5ef2176c-7f78-428e-8fe5-fba5aa704abb 4 4 5 decimal

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

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 :

t0 1 time :

Bézier parametric Cubic

X 033841 mat :

Y 7102441 mat :

<= User control points

XY X Y augment :

Cntrl X Y . 14 black plotG :

Bézier cubic 4 control points 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 sys

Bézier parametric 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 sys

t 1 - 10 0.99 - range :

Bz i 1 t rows range bX i el t i el bX : bY i el t i el bY : 21 line for bX bY augment 21 line :

Bézier Cubic 4 cntrl points

XY Bz Cntrl 3 1 sys

Isolate the repeated polygon.
Those X, Y used in  Sx(v), Sy(v) X 00338816 mat transpose : Y 771024416 mat transpose : 21 line

DeBoor 'u' vector

u 1 X rows n 2 + (+ range :

v j N0 μ j 11 line : u μ el v ≤ (v u μ 1 + el < (& 10 if 21 line :

v j N1 μ j 11 line : v u μ el - u μ 1 + el u μ el - / v μ N0 * u μ 2 + el v - u μ 2 + el u μ 1 + el - / v μ 1 + N0 * + 21 line :

v j N2 μ j 11 line : v u μ el - u μ 2 + el u μ el - / v μ N1 * u μ 3 + el v - u μ 3 + el u μ 1 + el - / v μ 1 + N1 * + 21 line :

v j N3 μ j 11 line : v u μ el - u μ 3 + el u μ el - / v μ N2 * u μ 4 + el v - u μ 4 + el u μ 1 + el - / v μ 1 + N2 * + 21 line :

n 2 : (DeBoor spline order ≡

v j N μ j 11 line : v μ N1 21 line 11 mat :

activate spline order 'n' = 1

v j N μ j 11 line : v μ N1 21 line μ j 11 line : v μ N2 21 line 21 mat :

activate spline order 'n' = 2

v j N μ j 11 line : v μ N1 21 line μ j 11 line : v μ N2 21 line μ j 11 line : v μ N3 21 line 31 mat :

activate spline order 'n' = 3

Defined as local definition v Sx v k N n el X k el * (k 1 X rows sum 11 line :

Defined as local definition v Sy v k N n el Y k el * (k 1 X rows sum 11 line :

λ X length : vx 31 λ + (3.05 range : 21 line

As it looks, 'vx' always starts @ 3 ... ends @ search (?+λ)

i 1 vx rows range SX i el vx i el Sx : for

vx rows 81

i 1 vx rows range SY i el vx i el Sy : for

DeBoor SX SY augment :

1 time t0 - 38.8 s *

Cntrl X Y . 14 black plotG :

Polygon X Y augment :

De Boor parametric order 2 wrt Smath ... kind of Convex Hull

Polygon DeBoor Cntrl 3 1 sys