FYI - WEbPlotDigitizer

[GreyGeek]

WebPlotDigitizer is a browser based (or standalone) app that lets the user pick data points off of a graph and then generate an equation which will plot the data. The graph can be on a web page or on a graphic image loaded locally. A nice tutorial video explains the details.

https://automeris.io/WebPlotDigitizer/

[woodsmoke]

This is just waaayyyy cool!
thanks!
woody

[GreyGeek]

Indeed! I pulled data for four plots presented as a stacked area graph. Fed the data points into SageMath and used it to generate a 6th order polynomial. Used that to generate the first derivative in order to find the inflection points. A good friend and former client whom I've known for almost 40 years, who has a degree in Ag Engineering and farms, wanted to pull the data from the stacked area graph of "Seasonal Nitrogen Update". The four areas were "Leaf Blades", "Stalk and Leaf Sheaths", "Tassel, Cob, Husk Leaves", and "Grain". He was using EXCEL and hand picking a dozen points. Excel's first derivative on a 5th order polynomial was nonsensical. I used the SageMath's Notebook() capability.

data = [(300.000000000000, 9.94809280595666),(350.000000000000, 11.9275313210500),(400.000000000000, 13.9069698361434),(450.000000000000, 16.4262552189894),(500.000000000000, 18.9455406018354),(550.000000000000, 21.6447749405990),(600.000000000000, 24.7039071911977),
(650.000000000000, 28.3028863095492),(700.000000000000, 32.4417122956534),(750.000000000000, 37.3003341054279),(800.000000000000, 43.4185986066254),
(850.000000000000, 51.1564037110811),(900.000000000000, 60.3338004628773),(950.000000000000, 73.2901252889426),(1000.00000000000, 91.1050719247825),
(1050.00000000000, 110.359610207963),(1100.00000000000, 128.534454755638),(1150.00000000000, 142.750422273126),(1197.30457668110, 152.648127676469),
(1241.91373004330, 161.106754260348),(1299.96717901590, 171.347320288342),(1349.96717901590, 178.365329569128),(1395.95686502165, 184.679298243736),
(1448.65023702904, 190.807360103322),(1499.99384606548, 195.686345871688),(1549.99589737699, 199.275014803774),(1601.33745510192, 201.465076419642),
(1700.00000000000, 205.012761020607),(1750.00000000000, 207.172148491617),(1800.00000000000, 208.971638050793),(1850.00000000000, 210.771127609969),
(1900.00000000000, 212.930515080980),(1950.00000000000, 216.169596287496),(2000.00000000000, 219.408677494012),(2050.00000000000, 222.287860788694),
(2100.00000000000, 225.526941995210),(2150.00000000000, 228.406125289891),(2200.00000000000, 231.645206496407),(2250.00000000000, 234.884287702924),
(2300.00000000000, 237.763470997605),(2350.00000000000, 240.642654292286),(2400.00000000000, 243.881735498802),(2450.00000000000, 246.760918793484),
(2500.00000000000, 250.000000000000),(235.758257041639, 7.56472400629349),(165.701866488339, 5.29494782489195),(95.6475272465450, 2.83491250130777),
(33.6753553384355, 0.753856978459226),(2590.23103921492, 255.214177434343),(1654.13349525019, 203.261380163407),]
# 6th degree polynomial
var('a,b,c,d,e,f,g')
model(x) = g*x^6 + f*x^5 + e*x^4 + d*x^3 + c*x^2 + b*x + a 
sol = find_fit(data,model)
#print sol
var('xx,dx,z')
f(xx) = -7.837682944101485e-17*xx^6 + 6.485420491152026e-13*xx^5 - 2.000835782210809e-09*xx^4 + 2.7746268049000093e-06*xx^3 - 0.001613868756524219*xx^2 + 0.384986221902241*xx - 17.913132237665565
dx = diff(f(xx),xx)
#print "dx=",dx
#first derivative of xx.  Use the printed equations to fill in f(xx) & f(z) for the next run

p = plot([])
p += list_plot(data,color='red')
p += plot(f(xx),xx,(xx,0,2500),color='blue',title="6th Order Polynomial Plot of Seasonal Corn Nitrogen Uptake - Blue Region")
show(p)
p = plot([])
print
q = plot([])
f(z) = -(4.70260976646089e-16)*z^5 + (3.24271024557601e-12)*z^4 - (8.00334312884324e-9)*z^3 + (8.323880414700028e-6)*z^2 - 0.00322773751304844*z + 0.384986221902241

q += plot(f(z),z,(z,0,2500),color='green')
show(q)

"Print sol" printed the solution for the coefficients. I copied and pasted them into the script to create the function "f(xx)=..."


The plot of just the blue curve

The plot of the 1st derivative of the blue curve