plot(data,char,size,clr)

adc0a881-4054-4059-83ba-52d5f1a380ea 29 15 12 decimal

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

Irregular Polygon Area/Perimeter

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 5 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

L1 x 2 el x 1 el - (2^y 2 el y 1 el - (2^+ sqrt : L2 x 3 el x 2 el - (2^y 3 el y 2 el - (2^+ sqrt : L3 x 4 el x 3 el - (2^y 4 el y 3 el - (2^+ sqrt : L4 x 5 el x 4 el - (2^y 5 el y 4 el - (2^+ sqrt : 41 mat 7.28 5.385 5.385 941 mat

L1 L2 + L3 + L4 + 27.05

============================================================================

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

θ π - 6 / : 0.524 -

Rotate the Polygon

New uv θ rot * : 0.732 2.732 1.036 - 9.794 4.294 10.562 8.526 7.232 0.732 2.732 52 mat

X New 1 col : Y New 2 col : 12 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 : 42

New

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 : 27.05

x 01001000051 mat :

y 00100100051 mat :

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 :

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

uv XY 2 1 sys

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 21 mat 1000040021 mat

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 410419728133717462055196417731582159122992810236103441045210360102681017610084999298100981089811698124981329814097148951569116382167701695617143173341732717223163141541114511136121271411817109201002491288226732064145510467374282192104532 mat :

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

native data A P 21 mat 1314847921 mat

pts data data 2 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 13148.5 479.2 21 mat

Center of gravity Xo abs Yo abs 21 mat 87.31 54.553 21 mat

pts Xo abs Yo abs + 200 black 1 5 mat 2 1 sys