plotG(vx,vy,char,size,color) ... Hermite Polyline modules

539ab46b-3fa0-492a-a123-c338a38891cd 5 15 12 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 : 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 0 8.25 12.375 16.5 3715 mat transpose : Yo 1111 5.5 0015 mat transpose : 21 sys

sub 1 :

sub[1]... NOT sub-divided

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

t 01 0.1 range :

<= populate for more points at will

Polyline construct

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

x c 10 x ≤ (x 1 ≤ (& cases :

t B t 3^- 3 t 2^* + 3 t * - 1 + 3 t 3^* 6 t 2^* - 3 t * + 3 t 3^* - 3 t 2^* + t 3^41 mat :

Hermite PolyLine t P 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 * :

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

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 : Polyline xy Strip : 21 sys

XY X Y o 7 red plotG : XoYo Xo Yo . 14 black plotG : TouchDown Polyline Polyline rows row . 25 black augment : Landed km datum 12 mat Polyline Polyline rows row stack : cruz 112 crusing altitude 11 km 12 blue 15 mat : distance 16.5 0.125 - landing distance km -->| 12 black 15 mat : Polyline Polyline . 10 red plot : 71 line

Xo Yo augment Polyline XoYo TouchDown cruz distance 6 1 sys

OBSERVE: center point ... does not need be in line

datum landing 
t[0,0.05..1]...   10 cm 
t[0,0.025..1]... 1.4 cm Landed km datum 32.46 0.00 22 mat

t x Polyline 1 col t el : t y Polyline 2 col t el : 12 mat

τ 1 Polyline rows range :

Cumulative landing path, i.e: descending altitude [km] vs distance [km]

t 1 ≡ path t x t y + 40 green 1 5 mat : path path t x t y . 14 black 1 5 mat stack : if 0 11 10 11 2 2 mat 32.5 1 32.5 1 - 2 2 mat 12.375 5.5 + 50 blue 1 5 mat 11 11.5 crusing altitude [km] 12 red 1 5 mat 30 1 runway 12 green 1 5 mat 6 1 sys