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How to extrapolate a contour plot?

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Balasubramanian Sundarapandian
Balasubramanian Sundarapandian 2020 年 7 月 3 日
編集済み: John D'Errico 2020 年 7 月 3 日
Hello,
I have measured the thickness of a quarter of an 8 inch substrate (the filled area in the below picture shows the area where thickness was measured). Basically I have a z value for different x and y values.
I have shown a sample of my data below:
x y z
-4 4.5 1015.21
-3 4.5 1015.01
-2 4.5 1013.46
-1 4.5 1011.95
0 4.5 1008.35
1 4.5 1002.58
I was able to make a contour plot with the data I have. Now, I want to extrapolate the data to predict the thickness in the other quadrants. Is this possible with MaLab? It would be great if someone can help me with this.
Thanks in advance
Best Regards,
Bala

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John D'Errico
John D'Errico 2020 年 7 月 3 日
編集済み: John D'Errico 2020 年 7 月 3 日
Let me see. You have data in only 25% of the region of interest. Now you want to extrapolate that data into a region that comprises 3 times as much area, based on only the 25% quadrant? I'm sorry, but this is a highly optimistic goal you have posed.
Perhaps if you are successful in this, you will next decide to go into long term climate forecasting, predicting the Earth's climate out a few million years from now? A crystal ball would do as well.
One of my favorite commentaries on the dangers of extrapolation comes from Mark Twain.
In the space of one hundred and seventy six years the Lower Mississippi has shortened itself two hundred and forty-two miles. That is an average of a trifle over a mile and a third per year. Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oölitic Silurian Period, just a million years ago next November, the Lower Mississippi was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-pole. And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo [Illinois] and New Orleans will have joined their streets together and be plodding comfortably along under a single mayor and a mutual board of aldermen. There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.
Mark Tain, Life on the Mississippi, 1884
Seriously, large amounts of extrapolation baed on minimal inputs are likely to produce nothing better than wild guesses about the result.

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