SplineInterpolation< FT > Class Template Reference

Cubic spline interpolation. More...

#include <easy3d/core/spline_interpolation.h>

Public Types
enum	BoundaryType { first_deriv = 1 , second_deriv = 2 }
	Boundary condition type. More...

Public Member Functions
	SplineInterpolation ()
void	set_boundary (BoundaryType left, FT left_value, BoundaryType right, FT right_value, bool linear_extrapolation=false)
void	set_data (const std::vector< FT > &x, const std::vector< FT > &y, bool cubic_spline=true)
FT	operator() (FT x) const
	Evaluates the spline at x.
FT	derivative (int order, FT x) const
	Returns the order -th derivative of the spline at x.

Detailed Description

template<typename FT>
class easy3d::SplineInterpolation< FT >

Cubic spline interpolation.

SplineInterpolation generates a piecewise polynomial function of degree 3 and is twice continuously differentiable everywhere. Boundary conditions default to zero-curvature at the end points. It extrapolates linearly, if default boundary conditions are used, or otherwise extrapolation is a quadratic function. The math behind this implementation is described here: https://kluge.in-chemnitz.de/opensource/spline/

Spline interpolation have many applications, e.g., curve interpolation (for any dimensions).

The following code shows how to use SplineInterpolation for 3D curve interpolation.

// a 3D curve is represented in the parametric form: x(t), y(t), and z(t).
std::vector<double> T(points.size()), X(points.size()), Y(points.size()), Z(points.size());
double t = 0.0;
for (std::size_t i = 0; i < points.size(); ++i) {
    const auto &p = points[i];
    if (i > 0)
        t += distance(points[i-1], p);
    T[i] = t;
    X[i] = p.x;
    Y[i] = p.y;
    Z[i] = p.z;
}
 
// class instantiation
typedef SplineInterpolation<double> Interpolator;
Interpolator x_spline, y_spline, z_spline;
// [optional] set the boundary conditions.
x_spline.set_boundary(Interpolator::second_deriv, 0.0, Interpolator::first_deriv, -2.0, false);
// set data
x_spline.set_data(T, X);
y_spline.set_data(T, Y);
z_spline.set_data(T, Z);
// evaluate the curve at equal intervals (this results in a sequence of points on the curve).
double total_length = t;
int steps = 1000;
double interval = total_length / steps;
for (int i=0; i<=steps; ++i) {
    double d = i * interval;
    vec3 p(x_spline(d), y_spline(d), z_spline(d));
    std::cout << p << std::endl;
}

Member Enumeration Documentation

BoundaryType

template<typename FT>

enum BoundaryType

Boundary condition type.

Enumerator
first_deriv	first derivative
second_deriv	second derivative

Constructor & Destructor Documentation

SplineInterpolation()

template<typename FT>

SplineInterpolation ( )

inline

Constructor. Sets default boundary condition to be zero curvature at both ends

Member Function Documentation

set_boundary()

template<typename FT>

void set_boundary	(	BoundaryType	left,
		FT	left_value,
		BoundaryType	right,
		FT	right_value,
		bool	linear_extrapolation = false )

Sets the boundary condition (optional).

Attention

If called, it has to come before set_points().

set_data()

template<typename FT>

void set_data	(	const std::vector< FT > &	x,
		const std::vector< FT > &	y,
		bool	cubic_spline = true )

Sets the data can carry out the interpolation. true for cubic spline interpolation; false for linear interpolation.

Attention

The x has to be monotonously increasing.

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

• G:/3_code/Easy3D/easy3d/core/spline_interpolation.h