plotG(vx,vy,char,size,color)

e02cbe0b-e851-4ae4-92c9-83e715d2c148 6 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 :

z n RepEnd m z rows : i 1 n range w i el z 1 el : for i n 1 + (m n + (range w i el z i n - el : for i m n + 1 + (m 2 n * + (range w i el z m el : for w 51 line :

data Strip nest stripped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows 1 - range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ R k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v R 1 el : j 2 R rows range v v R j el stack : for v 81 line :

M Unwrap V M 1 col : i 2 M cols range V V M i col stack : for V 31 line :

Understanding SVG

t0 1 time :

Model from jmG Mathcad 8 Pro. made work in Smath by Davide Carpi

svg 1 :

vary center point to shift fillet X 0333815 mat transpose : Y 71062415 mat transpose : 21 sys

XY X Y + 15 blue plotG :

p svg 073103632 mat 36328432 mat 21 mat * :

xy X Y augment :

Bezier polyline from DeCasteljau algorithm

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'. 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 50 : bezier NDP p 1 el DeCasteljauNDP : i 2 p length range Bezier bezier NDP p i el DeCasteljauNDP stack : for 31 line

Hermite Polyline

r 2 : X X r RepEnd : Y Y r RepEnd : 31 sys

x c 10 x ≤ (x 1 ≤ (& cases :

Hermite PolyLine t P 16 / t 3^- 3 t 2^* + 3 t * - 1 + (3 t 3^* 6 t 2^* - 4 + (3 t 3^* - 3 t 2^* + 3 t * + 1 + (t 3^41 mat * :

Hermite basis cubics 0...1

x P 1 el x c * x P 2 el x c * x P 3 el x c * x P 4 el x c * 4 1 sys

X Y augment 070707310363284848492 mat

t j XP μ j 11 line : t P 1 el X μ el * t P 2 el X μ 1 + el * + t P 3 el X μ 2 + el * + t P 4 el X μ 3 + el * + 21 line :

t j YP μ j 11 line : t P 1 el Y μ el * t P 2 el Y μ 1 + el * + t P 3 el Y μ 2 + el * + t P 4 el Y μ 3 + el * + 21 line :

t 01 0.025 range :

<= populate for more points at will

j runs 1..rows(X)-(r+1)

U j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hx i ct el t i el j XP eval : for ct ct 1 + : 21 line for Hx 41 line :

V j 1 X rows r 1 + (- (range : ct 1 : j j i 1 t rows range Hy i ct el t i el j YP eval : for ct ct 1 + : 21 line for Hy 41 line :

X rows r 1 + (- 6

collect the project xy U Unwrap V Unwrap augment : Hermite xy Strip : 21 sys

01 0.025 range

Parametric Polylines: redHermite, greenBézier

XY Hermite Bezier X Y augment 5 1 sys

Each "j" segment is collected in matrix of 't' rows * 'j' cols. Each U,V is Unwrapped in column, augmented in 'xy', then stripped of repeated pairs for export. From this basis Hermite Polyline you can draw from whatever control points XY vectors. The all thing is within the triplet programs 'U,V', Unwrap, strip.

1 time t0 - 18 s *

Explain:

Bernstein is NOT a polyline. It collects a single

set of values. Unlike Bernstein, Hermite polyline

collects over the sliding 'j' columns, which are

afterwards stacked [Unwrap]. and stripped of

repeated values.

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