<p> plotG</p>

0c346833-9370-4225-af6b-11f2e7b228e5 11 4 5 decimal

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

<p> plotG</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 :

u b 0 u 2 - ≤ 16 / 2 u + (3^* 2 - u ≤ (u 1 - ≤ (& 16 / 2 u + (3^* 23 / 1 u + (3^* - 1 - u ≤ (u 0 ≤ (& 23 / 1 u - (3^* - 16 / 2 u - (3^* + 0 u ≤ (u 1 ≤ (& 16 / 2 u - (3^* 1 u ≤ (u 2 ≤ (& 0 cases :

The Gaussian b-spline

Gaussian basis 'b-spline'

2 - x ≤ x 2 ≤ & x b Undefined if

0 b 0.6667

u v Bsp v m el u m - b * (m 1 v rows sum :

observe u b u 2 - 2 int 1

X 1.875 1.875 1.95 2 2.05 2.125 2.125 2.125 18 mat : Y 11101 - 1 - 1 - 1 - 18 mat : 21 line

The XY plot allows to plot in the reverse X direction. The choice of the control points is by "user". You may have to trick the ranging of 't'. "data" is an export. There is no limit in the length of X, Y. With this kind of spline, you always have to at least duplicate end points [here RHS is triplicate]

XY X transpose Y transpose augment : u oy u Y transpose Bsp : u ox u X transpose Bsp : 31 sys

Points X transpose Y transpose . 14 black plotG :

data t 1.75 6.75 1.8 range : i 1 t rows range vx i el t i el ox : vy i el t i el oy : 21 line for vx vy augment 31 line :

data rows 101

XY data 2 1 sys XY data Points 3 1 sys

Finite differences derivative X data 1 col : Y data 2 col : 12 mat n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - (range deriv i el 0.5 Y i 1 - el Y i el - X i 1 - el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for deriv 1 el deriv 2 el : deriv n el deriv deriv rows 1 - el : D X deriv augment : Arc integrand .................... xx D 1 col : δx D 2 col : 12 mat i 1 δx rows range yy i el 1 δx i el (2^+ sqrt eval : 11 line for Arc xx yy augment : Arc length ....................... vx Arc 1 col : vy Arc 2 col : 12 mat S 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : S i el S i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for Σ vx S augment : 181 line

D Arc Σ

Because

of the ranging of 't' that is difficult

to adjust, spooling to file is a

desirable conservative option.

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CWD C:\SmathFile CurrentDirectory :

Arc CWD ArcRobotics wfile 1

Arc CWD ArcRobotics rfile :

X Σ 1 col : Y Σ 2 col : 12 mat

arc length from interpolation x arc X Y x ainterp :

2 arc 1.0055