interpolation — ALE Interpolation Functions

namespace ale

Enums

enum RotationInterpolation

Interpolation enum for defining different methods of interpolating rotations.

Values:

enumerator SLERP

Spherical linear interpolation.

enumerator NLERP

Normalized linear interpolation.

enum PositionInterpolation

Interpolation enum for defining different methods of interpolating in R.

Values:

enumerator LINEAR

Interpolate using linear interpolation.

enumerator SPLINE

Interpolate using a cubic spline.

enumerator LAGRANGE

Interpolate using Lagrange polynomials up to 8th order.

Functions

double linearInterpolate(double x, double y, double t)

Linearly interpolate between two values.

Parameters

  • x – The first value.

  • y – The second value.

  • t – The distance to interpolate. 0 is x and 1 is y.

Returns

The interpolated value

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

Linearly interpolate between two vectors.

Parameters

  • x – The first vectors.

  • y – The second vectors.

  • t – The distance to interpolate. 0 is x and 1 is y.

Returns

The interpolated vector

Vec3d linearInterpolate(const Vec3d &x, const Vec3d &y, double t)

Linearly interpolate between two 3D vectors.

Parameters

  • x – The first vectors.

  • y – The second vectors.

  • t – The distance to interpolate. 0 is x and 1 is y.

Returns

The interpolated vector

int interpolationIndex(const std::vector<double> &times, double interpTime)

Compute the index of the first time to use when interpolating at a given time.

Parameters

  • times – The ordered vector of times to search. Must have at least 2 times.

  • interpTime – The time to search for the interpolation index of.

Returns

int The index of the time that comes before interpTime. If there is no time that comes before interpTime, then returns 0. If all times come before interpTime, then returns the second to last index.

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

Merge, sort, and remove duplicates from two vectors

Parameters

  • x – The first vector to merge

  • y – The second vector to merge

Returns

A new vector containing unique, sorted values from the two input vectors

double evaluateCubicHermite(const double interpTime, const std::vector<double> &derivs, const std::vector<double> &x, const std::vector<double> &y)

Evaluates a cubic hermite spline at an input time.

migrated from Isis::NumericalApproximation

Parameters

  • interpTime – The time to interpolate at, should be in the same units as x

  • x – The times of the spline nodes

  • derivs – The derivatives of the spline at the nodes

  • y – The values of the spline at the nodes

Returns

The value of the spline at the input time

double evaluateCubicHermiteFirstDeriv(const double interpTime, const std::vector<double> &deriv, const std::vector<double> &times, const std::vector<double> &y)

Evaluate the first derivative of a cubic hermite spline at an input time.

Parameters

  • interpTime – The time to interpolate at, should be in the same units as x

  • x – The times of the spline nodes

  • derivs – The derivatives of the spline at the nodes

  • y – The values of the spline at the nodes

Returns

The first derivative of the spline at the input time

double lagrangeInterpolate(const std::vector<double> &times, const std::vector<double> &values, double time, int order = 8)

Interpolate a set of values using lagrange polynomials.

Parameters

  • times – The vector of times to interpolate over

  • values – The vector of values to interpolate between

  • time – The time to interpolate at

  • order – The order of the lagrange polynomials to use

Returns

The interpolated value

double lagrangeInterpolateDerivative(const std::vector<double> &times, const std::vector<double> &values, double time, int order = 8)

Interpolate the first derivative of a set of values using lagrange polynomials.

Parameters

  • times – The vector of times to interpolate over

  • values – The vector of values to interpolate between

  • time – The time to interpolate at

  • order – The order of the lagrange polynomials to use

Returns

The interpolated first derivative

double interpolate(std::vector<double> points, std::vector<double> times, double time, PositionInterpolation interp, int d)

Interpolates a value from a set of points and times.

Parameters

  • points – A vector of points

  • times – A vector of times

  • time – The time to interpolate at

  • interp – An interpolation enum dictating what type of interpolation to use

  • d – The order of the derivative to generate when interpolating (Currently supports 0, 1, and 2)

Returns

The interpolated value