<p> Functions Dave Carpi </p>

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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 :

t = interpolation point in [0,1]
p = control points t p DeCasteljau De Casteljau SMath 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 31 line :

t = range of interpolation points in [0,1]
p = control points 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 :

ndp =  number of discretization points (> 1)
p = control points ndp p B 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 41 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 :

NDP 100 :

svg 1 :

p svg 3 - 4 - 4 - 2 - 2 - 00242 mat 022042 - 34 - 42 mat 21 mat * :

p1 svg 3 - 4 - 4 - 2 - 2 - 0022042 - 34 - 72 mat * :

bezier NDP p 1 el B :

Picture region

i 2 p length range bezier bezier NDP p i el B stack : for

This demo exemplifies the nested [,] construction of Bézier. "svg" scales both directions of the data set. All maths are active below the top border of the Picture region. Rotate at will. To access the QuickPlot: slide the Picture region up/down, or right. Smath background: [255, 255, 225]

a b c spec + 14 black 13 mat :

PTS p1 a b c spec pts :

Bézier mirror construction

p1 bezier PTS 3 1 sys

bezier 2 cols data set export ≡

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

θ π - 2 / :

θ 1.5708 -

RotData p1 θ rot * :

RotBezier bezier θ rot * :

RotData RotBezier 2 1 sys

Switch the border ON/OFF from menu. Picture region does not allow sub- background. The region switches OFF the grid lines for neater view.

SVG post processing: magify/reduce

α 3 :

Bα α p1 * 1 col α p1 * 2 col + 14 black plotG :

Minaret α bezier * 1 col α bezier * 2 col augment :

At this point, αp1 & Minaret can be exported to a graphic package for additional graphic stuff. This is conditional the graphic package can read these two pieces of information. For instance, points could be recentered except for the apex thus imitating the real view and by same token enable the carpenter view his finished product.

top 07 o 30 red 15 mat :

α p1 * Minaret Bα top 4 1 sys