868241d2-8c31-418e-a0e6-f4eb53043c0d 19 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 :

X 0 0.5 1 1.5 2 2.5 61 mat :

Y 12 3.1 2.9 1.7 2.8 61 mat :

u 0 0.75 1.25 1.75 2.75 51 mat :

t 1 el u 1 el 2 u 2 el u 1 el - (* - : t 2 el u 1 el u 2 el u 1 el - (- : 21 sys

t t u stack (: 1.5 - 0.75 - 0 0.75 1.25 1.75 2.75 71 mat

n u length : 5

t n 3 + el u n el u n el u n 1 - el - (+ : t n 4 + el u n el 2 u n el u n 1 - el - (* + : 21 sys

t transpose 1.5 - 0.75 - 0 0.75 1.25 1.75 2.75 3.75 4.75 19 mat

The vector of the control points 't' must be in ascending order

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Lagrange piecewise Quadratic [order 2] k x B1 k 4 el x - (2^k 4 el k 2 el - (k 4 el k 3 el - (* / : k x B2 k 4 el k 1 el - (k 3 el x - (2^* - k 4 el k 3 el - (k 3 el k 2 el - (* k 3 el k 1 el - (* / : k x B3 k 4 el k 1 el - (k 2 el x - (2^* k 4 el k 2 el - (k 3 el k 2 el - (* k 2 el k 1 el - (* / : 31 sys

Lagrange Quadratic Generatrix k x b k 1 el x ≤ (x k 2 el ≤ (& k x B1 k x B2 + k x B3 + k 2 el x ≤ (x k 3 el ≤ (& k x B1 k x B2 + k 3 el x ≤ (x k 4 el ≤ (& k x B1 0 if if if 11 line :

x t 1 el t t rows el t 1 el 0.01 + (range :

Lagrange poly from Quad knots. n x Bp t n el t n 1 + el t n 2 + el t n 3 + el 41 mat x b :

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 6 1 sys

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 61 sys

Tridiag of QuadCoeff r 1 X rows range : ii r j r M ii j el j X ii el Bp : for for 31 line

s M 1 -^Y * : 0.3748 1.6252 3.2912 3.0942 0.4684 8.3694 61 mat

tt t t augment : tx tt 1 col : ty tt 2 col : 31 line

XY X Y . 10 black plotG : cntrl t 0 t * o 5 blue plotG : txty tx ty o 5 blue plotG : 31 line

shadow in the context: 'i' converts imaginary 'i' to number ... Φ(α,x)

x L s j el j x Bp * (j 1 s rows sum :

x 2 - 6 1.99 - range :

Spline i 1 x rows range vy i el x i el L eval : for x vy augment 21 line :

Spline Spline :

XY Spline cntrl txty tt 51 sys

Complete plot of Lagrange Quadratic b_spline ... equivalent to Mathcad bspline(vx,vy,u,2) ... OBSERVE: the flat ends of the spline, a most desirable feature in Engineering/Scientific works.

XY Spline cntrl txty tt 5 1 sys

h 0.001 :

x f x L :

x h f deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

piecewise linear of quadratic segments

x h f deriv 1 1 sys

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + : 21 line for vx Y augment 61 line :

Spline Σ

===== Other stuff =====

b1 3.5 - : b2 1.5 : β 4 - : 13 mat

x spline1 β x * 2 β * b1 + (x 2^* - β b1 + (x 3^* + : x spline2 β x * 2 β * b2 + (x 2^* - β b2 + (x 3^* + : 21 line

α x Φ 1 i 2 * π * x * - exp - i 2 * π * x * / (α 1 +^:

x c 10 x ≤ (x 1 ≤ (& cases :

x λ 11 - x ≤ (x 1 ≤ (& cases :

x spline1 x c * x spline2 x c * 2 1 sys 1 x Φ Im x λ * 2 x Φ Im x λ * 3 x Φ Im x λ * 4 x Φ Im x λ * 4 1 sys

1 x spline1 x diff (2^+ sqrt x 01 int 1 x spline2 x diff (2^+ sqrt x 01 int 21 mat 1.83 1.83 21 mat