plot(data,char,size,color) ... Hermite Polyline modules

1c8c3b1f-73dc-4b12-80c0-b51793a8c462 23 6 12 decimal

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Hermite interpolation

EXPLAIN: you may need to smooth the given data set. Whether a data set is "true" or just data, it would not be correct to spline interpolate directly in sparse region(s). A good way to resolve for greater accuracy is to populate Hermite Interpolation, then spline over the Hermite populated, eventually pre-smoothed.

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 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 :

data sub subspace j 1 data rows 1 - (range Vsub j el i 1 sub range vx i el data j el i sub / data 1 j + el data j el - (* + : for vx 21 line eval : 11 line for v Vsub 1 el : j 2 Vsub rows range v v Vsub j el stack : for v 31 line 21 line :

Round OFF Matrix/Vector M n Round i 1 M rows range m i el M i el n round : for m 21 line :

user original polygon Xo 051015202530354019 mat transpose : Yo 50 63.2 68.5 70.6 71.4 71.7 71.9 727219 mat transpose : 21 sys

sub 1 :

subspaces is '1' for interpolation

New Xo sub subspace Yo sub subspace augment : New Xo 1 el Yo 1 el 12 mat New stack : 21 line

isolate New New :

X New 1 col : Y New 2 col : 21 line

populate reasonably t 01 0.1 range :

Polyline construct

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

x c 10 x ≤ (x 1 ≤ (& cases :

interpolate 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 41 mat *

Hermite interpolate t P 16 / t 3^- 3 t 2^* + 2 t * - 3 t 3^* 6 t 2^* - 3 t * - 6 + 3 t 3^* - 3 t 2^* + 6 t * + t 3^t - 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

polyline 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 *

t j XP t P 1 el X j el * t P 2 el X j 1 + el * + t P 3 el X j 2 + el * + t P 4 el X j 3 + el * + : t j YP t P 1 el Y j el * t P 2 el Y j 1 + el * + t P 3 el Y j 2 + el * + t P 4 el Y j 3 + el * + : 21 sys

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 :

collect the project xy U Unwrap V Unwrap augment : contour xy Strip : contour contour t rows contour rows range 12 range el : 31 sys

user interpolate U 7 :

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contour is the Hermite data set used 
to interpolate in-situ at user point vx contour 1 col : vy contour 2 col : x interpolate vx vy x ainterp : x f Xo Yo x cinterp : User U interpolate : 51 line

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

a b c spec o 5 red 13 mat : Hermite contour a b c spec pts : XoYo Xo Yo augment + 20 black plot : 31 line

U 100 U 0 2 2 mat XoYo U User + 50 blue 1 5 mat Hermite 4 1 sys

x c Xo Yo x cinterp :

XoYo Xo Yo augment + 15 black plot : x c 2 1 sys

user
cinterp
ainterp U U f User 31 mat 7 66.048 66.005 31 mat

contour 050 0.358 51.074 0.76 52.259 1.202 53.534 1.68 54.878 2.188 56.269 2.72 57.686 3.272 59.109 3.84 60.517 4.418 61.887 5 63.2 112 mat