DeCasteljauNDP(ndp,p)

4a4db73a-765b-45c2-8bae-410141cee6ff 16 15 12 decimal

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DeCasteljau SVG algorithm chained style

ndp =  number of discretization points (> 1) in the prescribed range  0..1
p = control points ... each segment is populated 'ndp'... modules from Davide Carpi ndp p DeCasteljauNDP t p DeCasteljau M 1 t - (p 1 row * t p 2 row * + : p rows 2 > i 2 p rows 1 - range M M 1 t - (p i row * t p i 1 + row * + stack : for t M DeCasteljau 21 line M if 21 line : --------------------------------------------------- t p DeCasteljauRange M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 31 line : ---------------------- t 011 ndp 1 - / range : M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 81 line :

NDP p bezier bezier NDP p 1 el DeCasteljauNDP : i 2 p length range bezier bezier NDP p i el DeCasteljauNDP stack : for bezier 31 line :

scale factor [B, p] svg 1 :

The all thing is about the construction of the 5 nest-vectors: join straight or join curved [Bézier/DeCasteljau]. Independently of each other, Paul De Casteljau implemented Pierre Bézier curves otherwise constructed. Since, CAD systems.

B svg 600603003006021560350603502035010 - 28550 - 92 mat * :

p svg 606000303023 mat 00030306023 mat 0021560606023 mat 21535035060602023 mat 3503502852010 - 50 - 23 mat 15 mat transpose * :

The red plot bezier 100 p bezier :

plot B bezier p 31 sys :

plot

svg 1

svg 1.25 :

polygon svg 10110132 mat * :

p svg 11001123 mat 00011123 mat 12 mat transpose * :

x C 1 x 2^- sqrt ± :

bezier 100 p bezier :

polygon bezier 2 1 sys

11001123 mat 00011123 mat 12 mat transpose 10110132 mat 01010132 mat 21 mat

The Smath filtrate bin CAD style Export this independent section.

DeCasteljau

ndp =  number of discretization points (> 1) in the prescribed range  0..1
p = control points ... each segment is populated 'ndp'... modules from Davide Carpi ndp p DeCasteljauNDP t p DeCasteljau M 1 t - (p 1 row * t p 2 row * + : p rows 2 > i 2 p rows 1 - range M M 1 t - (p i row * t p i 1 + row * + stack : for t M DeCasteljau 21 line M if 21 line : --------------------------------------------------- t p DeCasteljauRange M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 31 line : ---------------------- t 011 ndp 1 - / range : M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 81 line :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

XY 100020201015 - 05050015 - 26 mat transpose :

a b c spec . 14 black 13 mat :

xy XY a b c spec pts :

svg 1 :

p svg 1010015 - 15 - 023 mat 000005023 mat 0102050605023 mat 202020500023 mat 201010015 - 15 - 23 mat 15 mat transpose * :

NDP 100 :

NDP Number Discrete Points ≡

C 0200020000505025 mat transpose :

level 510151022 mat :

bin NDP p 1 el DeCasteljauNDP :

i 2 p length range bin bin NDP p i el DeCasteljauNDP stack : for

C bin level 31 sys

C bin level 3 1 sys

C 0020000050205052 mat

data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

Experiment  ... (svg>1)&(svg<1) svg 1 :

svg 1 > (svg 1 < (&

move 200 :

up 25 :

p svg 606000303023 mat 00030306023 mat 00 move 60606023 mat move 3503506060 up 23 mat 350350285 up 10 - 50 - 23 mat 15 mat transpose * :

p p 2 1 sys

p UnestV 6006030030030030060060060200602006035060350253502535010 - 28550 - 152 mat