Class Interpolation2D

java.lang.Object

org.episteme.core.mathematics.analysis.interpolation.Interpolation2D

public class Interpolation2D
extends Object

2D Interpolation methods.

Methods for interpolating values on a 2D grid or scattered points.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Interpolation2D()

Method Summary

Modifier and Type	Method	Description
static Real	bicubic(Real[][] p, Real x, Real y)	Bicubic interpolation (simplified).
static Real	bilinear(Real x, Real y, Real v00, Real v10, Real v01, Real v11)	Bilinear interpolation on a unit square.
static Real	bilinear(Real x, Real y, Real x1, Real x2, Real y1, Real y2, Real q11, Real q21, Real q12, Real q22)	Bilinear interpolation on an arbitrary rectangle.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

Interpolation2D

public Interpolation2D()

Method Details

bilinear

public static Real bilinear(Real x,
 Real y,
 Real v00,
 Real v10,
 Real v01,
 Real v11)

Bilinear interpolation on a unit square.

Interpolates value at (x, y) where 0 invalid input: '<'= x, y invalid input: '<'= 1. Values at corners: (0,0): v00 (1,0): v10 (0,1): v01 (1,1): v11

bilinear

public static Real bilinear(Real x,
 Real y,
 Real x1,
 Real x2,
 Real y1,
 Real y2,
 Real q11,
 Real q21,
 Real q12,
 Real q22)

Bilinear interpolation on an arbitrary rectangle.

Parameters:

x - target x coordinate

y - target y coordinate

x1 - left x coordinate

x2 - right x coordinate

y1 - bottom y coordinate

y2 - top y coordinate

q11 - value at (x1, y1)

q21 - value at (x2, y1)

q12 - value at (x1, y2)

q22 - value at (x2, y2)

Returns:

interpolated value at (x, y)

bicubic

public static Real bicubic(Real[][] p,
 Real x,
 Real y)

Bicubic interpolation (simplified).

Requires 16 points (4x4 grid) surrounding the target point. This implementation uses a simple convolution kernel (Catmull-Rom spline).

Parameters:

p - 4x4 array of values. p[1][1] is top-left of the central cell. p[i][j] is value at grid point (i-1, j-1) relative to cell origin.

x - normalized x coordinate within the cell (0 to 1)

y - normalized y coordinate within the cell (0 to 1)

Returns:

interpolated value