<content> img2xy </content>

2cc2e6d4-4fc6-4120-a472-51b8afb77a02 43 4 5 false false 0 decimal

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

Embedding images into a plot

\032E\c hex\0024\.2 hex\0324\ 0123456789ABCDEF : n\0324\ 0255 \032E\c 0 round 12 mat min 12 mat max : m\032E\ n\0324\ 16 mod : 12 mat n\0324\ m\032E\ - 16 mod 0 ≡ hex\0324\ n\0324\ m\032E\ - 16 / 1 + 1 substr hex\0324\ m\032E\ 1 + 1 substr concat hex\0324\ m\032E\ 1 + 1 substr if 31 line :

M a img2xyAux α # 255 a * hex\0024\.2 concat : C 0 : 12 mat M rows 1 ≡ R G B 13 mat M : R G B 13 mat R hex\0024\.2 vectorize G hex\0024\.2 vectorize B hex\0024\.2 vectorize 13 mat : k 1 G length range : C k el α R k el G k el B k el concat : 41 line G M hex\0024\.2 vectorize : k 1 G length range : C k el α G k el G k el G k el concat : 31 line if m G rows : n G cols : 12 mat k n m 1 k 1 - n / trunc + (- vectorize k 1 - n mod vectorize C 15 mat 41 line :

M ch sz a img2xy k n r c clr 15 mat M a img2xyAux eval : c r ch sz clr augment 21 line :

M a img2xy k n r c clr 15 mat M a img2xyAux eval : K 0 : K k el rect c k el r k el 11 stack 11 mat clr k el solid 1 clr k el stack eval : 11 mat 31 line :

Shorthand

P# Point P# str2num o 10 red augment P# str2num 1 - P# 10 red augment 21 sys eval 11 line :

M ch sz a img2xy

Plots the image in M with characters ch with size sz and transparency color a into a native SMath plot

M a img2xy

Plots the image in M with transparency color a into a XY plot plugin

<content> Example: LogSpiral </content>

Example: Logarithmic spiral

Nautilus shell

M Nautilus.jpg image2rgb :

a b Clear 1

Image from:
https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/318px-NautilusCutawayLogarithmicSpiral.jpg

Read this values from the graph

xo 68 :

yo 89 :

for

O xo yo 12 mat :

∞ - f O ≡

xa 174 :

A xa yo 12 mat :

0 f A ≡

xb 103 :

B xb yo 12 mat :

2 π * f B ≡

Logarithmic spiral equation

t f a b t^* t cos t sin - 12 mat * xo yo 12 mat + :

Solving numerically

a 0 f vectorize 1 el xa - a roots eval :

a 106

b 2 π * f vectorize 1 el xb - b 1 roots eval :

b 0.8383

Or by hand

0 f a 1012 mat * xo yo 12 mat + ≡

\0020\ xa yo 12 mat ≡

thus

a xa xo - : 106

b xb xo - a / 2 π * nthroot : 0.8383

2 π * f a b 2 π *^* 1012 mat * xo yo 12 mat + ≡

\0020\ xb yo 12 mat ≡

Plot in SMath

XY 02 matrix : t 06 π * (0.1 range XY XY t f stack eval : for Π XY A Point B Point O Point M █ 4 0.6 img2xy 51 sys : 31 line

Plot in XY plugin.

Π M 0.8 img2xy A Point B Point O Point XY 51 sys : 11 line

Image in this sample:

<content> Example: Catenary </content>

Example: Catenary

We use here the grayscale of the image.

Budapest Keleti Railway Station

M Budapest_Keleti_teto.jpg image2rgb :

GS 13 / M sum (* :

Image from:
https://upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Budapest_Keleti_teto_1.jpg/320px-Budapest_Keleti_teto_1.jpg

Read this points in the graph

A 86412 mat :

O 8211412 mat :

a xo yo Clear 1

Catenary equation

x f a x xo - a / cosh * yo + :

with

xo O 1 el :

yo A 2 el O 2 el + :

Find a

a O 1 el f O 2 el ≡ a 50 - roots eval : 64 -

Plot in SMath

B 2 O 1 el * A 1 el - A 2 el 12 mat : X A 1 el B 1 el A 1 el - 100 / 0100 range * + : Π X X f vectorize augment A Point B Point O Point GS █ 4 0.4 img2xy 51 sys : 31 line

Plot in XY plugin.

Π GS 0.8 img2xy A Point B Point O Point x f 51 sys : 11 line

Image in this sample:

Alvaro