plot(data,char,size,clr)

d3cf0376-db43-442b-bb8d-d2e07dda1de4 11 4 5 decimal

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

Part 1: Geometric Polygon(s)

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 1000000118 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

explore j 1 a rows range :

a b augment 0.7071 0 0.6036 0.25 0.3536 0.3536 0.1036 0.25 0 1.3 1014 -^* 0.1036 0.25 - 0.3536 0.3536 - 0.6036 0.25 - 0.7071 2.7 1014 -^* - 92 mat

Draw odd polygon

sX a j el * sY b j el * augment

x a : y b : 21 sys

As well, you can shift up/dn ... left/right and in combination with scaled directions.

Area Polygon wrt vertices coordinates x y A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates x y P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

Center of gravity x y Xo 16 x y 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 * : x y Yo 16 x y 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 * : 21 mat

Center of gravity x y Xo abs x y Yo abs 21 mat 0.3536 1.4095 1016 -^* 21 mat

XY sX a * sY b * augment :

Xo x y Xo abs : Yo x y Yo abs : 12 mat

Area
Perimeter x y A x y P 21 mat 0.3536 2.1648 21 mat

Draw odd polygon

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

M mirror M 1 M rows range M cols 1 range el :

M 0.19 0.59 0.35 0.82 0.71 0.61 0.27 0.59 0.12 0.03 2.66 4.21 0.45 0.23 5.48 5.20 44 mat :

M mirror 0.82 0.35 0.59 0.19 0.59 0.27 0.61 0.71 4.21 2.66 0.03 0.12 5.2 5.48 0.23 0.45 44 mat

Set heptagon ... to visualize 'mirror'

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

θ π - 4 / : 0.7854 -

Rot XY θ rot * :

x Rot 1 col : y Rot 2 col : 21 sys

Area
Perimeter x y A x y P 21 mat 0.3536 2.1648 21 mat

Center of gravity x y Xo abs x y Yo abs 21 mat 0.25 0.25 21 mat

Xo x y Xo abs : Yo x y Yo abs : 12 mat

Rot 0.5 0.5 0.25 0.6036 4.1342 1015 -^* 0.5 0.1036 - 0.25 9.1924 1015 -^* - 9.1924 1015 -^* 0.25 0.1036 - 0.5 1.2095 1014 -^* - 0.6036 0.25 0.5 0.5 92 mat

Rot Xo Yo + 150 red 1 5 mat 2 1 sys

Part 2: Irregular Polygon(s)

plot(data,char,size,clr)

Universal version  [Smath 6179]. It supports "data" sets from 
source ... data sets subject to be decimated from auxilliary
module Decimate(data,n)... reasonably fast on primitive PC. 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 :

data isolated

data 410419728133717462055196417731582159122992810236103441045210360102681017610084999298100981089811698124981329814097148951569116382167701695617143173341732717223163141541114511136121271411817109201002491288226732064145510467374282192104410542 mat :

j 10 :

x data 1 col : y data 2 col : 12 mat pts data o 5 black plot : 21 sys

explorer data 1 col j el data 2 col (j el augment :

explorer 159112 mat

pts data data explorer 3 1 sys

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

Center of gravity 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 * : 21 mat

Area
Perimeter A P 21 mat 13106.5 487.7 21 mat

Center of gravity Xo abs Yo abs 21 mat 87.574499 54.712649 21 mat

'a' = intercept of unary f(x)
passing through Xo, Yo a Yo abs data 12 el + 1.9692333 / - : 32.8618 -

sub data 1032 range 12 range el : H sub . 15 black plot : 21 sys

x G sub 1 col sub 2 col x ainterp :

b 1 :

Yo abs data 12 el + unk / - Xo abs + Yo abs - unk 13 solve 1.969233304

b = 1 through Yo x f a b x * + :

Yo abs data 12 el + 1.969233304 / - Xo abs + 54.712649

x λ 10 x ≤ (x 177 ≤ (& cases :

x f x G x λ * pts Xo abs Yo abs + 250 black 1 5 mat H 5 1 sys

Solve junction in this search ... bracket wisely. jnct x G x f - 0 ≡ x Yo abs 200 solve : 130.862

sanity intercept 0 f 32.8618498072795 -

sanity jnct jnct G jnct f 21 mat 989821 mat

Part 3: Critical Polygon(s)

x 24911215 mat transpose : y 2972215 mat transpose : uv x y augment : 31 sys

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

Adapt as needed wrt rotation

θ π - 5 / : 0.628 -

New uv θ rot * : 0.442 2.794 2.054 - 9.632 3.167 10.953 7.724 8.084 0.442 2.794 52 mat

uv New 2 1 sys

x a 2421 mat 2921 mat x linterp : x b 4921 mat 9721 mat x linterp : x c New 11 el New 41 el 21 mat New 12 el New 42 el 21 mat x linterp : 31 sys

'N' random in critical region N 1000 :

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 :

size/define critical region.
Plot first before filling xmin 2 : xmax 10 : ymin 2 : ymax 10 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x a ≤ (y x b ≤ (* y x c ≥ (* :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + (1 el : y 1 Random space_y * ymin + (1 el : 1 x y Test - x 1 Random space_x * xmin + (1 el : y 1 Random space_y * ymin + (1 el : 21 line while P i 1 el x 2 round vectorize : P i 2 el y 2 round vectorize : 51 line for P 21 line :

a b c spec . 5 #808080 13 mat : fill Pts a b c spec pts : 21 line

uv New x a x b x c fill 61 sys

uv New x a x b x c fill 6 1 sys

X x a x b - 0 ≡ x 010 solve x b x c - 0 ≡ x 010 solve x a x c - 0 ≡ x 010 solve 31 mat :

Y X 1 el a X 2 el b X 3 el c 31 mat :

X 4 7.215 2.694 31 mat

Y 9 7.714 4.43 31 mat

Area Polygon wrt vertices coordinates A 12 / X i el Y i 1 + el * X i 1 + el Y i el * - (i 1 X rows 1 - sum * abs : 11.451

CWD C:\SmathFile CurrentDirectory :

Pts CWD criticalpolygon wfile 1

Pts CWD criticalpolygon rfile :

Perimeter  Polygon wrt vertices coordinates P X i 1 + el X i el - (2^Y i 1 + el Y i el - (2^+ sqrt i 1 X rows 1 - sum : 9.05

Center of gravity wrt vertices coordinates 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 * : 21 mat

Center of gravity Xo abs Yo abs 21 mat 3.951 6.315 21 mat

uv New xx a xx b xx c Pts 6 1 sys

Part 4: Classroom Polygon(s)

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

2. Sparse Polygons

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 method for finding the area of any polygon when the coordinates of its vertices are known

x 24911215 mat transpose :

y 2972215 mat transpose :

uv x y augment :

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

a b c spec . 14 red 13 mat : XY uv a b c spec pts : 21 sys

Perimeter is calculated wrt each hypotenuse from the projections ... Inspect the plot.

uv XY 4 2 + 20 black 1 5 mat 9 2 + 20 black 1 5 mat 4 7 + 20 black 1 5 mat 6.25 4.75 + 100 red 1 5 mat 6 1 sys

uv 2249971122252 mat

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

A P 12 mat 42 27.05 12 mat

A P 21 mat 42 27.05 21 mat

Center of gravity wrt vertices coordinates 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 * : 21 mat

Center of gravity Xo abs Yo abs 21 mat 6.25 4.75 21 mat