dicinterpHermite.hpp

class Hermite : public Interpolator

Public Functions

Hermite(double *img, int px_hori, int px_vert)

Initializes the bicubic interpolator with deformed image data.

Sets up the necessary data structures and computes derivatives required for bicubic interpolation.

Parameters:

  • img – Pointer to the image data array

  • px_hori – Width of the image in pixels

  • px_vert – Height of the image in pixels

virtual double eval(const int ss_x, const int ss_y, const double subpx_x, const double subpx_y) const override

Evaluates the bicubic interpolation at a specified point.

Computes the interpolated value at (x,y) using bicubic interpolation from the surrounding pixel values.

Parameters:

  • x – The x-coordinate of the interpolation point

  • y – The y-coordinate of the interpolation point

Returns:

The interpolated value at (x,y)

virtual double eval_dx(const int ss_x, const int ss_y, const double subpx_x, const double subpx_y) const override

Evaluates the x-derivative of bicubic interpolation at a specified point.

Computes the partial derivative with respect to x at point (x,y).

Parameters:

  • x – The x-coordinate of the point

  • y – The y-coordinate of the point

Returns:

The x-derivative of the interpolated function at (x,y)

virtual double eval_dy(const int ss_x, const int ss_y, const double subpx_x, const double subpx_y) const override

Evaluates the y-derivative of bicubic interpolation at a specified point.

Computes the partial derivative with respect to y at point (x,y).

Parameters:

  • x – The x-coordinate of the point

  • y – The y-coordinate of the point

Returns:

The y-derivative of the interpolated function at (x,y)

virtual InterpVals eval_and_derivs(const int ss_x, const int ss_y, const double subpx_x, const double subpx_y) const override

Evaluates the bicubic interpolation and its derivatives at a specified point.

Computes the interpolated value and its partial derivatives at (x,y) in a single call.

Parameters:

  • x – The x-coordinate of the point

  • y – The y-coordinate of the point

Returns:

Data struct containing the interpolated value and its x and y derivatives

Private Functions

inline void coeff_calc(std::vector<double> &tridiag_solution, double dy, double dx, size_t index, double *b, double *c, double *d)

Calculates the coefficients for cubic spline interpolation.

Computes the coefficients b, c, and d for the cubic spline polynomial.

Parameters:

  • tridiag_solution – The solution vector from the tridiagonal system

  • dy – Difference in function values

  • dx – Difference in x values

  • index – Current index in the data array

  • b – Pointer to store the computed b coefficient

  • c – Pointer to store the computed c coefficient

  • d – Pointer to store the computed d coefficient

inline void index_lookup_xy(const int ss_x, const int ss_y, size_t &xi, size_t &yi, const double subpx_x, const double subpx_y) const
inline int index_lookup(const std::vector<double> &px, double x) const

Finds the index of the pixel that contains the given coordinate.

Determines the lower index of the interval containing the specified value.

Parameters:

  • px – Vector of pixel coordinates

  • x – The coordinate to look up

Returns:

The index of the pixel containing the coordinate

void cspline_init(const std::vector<double> &px, const std::vector<double> &data, std::vector<double> &local_tridiag_sol)

Initializes the cubic spline coefficients.

Sets up the tridiagonal system and solves it to obtain the cubic spline coefficients.

Parameters:

  • px – Vector of x coordinates

  • data – Vector of function values at the x coordinates

double cspline_eval_deriv(std::vector<double> &px, std::vector<double> &data, std::vector<double> &local_tridiag_sol, double value, int length)

Evaluates the derivative of a cubic spline at a specified point.

Computes the first derivative of the cubic spline function at the given value.

Parameters:

  • px – Vector of x coordinates

  • data – Vector of function values at the x coordinates

  • value – The point at which to evaluate the derivative

  • length – The length of the px and data arrays

Returns:

The derivative value at the specified point

Private Members

std::vector<double> dx
std::vector<double> dy
std::vector<double> dxy
std::vector<double> px_y
std::vector<double> px_x
double *image