<p> plotG(vx,vy,a,b,c) </p>

ab555324-62b7-4c89-9a08-eca88afaa9c1 7 15 12 decimal

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

Bézier parametric Cubic

scale 2 : (scale at will ≡

p scale 1 - 22 - 112 - 2 - 124 mat * transpose :

For more pairs of control points Bernstein procedure extends Bézier. Similarly, De Boor is not limited by the number of points.

X p 1 col :

Y p 2 col :

t b0 t 3^- 3 t 2^* + 3 t * - 1 + (: t b1 3 t 3^* 6 t 2^* - 3 t * + (: t b2 3 t 3^* - 3 t 2^* + (: t b3 t 3^: 41 line

θ rot θ cos θ sin - θ sin θ cos 22 mat :

p 2 - 244 - 4 - 4 - 2242 mat

θ 3 π * 4 / :

θ 2.3562

t bX t b0 X 1 el * t b1 X 2 el * + t b2 X 3 el * + t b3 X 4 el * + : t bY t b0 Y 1 el * t b1 Y 2 el * + t b2 Y 3 el * + t b3 Y 4 el * + : 21 line

t 01 0.005 range : (range 't' at will ≡

Bz i 1 t rows range bX i el t i el bX eval : bY i el t i el bY eval : 21 line for bX 3 round vectorize bY augment 21 line :

Bézier Cubic 4 cntrl points

p θ rot * Bz θ rot * 2 1 sys

Bézier Cubic 4 cntrl points

Bz 2 1 sys

Bz rows 201

M Bz :

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 0 if 41 line :

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

rowidx M 1 col 2 - FindIndex M 1 col 1 - FindIndex M 1 col 0 - FindIndex M 1 col 1 FindIndex M 1 col 2 FindIndex 51 mat : 11410118820151 mat

i j 21 mat transpose

XY Bz 1 row Bz 14 row Bz 101 row Bz 188 row Bz 201 row 51 mat :

Bezier XY UnestRow : 2 - 21 - 0.90605 0 2.5 - 1 0.90605 2252 mat

<p> plotG(vx,vy,a,b,c) </p>

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

V(sizechar,n)... V(colorchar,n) var n V n 1 ≡ var ct 1 : j 1 n range b ct 1 el var : ct ct 1 + : 21 line for U b 1 el : k 2 b rows range U U b k el stack : for U 51 line if :

nodes Bezier 1 col : NodesLabel nodes var2str vectorize : X Bezier 1 col : Y Bezier 2 col : 12 mat n X rows : Graph nodes Y augment : 51 line

plot symbol converted2Numbers

symbol color

nodes_label X Y NodesLabel 10 n V blue n V augment :

data X Y . 14 black plotG :

Bézier Cubic 4 cntrl points

data Bz nodes_label 3 1 sys

Bezier 2 - 21 - 0.90605 0 2.5 - 1 0.90605 2252 mat