plotG, RepEnd, Unwrap, Strip

a7ce8cfd-d884-41a2-b5a8-d62c3ee648b8 9 4 5 decimal

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

Esplina ... closed data set

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 :

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 :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ 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 :

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

XW 1.5 2.6 0 4.8 3.5 - 3.4 4.1 - 0 1.5 - 1.5 - 0 4.1 - 3.2 3.1 - 4.7 0 1.5 2.6 92 mat :

r 2 :

X XW 1 col r RepEnd : Y XW 2 col r RepEnd : XY X Y augment : 31 line

X XY 1 col : Y XY 2 col : Cntrl X Y . 14 black plotG : 31 line

α = 1/6 joins all points .
other α have  ± zoom effect α 110 / :

◄ Experiment α

populate @ will t 01 0.1 range :

Hermite Procedure

Hermite Interpolation t P α t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat * :

Each "j" segment is collected in matrix of 't' rows x 'j' cols. Each U,V is Unwrapped in column, augmented in 'xy', then stripped of repeated pairs for export.

t j XP μ j 11 line : t P 1 el X μ el * t P 2 el X μ 1 + el * + t P 3 el X μ 2 + el * + t P 4 el X μ 3 + el * + 21 line :

t j YP μ j 11 line : t P 1 el Y μ el * t P 2 el Y μ 1 + el * + t P 3 el Y μ 2 + el * + t P 4 el Y μ 3 + el * + 21 line :

j runs 1..rows(X)-(r+1)

U j 1 X rows r 1 + (- range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

xy U Unwrap V Unwrap augment :

xy xy Strip :

polygon XW 1 col XW 2 col . 14 black plotG :

strip both ends
for clean junction span xy rows t rows - 2 + : xy xy t rows span range 12 range el : 21 sys

H xy . 9 blue plot :

Hermite contour spline to Esplina

H XW polygon 3 1 sys

xy rows 81

xy [, xy # # el

range Finland Timo 111 range :

stuff Timo xy Timo 12 range el augment :

stuff 1 0.9 1.56 2 0.8554 1.69 3 0.8016 1.8298 4 0.7382 1.9757 5 0.6648 2.1245 6 0.5812 2.2725 7 0.4872 2.4163 8 0.3824 2.5525 9 0.2664 2.6774 10 0.139 2.7878 110 2.88 113 mat

data xy :

Locate 1rst exact value in vector V x col FindIdx j 1 : V j col el x ≠ j j 1 + : while j 0 ≡ inexistant j V j col el 12 mat if 31 line :

All values project

data data rows row 0.9 1.56 12 mat

data 1 col Max 2.8272

data 1 row 0.9 1.56 12 mat

# # # FindIdx

xy 2 col Max 2.88

xy 2 col Max xy 2 col Min 21 mat 2.88 2.484 - 21 mat

xy xy 1 col Max 1 findrows 2.8272 0.1982 - 12 mat

key data 1 col Max : col 1 : 12 mat

idxkey data 1 col key col FindIdx :

row of Max(X) idxkey 70 2.8272 12 mat

XY data idxkey 11 el row : 2.8 0.2 - 12 mat

key data 1 col Min : col 1 : 12 mat

idxkey data 1 col key col FindIdx :

row of Max(X) idxkey 28 2.5454 - 12 mat

XY data idxkey 11 el row : 2.5 - 0.6 12 mat

M key FindIndex r M rows : c M cols : 12 mat i 1 : j 1 : 12 mat j c ≤ (M i j el key ≠ (* i r < i i 1 + : i 1 : j j 1 + : 21 line if while j c ≤ i j 12 mat 0 if 41 line :

xy xy 2 col Max FindIndex 11212 mat

xy 112 el 2.88

xy 111 el 0

xy xy 2 col Min FindIndex 53212 mat

xy 112 el 2.88

xy 111 el 0

xy 532 el 2.484 -

xy 531 el 0.3677

range 115 range :

Hermite range xy range 12 range el augment :

Hermite 1 0.9 1.56 2 0.8554 1.69 3 0.8016 1.8298 4 0.7382 1.9757 5 0.6648 2.1245 6 0.5812 2.2725 7 0.4872 2.4163 8 0.3824 2.5525 9 0.2664 2.6774 10 0.139 2.7878 110 2.88 12 0.2045 - 2.8774 13 0.4181 - 2.8541 14 0.6378 - 2.8111 15 0.8606 - 2.7494 153 mat

range 4060 range :

Hermite range xy range 12 range el augment :

Hermite 40 1.0689 - 0.81 - 41 0.9 - 0.9 - 42 0.808 - 1.0728 - 43 0.721 - 1.2494 - 44 0.6371 - 1.427 - 45 0.5549 - 1.6027 - 46 0.4725 - 1.7738 - 47 0.3883 - 1.9373 - 48 0.3007 - 2.0905 - 49 0.2078 - 2.2306 - 50 0.1082 - 2.3547 - 510 2.46 - 52 0.1798 2.4824 - 53 0.3677 2.484 - 54 0.5617 2.4658 - 55 0.7598 2.4288 - 56 0.96 2.3737 - 57 1.1602 2.3016 - 58 1.3583 2.2132 - 59 1.5523 2.1096 - 60 1.7402 1.9916 - 213 mat