[PATCH] Split bicubicInterpolation to 1D and 2D so both are available

[FeXoR]

This is just an improvement of BicubicInterpolation.js. It splits the 1D part and uses it in the 2D part. That way it is much more readable as well as the 1D function is now also available.

Also the swapped x/y coordinates where fixed.

Thanks Vladislav for the changes!

[FeXoR]

Splits 1D and 2D interpolation, fixes x/y swaping

[FeXoR]

Removed some unneeded vars, removed licence links, changed eol to native

[elexis]

Tested the first version and couldnt notice a difference to the previous algorithm. Didn't solve the equations, so I don't know if there are hidden bugs. Like Vladislav said, the interpolation file could be renamed to mention the most common denominator of the functions present (perhaps interpolation?).

[FeXoR]

We are using the algorithm e.g. described at ​https://en.wikipedia.org/wiki/Bicubic_interpolation (see "Bicubic convolution algorithm")

An alternative would be using simple bicubic interpolation 2 times. That would be more precise throughout fx, fy in [-1; 2] but also slower. It's also more prone for oscillations (Runge's phenomenon) but that should'nt be a problem at 3rd degree polynimials.

Third degree polynomial: f(x) = ax^3^ + bx^2^ + cx + d
f(-1) = p0 <=> -a + b - c + d = p0
f(0)  = p1 <=>              d = p1
f(1)  = p2 <=>  a + b + c + d = p2
f(2)  = p3 <=> 8a +4b +2c + d = p3
<=> (Matrix)
-1  1 -1  1 = p0 | -II
 0  0  0  1 = p1
 1  1  1  1 = p2 | -II
 8  4  2  1 = p3 | -II
<=>
-1  1 -1  0 = p0 -p1 | +III
 0  0  0  1 = p1
 1  1  1  0 = p2 -p1
 8  4  2  0 = p3 -p1 | -2III
<=>
 0  2  0  0 = p0 -2p1 + p2
 0  0  0  1 =      p1
 1  1  1  0 =    - p1 + p2     | *2 -I
 6  2  0  0 =      p1 -2p2 +p3 | -I
<=>
 0  2  0  0 =  p0 -2p1 + p2
 0  0  0  1 =       p1
 2  0  2  0 = -p0      + p2     | *3 -IV
 6  0  0  0 = -p0 +3p1 -3p2 +p3
<=>
 0  2  0  0 =   p0 -2p1 + p2
 0  0  0  1 =       p1
 0  0  6  0 = -2p0 -3p1 +6p2 -p3
 6  0  0  0 = - p0 +3p1 -3p2 +p3

[FeXoR]

Added non-spline implementation , renamed file to interpolation.js

[elexis]

Feature freeze in 2 days.

[FeXoR]

Patch as I think should be committed (removed "convolution" argument)

[fatherbushido]

L2

• Perhaps replace "Two dimensional interpolation within four equidistant points using polynomials of 3rd degree." by "One dimensional interpolation within four uniformly spaced points using polynomials of 3rd degree.
• Perhaps add somewhere it's a Catmull-Rom spline.

L31

• To be remove (useless now)

L18-L19

• Use the same case for x and y

Else you can commit.

[FeXoR]

Some style and comment changes, removed a wrong colon

[fatherbushido]

@FeXoR: You can commit it. (We waited for a21 release).

[FeXoR]

In 18925:

Split the 1D and 2D interpolation into 2 Functions. Renamed BicubicInterpolation.js to interpolation.js. Original patch by Vladislav. Reviewed by fatherbushido. Fixes #4218

[elexis]

In 20383:

Extend the cubicInterpolation function to consume a tension argument allowing to modulate the smoothness of the interpolation.

Thereby unify the chordal Catmull-Rom spline interpolation of the ClumpPlacer (C++ rP2378, JS rP9096),
the copy of that in the PathPlacer (rP11152, refs #892) and
the centripetal Catmull-Rom spline of the bicubicInterpolation function from rP18925, refs #4218
and don't claim the latter to be a uniform Catmull-Rom spline.

Reviewed in part by fatherbushido, discussed in rP18925.