/**
* @class
* Interpolates the value of a point that is located between four known equidistant points with given values by
* constructing a polynomial of degree three that goes through all points.
* Computes a cardinal or Catmull-Rom spline.
*
* @param {number} tension - determines how sharply the curve bends at the given points.
* @param {number} x - Location of the point to interpolate, relative to p1
*/
function cubicInterpolation(tension, x, p0, p1, p2, p3)
{
let P = -tension * p0 + (2 - tension) * p1 + (tension - 2) * p2 + tension * p3;
let Q = 2 * tension * p0 + (tension - 3) * p1 + (3 - 2 * tension) * p2 - tension * p3;
let R = -tension * p0 + tension * p2;
let S = p1;
return ((P * x + Q) * x + R) * x + S;
}
/**
* Two dimensional interpolation within a square grid using a polynomial of degree three.
*
* @param {Vector2D} position - Location of the point to interpolate, relative to p11
*/
function bicubicInterpolation
(
position,
p00, p01, p02, p03,
p10, p11, p12, p13,
p20, p21, p22, p23,
p30, p31, p32, p33
)
{
let tension = 0.5;
return cubicInterpolation(
tension,
position.x,
cubicInterpolation(tension, position.y, p00, p01, p02, p03),
cubicInterpolation(tension, position.y, p10, p11, p12, p13),
cubicInterpolation(tension, position.y, p20, p21, p22, p23),
cubicInterpolation(tension, position.y, p30, p31, p32, p33));
}