c1da9572-8824-4140-983a-b4638d8caaf6 16 4 5 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]
 <p> rgb Venturi </p> 0 255 2 1 mat

A robust construct of the Matrix Scale function

M Low High Scale min M Min : max M Max : maxmin max min - ( 10 12 - ^ + : HighLow High Low - ( : i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / eval : for for HighLow N * Low + 6 1 line :

1. Define the functions

 64 33 1 2 mat 0 255 2 1 mat

2. Fourier 2D Procedure

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3. Conclude the zoom demo

Group the recovered rgb

S rgb 32 16 Pad : iVrgb S mwifft2 eval : RGB iVrgb mwabs eval : s RGB 0 255 Scale : zoom s mwround : 5 1 line 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 Venturi

Smath 5346 takes "if/else" linterp. 6179 does not

x f x lo ≤ 0 x hi ≥ 255 lo hi 2 1 mat 0 255 2 1 mat x linterp if if :

Typical RGB light intensifier

 x f 1 1 sys
Smath 6179 does NOT vectorise from the calculated zoom matrix, neither from it spooled to file.
It vectorises from an isolated matrix ... QED below. In short: the zoom system breaks the algo
suite. This type of broken suite existed in Mathcad 11 and earlier versions.
]]> 127 116 91 67 41 17 0 0 2 25 51 127 117 95 71 48 25 1 0 0 10 35 127 119 101 76 57 32 14 0 0 0 17 127 123 104 82 63 41 24 1 0 0 2 4 11 mat 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