Utilities

5bd2aa65-bf43-4346-9a5b-27e05728acbb 27 4 5 decimal

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

Label truss . . . project

]]> Utilities

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 UnestRow v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

Create your own vector M n Vect n 1 ≡ M ct 1 : j 1 n range a ct 1 el M : ct ct 1 + : 21 line for v a 1 el : k 2 a rows range v v a k el stack : for v 51 line if :

Scale the truss

svg 0.5 :

Truss Construction

create the nest above the sys2mat(XY)converter ... =>

XY 001022 mat 001122 mat 101122 mat 102022 mat 112022 mat 112122 mat 202122 mat 203022 mat 213022 mat 211022 mat 101 sys :

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XY XY sys2mat svg * : truss XY UnestRow : 21 line

view below UnestRow(XY)

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truss 00 0.5 000 0.5 0.5 0.5 0 0.5 0.5 0.5 010 0.5 0.5 10 0.5 0.5 1 0.5 101 0.5 10 1.5 01 0.5 1.5 01 0.5 0.5 0202 mat

nodes 12345616 mat transpose : NodesLabel nodes var2str vectorize : 21 line

X 01122316 mat transpose svg * : Y 00101016 mat transpose svg * : n X rows : 31 line

nodes truss 1 col truss 2 col . 14 red plotG : nodes_label X Y NodesLabel 10 n Vect red n Vect augment : 21 line

Plot truss nodes nodes_label 31 sys :

10 n Vect sets the size of labels ≡ red n Vect sets color of labels ≡ 21 line

Plot Settings

Starting Time

hour hand HH 16 hr * :

minute hand MM 26 min * :

second hand SS 50 s * :

Duration

duration D 0 hr * 2 min * + 35 s * + :

Accuracy

frame skip accuracy 1 s * :

Clock geometry

radius of hour hand r.hh 1.25 :

radius of minute hand r.mm 2 :

radius of second hand r.ss 2 :

dial radius r.dial r.hh r.mm r.ss 31 mat max 1.1 * eval :

rim radius r.rim r.dial 1.1 * :

Algorithms

dial k 112 range dial k 1 el r.dial 2 π * 12 / k * sin * eval : dial k 2 el r.dial 2 π * 12 / k * cos * eval : dial k 3 el . : dial k 4 el 15 : dial k 5 el #cc000000 : 51 line for

rim k 1120 range rim k 1 el r.rim 2 π * 120 / k * sin * eval : rim k 2 el r.rim 2 π * 120 / k * cos * eval : rim k 3 el . : rim k 4 el 8 : rim k 5 el #cc000000 : 51 line for

fastest way to plot the rim rim r.rim (2^x 2^- sqrt ± :

tRange 0 D s / accuracy s / range eval :

s clock ss SS s / s + eval : mm MM min / ss 60 / trunc + eval : hh HH hr / mm 60 / 2 round + eval : r.mm 002 π * 60 / mm * sin 2 π * 60 / mm * cos 22 mat * eval r.ss 002 π * 60 / ss * sin 2 π * 60 / ss * cos 22 mat * eval r.hh 002 π * 12 / hh * sin 2 π * 12 / hh * cos 22 mat * eval dial rim 00.20 #101010 15 mat 61 sys 41 line :

use this to have movements of hour hand every 60 minutes hh HH hr / ss 3600 / trunc + :

collected Ber7 Smath forum.

t clock Circles

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

data UnestH v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

Circle definition t u D u 2 el u 1 el - 21 mat :

IC 0121 mat :

t0 0 : t1 2 π * : 21 line

s60 IC t0 t1 60 t u D rkfixed : s12 IC t0 t1 12 t u D rkfixed : 21 line

C1 s60 2 col s60 3 col augment : C2 s12 2 col s12 3 col augment : 21 line

min C1 . 10 black plot : hr C2 . 15 red plot : 21 line

Autocalc mode

decimal

(-) decimal rotates  clockwise
the blue 'min' needle one at time r 02 π * 60 / decimal * + : 2.618 -

arrows

s 0.5 : α 10 s * : 12 mat

z 0 s s s i * + s i * 051 mat :

j 15 range :

minutes j 15 range v2 j el 1.125 α * z j el (α^* 1 r * i * exp * : for

x y axes x y / - :

hours j 15 range v1 j el 0.875 α * z j el (α^* 112 / r * i * exp * : for

V2 v2 Re v2 Im 12 mat : V1 v1 Re v1 Im 12 mat : 21 line

β rot β cos β sin β sin - β cos 22 mat :

CWD C:\SmathFile CurrentDirectory :

V2 CWD Arrow2 wfile V1 CWD Arrow1 wfile Needle2 CWD Arrow2 rfile : Needle1 CWD Arrow1 rfile : 41 sys

N2 Needle2 UnestH : N1 Needle1 UnestH : 21 line

N2 135 - ( ° * rot * N1 135 - ( ° * rot * min hr 4 1 sys

c Adjacency i 1 c rows range M c i 1 el c i 2 el el 1 : M c i 2 el c i 1 el el 1 - : 21 line for M M 1 row stack 21 line :

A 3221144342 mat :

connectivity matrix A Adjacency 01 - 01101 - 00101 - 1 - 01001 - 0154 mat

U A Adjacency 1 col A Adjacency 2 col augment :

U Some data

Connect 2151611232112234316334542141545265167610667873077898428891093896109101210211121115111012111213121213141337131314151433141115141517153161716201615171617181717181918321818192019531916201920222042122212521202221222322222324235223232425244824212524252725526272630262527262728272728292847282829302943297302630293032313531543118323132333214333233343333343534363431353435563534363736403613373637383793837383938383940394139364039405740394142414541842414243422943424344434344454446444145444558454446474650462847464748472448474849484849504951494650495059504951525155512352515253521953525354533154535455545155545560553556575660564057565758574558575859585059585960595560566059601802 mat :

Coord 0.343 0 0.939 0.106 0.327 0.939 0.278 - 0.202 0.939 0.278 - 0.202 - 0.939 0.106 0.327 - 0.939 0.687 0 0.727 0.793 0.327 - 0.515 0.964 0.202 - 0.172 0.964 0.202 0.172 0.793 0.327 0.515 0.212 0.653 0.727 0.555 0.653 0.515 0.49 0.855 0.172 0.106 0.979 0.172 0.066 - 0.855 0.515 0.555 - 0.404 0.727 0.449 - 0.73 0.515 0.662 - 0.73 0.172 0.889 - 0.404 0.172 0.883 - 0.202 0.515 0.555 - 0.404 - 0.727 0.833 - 0.202 - 0.515 0.899 - 0.404 - 0.172 0.662 - 0.73 - 0.172 0.449 - 0.73 - 0.515 0.212 0.653 - 0.727 0.066 - 0.855 - 0.515 0.106 0.979 - 0.172 0.49 0.855 - 0.172 0.555 0.653 - 0.515 0.555 - 0.653 0.515 - 0.49 - 0.855 0.172 - 0.106 - 0.979 0.172 - 0.066 0.855 0.515 - 0.212 - 0.653 0.727 - 0.449 0.73 0.515 - 0.662 0.73 0.172 - 0.899 0.404 0.172 - 0.833 0.202 0.515 - 0.555 0.404 0.727 - 0.833 0.202 - 0.515 - 0.899 0.404 - 0.172 - 0.662 0.73 - 0.172 - 0.449 0.73 - 0.515 - 0.555 0.404 - 0.727 - 0.066 0.855 - 0.515 - 0.106 - 0.979 - 0.172 - 0.49 - 0.855 - 0.172 - 0.555 - 0.653 - 0.515 - 0.212 - 0.653 - 0.727 - 0.793 - 0.327 - 0.515 - 0.964 - 0.202 - 0.172 - 0.964 - 0.202 0.172 - 0.793 - 0.327 0.515 - 0.687 - 0 0.727 - 0.106 - 0.327 0.939 - 0.278 0.202 0.939 - 0.278 0.202 - 0.939 - 0.106 - 0.327 - 0.939 - 0.343 - 0 0.939 - 603 mat :

from Some data

XY Coord 1 col Coord 2 col augment : a b c spec . 14 black 13 mat : Bucky XY a b c spec pts : Nest XY 2130 NestRow : 41 sys

n 1 :

Coord Coord 1 col Coord 2 col Coord 3 col augment :

Nest n el XY Bucky 3 1 sys Coord

The Buckyball

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 :

data r s k NestRow r k * data rows ≤ memo ≡ k s k range i 1 r range j 1 data cols range M i j el data i r k * + r - (j el : for for Q k el M : k k 1 + : 31 line for Q 31 line :

Connect, Coord

Connect 2151611232112234316334542141545265167610667873077898428891093896109101210211121115111012111213121213141337131314151433141115141517153161716201615171617181717181918321818192019531916201920222042122212521202221222322222324235223232425244824212524252725526272630262527262728272728292847282829302943297302630293032313531543118323132333214333233343333343534363431353435563534363736403613373637383793837383938383940394139364039405740394142414541842414243422943424344434344454446444145444558454446474650462847464748472448474849484849504951494650495059504951525155512352515253521953525354533154535455545155545560553556575660564057565758574558575859585059585960595560566059601802 mat :

Coord 0 0.343 0 0.939 1 0.106 0.327 0.939 2 0.278 - 0.202 0.939 3 0.278 - 0.202 - 0.939 4 0.106 0.327 - 0.939 5 0.343 0 0.939 6 0.687 0 0.727 7 0.793 0.327 - 0.515 8 0.555 0.653 - 0.515 9 0.212 0.653 - 0.727 10 0.106 0.327 - 0.939 11 0.278 - 0.202 - 0.939 12 0.555 - 0.404 - 0.727 13 0.833 - 0.202 - 0.515 14 0.833 - 0.202 0.515 15 0.555 - 0.404 0.727 16 0.278 - 0.202 0.939 17 0.106 0.327 0.939 18 0.212 0.653 0.727 19 0.555 0.653 0.515 20 0.793 0.327 0.515 21 0.687 0 0.727 22 0.793 0.327 - 0.515 23 0.964 0.202 - 0.172 24 0.899 0.404 - 0.172 - 25 0.661 0.73 - 0.172 - 26 0.49 0.855 - 0.172 27 0.555 0.653 - 0.515 28 0.212 0.653 - 0.727 29 0.066 - 0.855 - 0.515 30 0.449 - 0.73 - 0.515 31 0.555 - 0.404 - 0.727 32 0.833 - 0.202 - 0.515 33 0.899 - 0.404 - 0.172 34 0.964 - 0.202 - 0.172 - 35 0.964 - 0.202 0.172 - 36 0.899 - 0.404 0.172 37 0.833 - 0.202 0.515 38 0.555 - 0.404 0.727 39 0.449 - 0.73 0.515 40 0.066 - 0.855 0.515 41 0.212 0.653 0.727 42 0.555 0.653 0.515 43 0.49 0.855 0.172 44 0.661 0.73 0.172 - 45 0.899 0.404 0.172 - 46 0.964 0.202 0.172 47 0.793 0.327 0.515 48 0.687 0 0.727 49 0.793 0.327 - 0.515 50 0.964 0.202 - 0.172 51 0.964 0.202 0.172 52 0.899 0.404 0.172 - 53 0.833 0.202 0.515 - 54 0.555 0.404 0.727 - 55 0.449 0.73 0.515 - 56 0.661 0.73 0.172 - 57 0.49 0.855 0.172 58 0.106 0.979 0.172 59 0.066 - 0.855 0.515 60 0.106 0.979 0.172 61 0.106 - 0.979 0.172 - 62 0.49 - 0.855 0.172 - 63 0.661 - 0.73 0.172 64 0.449 - 0.73 0.515 65 0.661 - 0.73 0.172 66 0.899 - 0.404 0.172 67 0.964 - 0.202 0.172 - 68 0.793 - 0.327 0.515 - 69 0.687 - 0 0.727 - 70 0.793 - 0.327 - 0.515 - 71 0.964 - 0.202 - 0.172 - 72 0.899 - 0.404 - 0.172 73 0.661 - 0.73 - 0.172 74 0.449 - 0.73 - 0.515 75 0.066 - 0.855 - 0.515 76 0.106 0.979 - 0.172 77 0.106 - 0.979 - 0.172 - 78 0.49 - 0.855 - 0.172 - 79 0.661 - 0.73 - 0.172 80 0.49 - 0.855 - 0.172 - 81 0.555 - 0.653 - 0.515 - 82 0.793 - 0.327 - 0.515 - 83 0.687 - 0 0.727 - 84 0.343 - 0 0.939 - 85 0.106 - 0.327 - 0.939 - 86 0.212 - 0.653 - 0.727 - 87 0.555 - 0.653 - 0.515 - 88 0.212 - 0.653 - 0.727 - 89 0.066 0.855 - 0.515 - 90 0.106 - 0.979 - 0.172 - 91 0.106 0.979 - 0.172 92 0.49 0.855 - 0.172 93 0.661 0.73 - 0.172 - 94 0.449 0.73 - 0.515 - 95 0.066 0.855 - 0.515 - 96 0.449 0.73 - 0.515 - 97 0.555 0.404 - 0.727 - 98 0.278 0.202 - 0.939 - 99 0.106 - 0.327 - 0.939 - 100 0.278 0.202 - 0.939 - 101 0.555 0.404 - 0.727 - 102 0.833 0.202 - 0.515 - 103 0.899 0.404 - 0.172 - 104 0.833 0.202 - 0.515 - 105 0.833 0.202 0.515 - 106 0.555 0.404 0.727 - 107 0.278 0.202 0.939 - 108 0.278 0.202 - 0.939 - 109 0.278 0.202 0.939 - 110 0.106 - 0.327 0.939 - 111 0.212 - 0.653 0.727 - 112 0.066 0.855 0.515 - 113 0.449 0.73 0.515 - 114 0.066 0.855 0.515 - 115 0.106 - 0.979 0.172 - 116 0.49 - 0.855 0.172 - 117 0.555 - 0.653 0.515 - 118 0.793 - 0.327 0.515 - 119 0.555 - 0.653 0.515 - 120 0.212 - 0.653 0.727 - 121 0.106 - 0.327 0.939 - 122 0.343 - 0 0.939 - 1234 mat :

k 122 :

Connect rows Coord rows 21 mat 18012321 mat

sanity Coord 1 k + (row : 122 0.343 - 0 0.939 - 14 mat

Coord Coord 2 col Coord 3 col Coord 4 col augment : φ 0 ° * : θ 0 ° * : 12 mat zoom 10 : Rot θ cos θ sin - 0 θ sin φ cos * θ cos φ cos * φ sin - θ sin φ sin * θ cos φ sin * φ cos 33 mat : 41 sys

a b c spec + 5 black 13 mat :

Matlab/Mathcad Buckyball C60

Coord Rot * zoom *

pts Connect a b c spec pts :

The adjacency matrix

pts

XY Coord 1 col Coord 3 col augment : a b c spec . 14 black 13 mat : Bucky XY a b c spec pts : Nest XY 2161 NestRow : 41 sys

Plot Nest n el XY Bucky 31 sys

n 48 :

2931584814 mat

Nest n el 0.449 0.515 - 0.066 0.515 - 22 mat

Nest n el XY Bucky 3 1 sys

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 :

1. Regular Polygon Area/Perimeter

N 5 :

n 13 :

m 4 :

'a' vertices a N 1 - :

'b' vertices b n 1 - :

'c' vertices c m 1 - :

j 1 N range sqr j 1 el j a / 2 * π * cos : sqr j 2 el j a / 2 * π * sin : 21 line for sqr 21 line

j 1 n range circle j 1 el j b / 2 * π * cos : circle j 2 el j b / 2 * π * sin : 21 line for circle 21 line

j 1 m range tria j 1 el j c / 2 * π * cos : tria j 2 el j c / 2 * π * sin : 21 line for tria 21 line

θ rot θ cos θ sin - θ sin θ cos 22 mat :

data tria :

θ π 2 / :

θ 1.5708

vertices 2 circle * . 10 black plot :

NOT commutative Triangle tria θ rot * :

sqr circle 2 * Triangle 2 * vertices 4 1 sys

x data 1 col : y data 2 col : 12 mat Area 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * : Perimeter x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum : 31 sys

native figure ...
i.e: NOT as plotted Area Perimeter 21 mat 1.299 5.196 21 mat

Fourier "ifft" from padded created vector [Numeric] v ifft N v length : s 1 N sqrt / : 12 mat n 0 N range I n 1 + el s (v k 1 + el e i 2 π * n * N / (* k * -^* (k 0 N 1 - sum eval * : for I 31 line :

add/remove '0' Y 10000116 mat transpose :

shape/scale directions sX 1 : sY 1 : 12 mat

U Y ifft mat2sys sys2mat : a U Re mat2sys sys2mat : b U Im mat2sys sys2mat : 31 line

a b augment 0.8165 0 0.6124 0.3536 0.2041 0.3536 0 1.1 1014 -^* 0.2041 0.3536 - 0.6124 0.3536 - 0.8165 2.3 1014 -^* - 72 mat

end 0 - :

explore j 1 a rows end + (range :

data sX a j el * sY b j el * augment :

x data 1 col : y data 2 col : 12 mat A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * : P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum : Xo 16 A * / x i el x i 1 + el + (x i el y i 1 + el * x i 1 + el y i el * - (* i 1 x rows 1 - sum * : Yo 16 A * / y i el y i 1 + el + (x i el y i 1 + el * x i 1 + el y i el * - (* i 1 x rows 1 - sum * : 51 line

Area Perimeter Xo abs Yo abs 21 mat 31 mat 1.299 5.1962 0.4082 3.6649 1016 -^* 21 mat 31 mat

Draw odd polygon

data Xo Yo + 200 red 1 5 mat 2 1 sys