Subdivide ... strip repeated

ab9ee5e5-f762-4cd7-af8d-b8ce45b0525e 28 15 12 decimal

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

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 :

Strip repeated in vector data Strip v data 1 col : k 0 : i 1 data rows 1 - (range v i 1 + el v i el ≠ R k k 1 + : el v i el : 11 line end of strip recover last u 21 line if 11 line for R X X cols el stack 41 line :

Subdivide X vector in 'n' subintervals X n split i 2 X cols (range determine 'p' the pivots p i el X i el X i 1 - el - (: u i 1 - el n p i el * p i el interval : 31 line for recompose the subdivided X v u 1 el X 1 el + : j 2 u rows range v v u j el X j el + (stack : for v 51 line :

Subdivide a range in 'n' intervals ... demo n pivot interval j 1 n 1 + (range h j el pivot - pivot j * + n / : for h 21 line :

Part 1 subdivide X-integer pivot range

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S 123 interval (:

S transpose 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3113 mat

On the pivot, you can ± add any bias at will

S transpose 2 ln - 11 mat 0.693 - 0.443 - 0.193 - 0.057 0.307 0.557 0.807 1.057 1.307 1.557 1.807 2.057 2.307 113 mat 11 mat

subdivide X 'n'
subdivided 'X' X 37912171816 mat : n 2 : 12 mat V X n split Strip : 21 sys

V 11 mat 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18311 mat 11 mat

XY X transpose X transpose augment : pts XY o 5 black plot : xy V V augment : mesh xy . 9 red plot : 41 sys

pts mesh 2 1 sys

Part 2 subdivide pair wise [vectors square Spline2D(M,x,y)]

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data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

user original polygon Xo 0.5 - 123456718 mat transpose : Yo 6 7.5 7.5 1.25 1.25 64718 mat transpose : 21 sys

sub 4 :

select subspaces

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

New 11 mat 0.5 - 6 0.125 - 6.375 0.25 6.75 0.625 7.125 1 7.5 1.25 7.5 1.5 7.5 1.75 7.5 2 7.5 2.25 5.938 2.5 4.375 2.75 2.812 3 1.25 3.25 1.25 3.5 1.25 3.75 1.25 4 1.25 4.25 2.438 4.5 3.625 4.75 4.812 56 5.25 5.5 5.5 5 5.75 4.5 64 6.25 4.75 6.5 5.5 6.75 6.25 77292 mat 11 mat

Part 3 subdivide pair wise [convex polyline]

]]> plotG(vx,vy,char,size,color) ... Hermite Polyline modules

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 :

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 :

data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

user original polygon Xo 0.5 - 123456718 mat transpose : Yo 6 7.5 7.5 1.25 1.25 64718 mat transpose : 21 sys

sub 3 :

select subspaces

t0 1 time :

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

X New 1 col : Y New 2 col : 21 line

t 01 0.05 range :

<= populate for more points at will

Polyline construct

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

t B t 3^- 3 t 2^* + 3 t * - 1 + 3 t 3^* 6 t 2^* - 3 t * + 3 t 3^* - 3 t 2^* + t 3^41 mat :

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

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 :

collect the project xy U Unwrap V Unwrap augment : Polyline xy Strip : 21 sys

XY X Y . 14 black plotG : XoYo Xo Yo + 15 black plotG : 21 line

Xo Yo augment Polyline XY XoYo 4 1 sys

1 time t0 - min 0.7

Part 4 populate rectangular Spline2D(M,x,y) vectors

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Xo 0.5 - 1.23 2.45 3.67 4.89 5.98 6.76 7.54 18 mat transpose :

sub 3 :

select subspaces

Sub Xo sub subspace : Xwild Xo 1 el Sub stack : 21 sys

Xwild 11 mat 0.5 - 0.0767 0.6533 1.23 1.6367 2.0433 2.45 2.8567 3.2633 3.67 4.0767 4.4833 4.89 5.2533 5.6167 5.98 6.24 6.5 6.76 7.02 7.28 7.54 221 mat 11 mat

uv Xo Xo augment : pts uv o 5 black plot : xy Xwild Xwild augment : mesh xy . 9 red plot : 41 sys

pts mesh 2 1 sys