<p> Utilities </p>

f4edfdba-2c20-4731-8f5a-be8b8563cdfd 5 4 5 decimal

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

<p> Utilities </p>

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Mesh U, V  within the bounds L, H L H N xd N intervals U 0 : dx H L - N / : i 1 N 1 + range U i el L dx i * dx - (+ : for U 51 line :

The contour extractor , pair wise in X direction M ε cntr CONTR count 1 : i 1 M rows range j 1 M cols range u count el i : v count el j : 21 line M i j el cntr - abs ε ≤ count count 1 + : cases for for u v augment 31 line :

data Strip2 nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

L 1 - :

H 1 :

N 48 :

t0 1 time :

U L H N xd :

V U :

This document has nothing to wrt RHMSD. It illustrates extracting an isocurve from discretizing an image. This project is easy to clean/sort. Closed isocurve needs be sorted by hand or via program not yet designed in Smath.

x y f x 2^y 2^- 1 + :

M x y f U V Sym eval :

M M 0255 Scale :

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rotate 90°

ε 1 :

level 120 :

in this example [0..255] the search within 1 pixel is OK.

Q M ε level CONTR :

XY Q Strip2 : Export the project ≡

Shift/center the system

v i 1 XY rows range v i el XY 2 col i el : for v 2 v * v Min - v Max - v Max v Min - / : 21 line :

i 1 XY rows range u i el XY 1 col i el : for u 2 u * u Min - u Max - u Max u Min - / : 21 line

Export u v augment eval :

pts Export . 9 red plot :

c 00 + 100 cyan 15 mat :

S Export 1 col Export 2 col sort augment :

c pts 2 1 sys

S S eval :

sub S 219 range 12 range el :

neg sub 1 col 1 - (* reverse sub 2 col reverse augment :

st sub neg stack :

1 time t0 - min 0.4

st - st 2 1 sys

x y axes x y / - :

f axes 2 1 sys

maple solve implicit f(x,y)≡ 0 x m x y f y solve maple :

x m 1 el x m 2 el 2 1 sys

At this point, you may want to smooth the project then pass a spline function.