficients.
void	sortData ()
	Sorts the data points by x-coordinate.
double	h (int i) const
	Computes the difference between successive x-coordinates.
double	delta (int i) const
	Computes the slope of the segment between successive data points.

Private Attributes
std::vector< double >	x_
	The x-coordinates of the data points.
std::vector< double >	y_
	The y-coordinates of the data points.
std::vector< double >	h_
	The differences between successive x-coordinates.
std::vector< double >	delta_
	The slopes of the segments between successive data points.
std::vector< double >	d_
	The derivatives at the data points.

Detailed Description

A helper class to perform Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation.

Constructor & Destructor Documentation

PchipInterpolatorHelper() [1/2]

PchipInterpolatorHelper::PchipInterpolatorHelper ( )

default

Default constructor.

PchipInterpolatorHelper() [2/2]

PchipInterpolatorHelper::PchipInterpolatorHelper	(	const std::vector< double > &	x,
		const std::vector< double > &	y )

Constructs the PCHIP interpolator with given data points.

Parameters

x	The x-coordinates of the data points.
y	The y-coordinates of the data points.

                                                                                                       {
    setData(x, y);
}

References setData().

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Member Function Documentation

computePCHIP()

void PchipInterpolatorHelper::computePCHIP ( )

private

Computes the PCHIP coefficients.

                                           {
    size_t n = x_.size() - 1;
    h_.resize(n);
    delta_.resize(n);
    d_.resize(n+1);
 
    for (size_t i = 0; i < n; ++i) {
        h_[i] = h(i);
        delta_[i] = delta(i);
    }
 
    d_[0] = delta_[0];
    d_[n] = delta_[n-1];
    for (size_t i = 1; i < n; ++i) {
        if (delta_[i-1] * delta_[i] > 0) {
            double w1 = 2 * h_[i] + h_[i-1];
            double w2 = h_[i] + 2 * h_[i-1];
            d_[i] = (w1 + w2) / (w1 / delta_[i-1] + w2 / delta_[i]);
        } else {
            d_[i] = 0;
        }
    }
}

References d_, delta(), delta_, h(), h_, and x_.

Referenced by setData().

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delta()

double PchipInterpolatorHelper::delta ( int i ) const

inlineprivate

Computes the slope of the segment between successive data points.

Parameters

i	The index of the segment.

Returns

The slope of the segment between y_[i] and y_[i+1].

{ return (y_[i+1] - y_[i]) / h(i); }

References h(), and y_.

Referenced by computePCHIP().

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h()

double PchipInterpolatorHelper::h ( int i ) const

inlineprivate

Computes the difference between successive x-coordinates.

Parameters

i	The index of the x-coordinate.

Returns

The difference between x_[i+1] and x_[i].

{ return x_[i+1] - x_[i]; }

References x_.

Referenced by computePCHIP(), and delta().

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interpolate()

double PchipInterpolatorHelper::interpolate

(

double

xi

)

const

Interpolates the value at a given point.

Parameters

xi	The x-coordinate at which to interpolate.

Returns

The interpolated y-coordinate.

                                                           {
    if (xi <= x_.front()) return y_.front();
    if (xi >= x_.back()) return y_.back();
 
    auto it = std::lower_bound(x_.begin(), x_.end(), xi);
    size_t i = std::distance(x_.begin(), it) - 1;
 
    double h_i = h_[i];
    double t = (xi - x_[i]) / h_i;
    double t2 = t * t;
    double t3 = t2 * t;
 
    double h00 = 2 * t3 - 3 * t2 + 1;
    double h10 = t3 - 2 * t2 + t;
    double h01 = -2 * t3 + 3 * t2;
    double h11 = t3 - t2;
 
    return h00 * y_[i] + h10 * h_i * d_[i] + h01 * y_[i+1] + h11 * h_i * d_[i+1];
}

References d_, h_, x_, and y_.

Referenced by AdaptivePAInterpolator::operator()().

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setData()

void PchipInterpolatorHelper::setData	(	const std::vector< double > &	x,
		const std::vector< double > &	y )

Sets the data points for the interpolator.

Parameters

x	The x-coordinates of the data points.
y	The y-coordinates of the data points.

Exceptions

std::invalid_argument

if x and y have different sizes or if they contain fewer than two points.

                                                                                            {
    if (x.size() != y.size() || x.size() < 2) {
        throw std::invalid_argument("Input vectors must have the same size and contain at least two points.");
    }
    x_ = x;
    y_ = y;
    sortData();
    computePCHIP();
}

References computePCHIP(), sortData(), x_, and y_.

Referenced by PchipInterpolatorHelper().

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sortData()

void PchipInterpolatorHelper::sortData ( )

private

Sorts the data points by x-coordinate.

                                       {
    std::vector<std::pair<double, double>> data;
    for (size_t i = 0; i < x_.size(); ++i) {
        data.emplace_back(x_[i], y_[i]);
    }
    std::sort(data.begin(), data.end());
 
    for (size_t i = 0; i < data.size(); ++i) {
        x_[i] = data[i].first;
        y_[i] = data[i].second;
    }
}

References x_, and y_.

Referenced by setData().

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Member Data Documentation

d_

std::vector<double> PchipInterpolatorHelper::d_

private

The derivatives at the data points.

Referenced by computePCHIP(), and interpolate().

delta_

std::vector<double> PchipInterpolatorHelper::delta_

private

The slopes of the segments between successive data points.

Referenced by computePCHIP().

h_

std::vector<double> PchipInterpolatorHelper::h_

private

The differences between successive x-coordinates.

Referenced by computePCHIP(), and interpolate().

x_

std::vector<double> PchipInterpolatorHelper::x_

private

The x-coordinates of the data points.

Referenced by computePCHIP(), h(), interpolate(), setData(), and sortData().

y_

std::vector<double> PchipInterpolatorHelper::y_

private

The y-coordinates of the data points.

Referenced by delta(), interpolate(), setData(), and sortData().

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The documentation for this class was generated from the following files:

• /home/runner/work/OrcaSlicer/OrcaSlicer/src/libslic3r/GCode/PchipInterpolatorHelper.hpp
• /home/runner/work/OrcaSlicer/OrcaSlicer/src/libslic3r/GCode/PchipInterpolatorHelper.cpp