fa9bf39e-3800-448e-bac5-2f020f0be63c 25 4 5 decimal

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

u v char size clr plotG n u length : plot u 1 el v 1 el char size clr augment : i 2 n range plot plot u i el v i el char size clr augment stack : for plot 41 line :

X 2 - 0231 mat :

Y 02031 mat :

<= User control points

XY X Y augment :

Cntrl X Y . 14 black plotG :

Bézier parametric Quadratic

t b0 1 t - (2^(:

t b1 2 t * 1 t - (* :

t b2 t 2^:

t bX t b0 X 1 el * t b1 X 2 el * + t b2 X 3 el * + :

t bY t b0 Y 1 el * t b1 Y 2 el * + t b2 Y 3 el * + :

t 3 - 3 2.99 - range :

B 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 Quadratic 3 cntrl points

XY B Cntrl 3 1 sys

XY 2 - 0022032 mat

Bézier parametric Cubic

X 033841 mat :

Y 7102441 mat :

<= User control points

XY X Y augment :

Cntrl X Y . 14 black plotG :

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^:

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 * + :

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

shiftXdomain 3 :

X 3 - 2 - 1 - 0012318 mat transpose shiftXdomain + :

Bézier-Bernstein

t0 1 time :

Y 0122 - 2 - 21018 mat transpose :

Smath is capricious with Bézier-Bernstein. Because of the indexing starting at '1', it does NOT run with X in the negative domain. In this demo, we shift the X domain to enable Smath compute. Once the plot is done, it's possible to shift the system back. NOT done ! Experiment with the weight vectors Wx, Wy and adapt the control polygon for the plot. -------- Bézier-Bernstein hyperfast ---------

n X rows :

n 8

Wy 1111111118 mat transpose :

Wx 1111111118 mat transpose :

Bézier-Bernstein procedure j n t Q n! j! (n j - (! (* / t j^* 1 t - (n j -^* :

t QX j n t Q X j el * Wx j el * (j 1 n sum :

t QY j n t Q Y j el * Wy j el * (j 1 n sum :

t 01 0.005 range :

BezBern i 1 t rows range qX i el t i el QX : qY i el t i el QY : 21 line for qX qY augment 21 line :

XY X Y augment :

Cntrl X Y . 14 black plotG :

Bézier-Bernstein cntrl points

XY BezBern Cntrl 3 1 sys

data 1 - 0.242 0.888 - 0.157 0.756 - 0.085 0.609 - 0.003 0.453 - 0.005 0.294 - 0 0.142 - 0.015 0 0.035 0.134 0.068 0.266 0.099 0.41 0.129 0.513 0.183 0.627 0.235 0.729 0.307 0.824 0.376 0.902 0.462 0.948 0.557 0.99 0.649 1 0.735 1 0.809 0.987 0.871 0.962 0.918 0.939 0.952 0.91 0.981 0.879 0.992 0.847 1 0.819 0.997 0.799 0.991 0.78 0.979 0.761 0.961 0.744 0.937 0.721 0.907 0.698 0.872 0.675 0.83 0.659 0.781 0.649 0.725 0.649 0.659 0.66 0.582 0.676 0.487 0.695 0.369 402 mat :

1 - 0.5 - 2.95 0.245 0.575 0.729 0.242 0.45 - 0.15 2.18 0.69 0.307 26 mat

1 time t0 - 1.2 sec *

------------ The Lobe project ----------

p 0 1.5 3.65 1.32 1.57 1.73 0.25 0.25 - 0.15 2.275 0.675 0.3 26 mat transpose :

shift 1 :

X p 1 col :

Y p 2 col :

data data 1 col shift + data 2 col augment :

XY X Y augment :

n X rows :

The Lobe project fails to reproduce Mathcad 11 with the same control polygon. Modify this polygon hopping for a better fit. The left end part looks recalcitrant, can't fix.

t QX j n t Q X j el * (j 1 n sum :

t QY j n t Q Y j el * (j 2 n sum :

t 01 0.01 range :

Lobe i 1 t rows range LX i el t i el QX : LY i el t i el QY : 21 line for LX LY augment 21 line :

The Bézier-Bernstein procedure need not be repeated here, i.e: a function like any built-in.

XY X Y augment :

Cntrl X Y . 14 black plotG :

data data 1 col data 2 col o 5 green plotG :

XY Lobe Cntrl data 4 1 sys