<p> hatch, scale </p>

9f0a2fc3-2a8f-4276-b8ba-909f27e53c68 45 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

x r Ψ 12 r * sqrt / x r - ≥ (x r ≤ (* 0 cases :

x f x 2 Ψ abs (2^:

Fourier Quantum: pin hole diffraction

x g 0 :

coordinate-space prob. density

f g 2 - 2 20 hatch 2 1 sys

W 0.5 : M 0.0375 : xo 0 : 13 mat U 10000 : α 4 : 12 mat 21 line

x q 0.1 12 x xo - (* U * W / (α^+ (M^/ :

asymmetric mapping x f 11 x 0.325^+ / :

The mapping function

x q x f

r 0.5 : (pin hole radius ≡ Δ 10 : (size momentum ≡ N 10 : (canvas size ≡ N Δ ≥ (Δ>N not diffraction ≡ px py 12 mat position momentum ≡ j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 81 line

Memo:

In this document, simple/double integrals are "Cartesian".

"Simple Integral" is a curve in the XY domain.

"Double Integral" is essentially a 2D matrix.

Both integrators are scalar at the algorithm level.

Fourier Quantum diffraction supports this Smath session.

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Optimiz numeric, set options integral accuracy 50.
default integral accuracy 100 => does not converge. px py Φ i px x * y py * + (* - exp y r 2^x 2^- sqrt - r 2^x 2^- sqrt int x r - r int :

Δ N 12 mat 10 ≡ (17 min * ≡ Δ N 12 mat 20 ≡ (70 min * ≡ Δ N 12 mat 30 ≡ (160 min * ≡ 31 mat

t0 1 time :

P m 1 N range n 1 N range Fo m n el px m el py n el Φ abs (2^: for for Fo 21 line :

P P : x f x q : fmap P f vectorize : CoC fmap - 0255 Scale : 41 line

iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAIAAAACUFjqAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACESURBVChThY8xDkUREEVn5WxDxALsQBQK1FqdJWh0EpF3/gY+xc11ZuYOwnHOxRhzzrXWUgqKh8B/tZQSNIRgrVVKoXgIXOjCee+NMa213juKh8CFHHq5jzHmnGstFA+BC5tIYwK69z7noHgIXEjQWpPJHLV7L4qHwF/Tj92Pl//7d0ofNKDhDdv5KzEAAAAASUVORK5CYII= CoC

<= CoC 30/30

1 time t0 - min 16.4

X1 1.57 0.25 1.57 0.25 - 22 mat :

X2 π 0.25 π 0.25 - 22 mat :

Airy CoC [Circle of Confusion] xx r Ψ 12 r * sqrt / xx r - ≥ (xx r ≤ (* 0 cases : r 2 : v r Φ 12 π * sqrt / (i v * xx * - exp xx r Ψ * xx r - r int * : 31 line

Airy x 5 - 5 4.95 - range : j 1 x rows range Airy j el x j el r Φ abs (2^eval : for x Airy augment 31 line :

x r Φ abs 2 ^ X1 X2 3 1 sys Airy

π 2 / r Φ abs (2^π r Φ abs (2^21 mat 31031 -^* 31031 -^* 21 mat