# How to get a plot with more precision in the data points?

Working with other software called SolidWorks I was able to get a plot with a curve very close to my data points: I tried to get a plot as accurate as this, but using the Fit function, I could not get a plot as accurate.

Clear["Global*"] Is there something I need to modify or another method more effective than this?

• Attempting to fit 8 parameters (7 coefficients and an error variance) with 6 data points can not be warranted on any circumstances. – JimB Nov 28 '18 at 17:37
• I'm voting to close this question as off-topic because fitting 8 parameters with just 6 data points is just plain wrong. – JimB Nov 28 '18 at 17:38
• There are many ways to fit curves to data. Sometimes splines can be useful. What are you going to do with the curve after you get it? – Somos Nov 28 '18 at 18:45

If you want to reproduce that graph exactly, add in the derivatives at each point when using the Interpolate function.

Clear["Global*"]
dados = {{{0}, 0, 0}, {{1}, 1000, 0}, {{2}, -750, 0}, {{3}, 250,
0}, {{4}, -1000, 0}, {{5}, 0, 0}};
Plot[
{x, 0, 5},
ImageSize -> 500,
Epilog -> {
Red,
PointSize[0.01],
}]


This should give you: which looks pretty close to your original graph.

However, I strongly caution making any assumptions based off the interpolation from 6 data points unless you have some other reason to believe that this shape is correct. As others have pointed out, your own answer attempts to use a high-order polynomial to fit the data. A 7-term polynomial will fit almost any (except something really ugly like a perfectly vertical line) 6 data points perfectly. Similarly, this interpolation will work for any 6 data points and doesn't necessarily mean the values in between are correct.

• +1. I think this is what the software is doing, but why it is using such a model is unexplained. (E.g. it might be that the data represent the local extrema, it which case, it's not a bad model.) – Michael E2 Nov 28 '18 at 21:00

Using halirutan an J.M.'s IPCUMonotonicInterpolation from this q/a:

Plot[IPCUMonotonicInterpolation[dados]@t, {t, 0, 5},
AspectRatio -> 1/GoldenRatio, GridLines -> Transpose[dados]] Clear["Global*"]
dados = {{0, 0}, {1, 1000}, {2, -750}, {3, 250}, {4, -1000}, {5, 0}};

(* {0, 5} *)

f = Interpolation[dados, InterpolationOrder -> 5];

Plot[f[x], {x, xmin, xmax}, Alternatively, use InterpolatingPolynomial

g[x_] = InterpolatingPolynomial[dados, x] // Simplify

(* 125/6 x (520 - 829 x + 450 x^2 - 101 x^3 + 8 x^4) *)

Plot[g[x], {x, xmin, xmax}, EDIT: Using Fit
g[x] == Fit[dados, {1, x, x^2, x^3, x^4, x^5}, x] //
`