c1f54e0c-cadc-415f-ab32-0c338d66091d 31 4 5 decimal

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

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 :

P 1.5 0 3.5 - 4.1 - 1.5 - 0 3.2 4.7 2.6 4.8 3.4 0 1.5 - 4.1 - 3.1 - 028 mat transpose :

t0 1 time :

X P 1 col : Y P 2 col : XY X Y o 7 red plotG : 31 line

For 'u' & cinterp X X X X stack : Y Y Y Y stack : 21 line

N 200 :

Linear vector 'u' for cspline S n P rows : u 1 el 0 : i 2 n 2 n * + (range u i el u i 1 - el X i el X i 1 - el - Y i el Y i 1 - el - 22 mat det + : for |,| determinant uN u n 1 + el u 1 el - N / : (increments ≡ i 1 N range ux i el i uN * : for i 1 N range Sx i el u X ux i el cinterp : Sy i el u Y ux i el cinterp : 21 line for Sx Sy augment 31 line eval 61 line :

S S :

S XY 2 1 sys

"Esplina": courtesy Mathcad 11. Coded for Smath. Permission granted from Mathsoft Collab AI2000.

The cspline proceeds in sorted order of 'vx', thus excluding splining closed data sets. The vector 'u' is created from the descending vector of the determinants |X,Y|... thus: directly parent to X,Y. This condition is necessary and sufficient to spline a closed data set. 'uN' [incremental] determines the spacing of the interpolated points over the "N user points".

U S 1 col sys2mat : V S 2 col sys2mat : 12 mat

area 0.5 U i el V i 1 + el * U i 1 + el V i el * - (i 1 S rows 1 - sum * :

length U i 1 + el U i el - V i 1 + el V i el - 22 mat det i 1 S rows 1 - sum :

area length 21 mat 51.9 103.7 21 mat

1 time t0 - 1.2 s *