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

05f8c1a1-bbb0-4ae9-b27b-5b477739fdee 23 6 12 decimal

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

Hermite smooth travel

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 :

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 12 4.5 5.55 7.5 911 8.5 18 mat transpose : Yo 7.5 7765 3.5 5718 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

t 01 0.05 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 :

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 PolyLine 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 : 21 sys

low t rows : high contour rows low - 2 + : 12 mat

XY X Y o 7 red plotG : XoYo Xo Yo + 15 black plotG : contour contour low high range 12 range el : 31 line

user interpolate U 8 :

vx contour 1 col : vy contour 2 col : x interpolate vx vy x ainterp : 31 line

i 1 contour rows range : global i contour augment : 21 line

User U interpolate 6.5 interpolate 21 mat : 4.3865 5.5297 21 mat

global 11 mat 11 7.5 2 1.022 7.479 3 1.047 7.456 4 1.074 7.432 5 1.104 7.408 6 1.137 7.383 7 1.172 7.357 8 1.211 7.331 9 1.252 7.304 10 1.296 7.277 11 1.344 7.25 12 1.394 7.223 13 1.448 7.196 14 1.505 7.169 15 1.565 7.143 16 1.629 7.117 17 1.696 7.092 18 1.767 7.068 19 1.841 7.044 20 1.919 7.021 212722 2.114 7.001 23 2.231 7.002 24 2.351 7.005 25 2.474 7.008 26 2.6 7.012 27 2.727 7.016 28 2.855 7.02 29 2.985 7.024 30 3.116 7.028 31 3.247 7.031 32 3.378 7.034 33 3.509 7.036 34 3.639 7.037 35 3.768 7.037 36 3.896 7.035 37 4.022 7.032 38 4.145 7.027 39 4.267 7.02 40 4.385 7.011 41 4.5 742 4.567 6.965 43 4.631 6.928 44 4.693 6.889 45 4.751 6.848 46 4.807 6.805 47 4.86 6.76 48 4.912 6.713 49 4.962 6.664 50 5.011 6.614 51 5.059 6.562 52 5.107 6.51 53 5.154 6.456 54 5.2 6.401 55 5.247 6.346 56 5.295 6.289 57 5.343 6.232 58 5.393 6.174 59 5.443 6.116 60 5.496 6.058 61 5.55 662 5.637 5.954 63 5.727 5.908 64 5.818 5.862 65 5.911 5.816 66 6.006 5.77 67 6.102 5.723 68 6.199 5.676 69 6.298 5.628 70 6.397 5.58 71 6.497 5.531 72 6.597 5.482 73 6.698 5.432 74 6.8 5.381 75 6.901 5.33 76 7.002 5.277 77 7.103 5.224 78 7.203 5.17 79 7.303 5.114 80 7.402 5.058 81 7.5 582 7.578 4.908 83 7.655 4.815 84 7.73 4.721 85 7.806 4.628 86 7.88 4.535 87 7.954 4.443 88 8.028 4.353 89 8.101 4.264 90 8.174 4.178 91 8.247 4.094 92 8.32 4.013 93 8.393 3.936 94 8.467 3.863 95 8.541 3.794 96 8.615 3.73 97 8.69 3.672 98 8.766 3.619 99 8.843 3.573 100 8.921 3.533 1019 3.5 102 9.13 3.525 103 9.26 3.556 104 9.39 3.595 105 9.52 3.64 106 9.648 3.691 107 9.775 3.749 108 9.899 3.812 109 10.02 3.88 110 10.137 3.953 111 10.25 4.031 112 10.358 4.114 113 10.46 4.2 114 10.556 4.29 115 10.645 4.384 116 10.727 4.48 117 10.8 4.58 118 10.865 4.682 119 10.92 4.786 120 10.965 4.892 121115122 10.924 5.109 123 10.837 5.219 124 10.741 5.329 125 10.636 5.44 126 10.523 5.551 127 10.404 5.661 128 10.279 5.771 129 10.148 5.88 130 10.013 5.988 131 9.875 6.094 132 9.734 6.198 133 9.592 6.3 134 9.449 6.4 135 9.306 6.496 136 9.164 6.59 137 9.024 6.68 138 8.887 6.766 139 8.753 6.849 140 8.624 6.927 141 8.5 71413 mat 11 mat

Find the 1rst element in vector that exceeds
 a prescribed threshold. V treshold FindIdx j 1 : V j el abs treshold ≤ j j 1 + : while j 1 - V j el 21 mat 31 line :

idx vx 8.75 FindIdx : 97 8.766 21 mat

idx idx 1 el :

Incomplete setup .... submatrix last segment

Ux 1 el vx idx 1 - el : Vy 1 el vy idx 1 - el : Ux 2 el vx idx el : Vy 2 el vy idx el : Ux 3 el vx idx 1 + el : Vy 3 el vy idx 1 + el : 32 mat

Ux Vy 12 mat 8.615234 8.6904 8.766341 31 mat 3.730469 3.672 3.619281 31 mat 12 mat

bu 4.5 1121 mat :

bv 7521 mat :

bu bv birdDistance bu bv - (2^(vectorize sum sqrt :

bird bu bv augment :

bu bv birdDistance 6.5

8.5 |

interp [vx,vy]

interp [Ux,Vy]

Xo Yo augment contour bird 8.5 10 8.5 0 2 2 mat XY XoYo 6 1 sys