DeBoor Colibri Triplet

73e0d95b-f1db-4f2e-bd2e-21a4a972339b 12 6 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 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

data 3 1.5 0 3.05 1.5019 0.0012 3.1 1.5075 0.005 3.15 1.5169 0.0112 3.2 1.53 0.02 3.25 1.5469 0.0312 3.3 1.5675 0.045 3.35 1.5919 0.0612 3.4 1.62 0.08 3.45 1.6519 0.1013 3.5 1.6875 0.125 3.55 1.7269 0.1512 3.6 1.77 0.18 3.65 1.8169 0.2112 3.7 1.8675 0.245 3.75 1.9219 0.2812 3.8 1.98 0.32 3.85 2.0419 0.3612 3.9 2.1075 0.405 3.95 2.1769 0.4512 4 2.25 0.5 4.05 2.3256 0.5475 4.1 2.4025 0.59 4.15 2.4806 0.6275 4.2 2.56 0.66 4.25 2.6406 0.6875 4.3 2.7225 0.71 4.35 2.8056 0.7275 4.4 2.89 0.74 4.45 2.9756 0.7475 4.5 3.0625 0.75 4.55 3.1506 0.7475 4.6 3.24 0.74 4.65 3.3306 0.7275 4.7 3.4225 0.71 4.75 3.5156 0.6875 4.8 3.61 0.66 4.85 3.7056 0.6275 4.9 3.8025 0.59 4.95 3.9006 0.5475 54 0.5 5.05 4.1 0.4563 5.1 4.2 0.425 5.15 4.3 0.4063 5.2 4.4 0.4 5.25 4.5 0.4062 5.3 4.6 0.425 5.35 4.7 0.4562 5.4 4.8 0.5 5.45 4.9 0.5562 5.5 5 0.625 5.55 5.1 0.7062 5.6 5.2 0.8 5.65 5.3 0.9062 5.7 5.4 1.025 5.75 5.5 1.1562 5.8 5.6 1.3 5.85 5.7 1.4562 5.9 5.8 1.625 5.95 5.9 1.8062 662 6.05 6.0937 2.1925 6.1 6.175 2.37 6.15 6.2437 2.5325 6.2 6.3 2.68 6.25 6.3437 2.8125 6.3 6.375 2.93 6.35 6.3937 3.0325 6.4 6.4 3.12 6.45 6.3938 3.1925 6.5 6.375 3.25 6.55 6.3438 3.2925 6.6 6.3 3.32 6.65 6.2438 3.3325 6.7 6.175 3.33 6.75 6.0938 3.3125 6.8 6 3.28 6.85 5.8938 3.2325 6.9 5.775 3.17 6.95 5.6438 3.0925 7 5.5 3 7.05 5.355 2.905 7.1 5.22 2.82 7.15 5.095 2.745 7.2 4.98 2.68 7.25 4.875 2.625 7.3 4.78 2.58 7.35 4.695 2.545 7.4 4.62 2.52 7.45 4.555 2.505 7.5 4.5 2.5 7.55 4.455 2.505 7.6 4.42 2.52 7.65 4.395 2.545 7.7 4.38 2.58 7.75 4.375 2.625 7.8 4.38 2.68 7.85 4.395 2.745 7.9 4.42 2.82 7.95 4.455 2.905 8 4.5 3 8.05 4.5419 3.1 8.1 4.5675 3.2 8.15 4.5769 3.3 8.2 4.57 3.4 8.25 4.5469 3.5 8.3 4.5075 3.6 8.35 4.4519 3.7 8.4 4.38 3.8 8.45 4.2919 3.9 8.5 4.1875 4 8.55 4.0669 4.1 8.6 3.93 4.2 8.65 3.7769 4.3 8.7 3.6075 4.4 8.75 3.4219 4.5 8.8 3.22 4.6 8.85 3.0019 4.7 8.9 2.7675 4.8 8.95 2.5169 4.9 9 2.25 5 9.05 1.9819 5.0975 9.1 1.7275 5.19 9.15 1.4869 5.2775 9.2 1.26 5.36 9.25 1.0469 5.4375 9.3 0.8475 5.51 9.35 0.6619 5.5775 9.4 0.49 5.64 9.45 0.3319 5.6975 9.5 0.1875 5.75 9.55 0.0569 5.7975 9.6 0.06 - 5.84 9.65 0.1631 - 5.8775 9.7 0.2525 - 5.91 9.75 0.3281 - 5.9375 9.8 0.39 - 5.96 9.85 0.4381 - 5.9775 9.9 0.4725 - 5.99 9.95 0.4931 - 5.9975 10 0.5 - 61413 mat :

Cntrl 1.5 0 1.5 03150744254 0.5 - 6 0.5 - 692 mat :

DeBoor data 2 col data 3 col augment data 1 col data 2 col augment data 1 col data 3 col augment 31 sys :

XY axes system x y XY x y / - :

data rows 141

DeBoor XY 2 1 sys

control polygon X 1.5 35745 0.5 - 71 mat : Y 010424671 mat : 12 mat

Points X Y . 14 black plotG :

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

X Y augment DeBoor 1 el Points 3 1 sys Finite differences ArcLength

Finite differences derivative X data 2 col : Y data 3 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 : 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 - abs : 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

Length Σ Σ rows row : 0.5 - 16.01601 12 mat

j 120 :

Σ j row 2.5169 12.803128 12 mat

1rst element in 'V' that exceeds threshold. V threshold FindIdx j 1 : V j el abs threshold ≤ j j 1 + : while j 1 - V j el 12 mat 31 line :

search idx for value λ 8 :

idx Σ 2 col λ FindIdx : 82 8.157 12 mat

User system specifications User 16.016 0.20 blue 15 mat Σ 2 col Σ 1 col 0 * augment . 10 red plot Σ Σ j row 12 el 0.20 black 15 mat Σ j row 11 el Σ j row 12 el . 14 black 15 mat idx 12 el 0 + 40 blue 15 mat 61 sys :

For better visibility, deploy the 'Y' direction of arc length Σ on flat fake direction 'X'.

User

Random user 'J' DeBoor arc length on running 'x' j Σ j row 12 mat 120 2.5169 12.803128 12 mat 12 mat