Happy Valentine's Day?Who says math can't be romantic?LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSV3aXRoRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEmcGxvdHNGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOUY1RlpGOQ==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But this is not the problem.The problem: how to evaluate a double integral for the volume of a region in space that can only be implicitly plotted as the surface 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, where one can only solve this condition numerically for any variable in terms of the others, and for each such solution there are only two solutions, a max and a min for that variable, and the surface contains all the points in between as in the explicit 3-d heart example below.Method of Attack:
Assume we want to set up the integral in the form 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 , where the outermost limits are found numerically explicitly at the start, while LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEleW1heEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEleW1pbkYnRi9GMkY1RjJGPA== can be found by a numerical procedure from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJ6RidGNEY3RjpGN0ZBRjdGQUY3RkE= while for a given LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, 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 must be found by a numerical procedure. In fact in our explicit example there is a reflection symmetry in both LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn: 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. It seems we have to resort to Riemann discrete sum approximate integration, BUT the procedures we introduce just won't cooperate.3d heartThe following graphic is a bit heavy. From this webpage. Not sure why I continued to use the capitalized variable names.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Heart in a box?how to find its volume?We put back in the tickmarks.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From the first plot it appears that the extreme value of Y occurs at the origin in the X-Z plane, where the value is 2/3, see below. maxThis is a local max at the origin 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 the implicit function 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 at 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: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First we look at the projection onto the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn-Zplane, which will be the region of integration for our double integral.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We cannot solve this border curve relation for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, so we will have to introduce a numerical procedure to do so. There will be two solutions for all values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn in the interior.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYlUSJmRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJaRidGL0YyLyUrZXhlY3V0YWJsZUdGRUZBRkFGZW5GQQ==We use fsolve for solving the polynomical equation for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, given a numerical value for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn.JSFHfsolve will produce all real roots of polynomials ordered as a sequence of real numbers from left to right. There are two for our case for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JVEiMEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPEYnRi9GMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtaUdGJDYmUSJYRicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGNS1GTTYmUSVYbWF4RidGUEYvRlNGL0Yy , where Xmax is to be determined below.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Now by trial and error we increase the input to narrow the distance between these two roots until we get more and more accurate digits. For this value LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMS4xMzkwMjgxNjQ2RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn we go too far, and backing off one digit in the final digit LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JFEtMS4xMzkwMjgxNjQ1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn gives two roots differing in the fourth significant digit. We could increase the number of digits to get better accuracy, but let's just go with this approximation.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 minimal box containing the heart has dimensions of 2 Xmax times 4/3 times 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. To put the volume in context we will compute the percentage of the minimum box which contains the heart. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVElVmJveEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNictSSNtbkdGJDYkUSIyRidGOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlktRiw2JVElWG1heEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGWEZaLUkmbWZyYWNHRiQ2KC1GUjYkUSI0RidGOS1GIzYlLUZSNiRRIjNGJ0Y5Ri9GMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXXAvJSliZXZlbGxlZEdGPUZqbi1JKG1mZW5jZWRHRiQ2JC1GIzYqLUZSNiRGam9GOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl1xRlUtRiw2JVEmWnJvb3RGJ0YvRjItRmNwNiQtRiM2JS1GUjYkUSQwLjVGJ0Y5RmhuRjlGOS1GY3A2Ji1GIzYlRlFGaG5GOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmhuRjlGOUZobkY5To handle the case in which one might get 6 roots (2 repeated 3 times), we modify our procedure to take the minimum and maximum, but for now let's not utilize this.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=This produces the two desired values, or did at one point but now does not, giving the same frustrating error.JSFHNext we introduce a numerical procedure to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEleW1heEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYyRjw=for each pair 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solving it for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGQQ== and then taking the positive square root.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmWXJvb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JI21uR0YkNiRRIjBGJy9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0Y6LyUrZXhlY3V0YWJsZUdGRkY+Rj5GWUY+Not much hope that something naive like this will work but why not give it a shot.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What is this error that pops up each time I try to do something with a numerical procedure feeding into another procedure which expects a real number:
Error, (in fsolve) Can't handle expressions with typed proceduresand Maplesoft online seems never to have a Help page for these purple error messages!
but see https://www.mapleprimes.com/questions/203085-Error-In-Solving-Equation-Involvingthe solution is: fsolve(f(x),x) -> fsolve(unapply(f(x),x)) to convert it to a variablefree function name.
So now let's try a Riemann sum approach to the double integral. Midpoint evaluation.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And here is the catch, this infuriating error triggered by inserting a procedure into another procedure which derails, when the first procedure produces a decimal number and the second procedure expects a decimal number.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Now we give it a try. Some edge effects lead to the small imaginary contributions.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRLDMuMzM2MDExOTU1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiUtSSNtaUdGJDYlUSVWYm94RicvJSdpdGFsaWNHUSV0cnVlRicvRjNRJ2l0YWxpY0YnRjtGPi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRS8lKWJldmVsbGVkR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRkpGMg==Hmm, nearly 1/2 the minimal box which contains is. Interesting.afterthoughts (and a smooth heart!)This is actually a third degree polynomial in 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 and so can be solved exactly for either as a function of the other two variables, in particular 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 for the "thickness" function. It is only a nontrivial sextic in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn.refining the grid100x100x100 leads to about a 23MB graphics file after 2.6 seconds in Maple 2017. This still rotates in real time.200x200x200 leads to about a 103MB graphics file after 20.7 seconds in Maple 2017. It is so unwieldy that trying to rotate the plot leads to jumpy response. The surface grid irregularities remain.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2d cross section heartWe can close in a bit the intervals around the heart by looking at the cross-sections in the coordinate plane.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If we double the grid divisions in the thickness dimension LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, perhaps that will improve the visible roughness at the extreme values of that coordinate?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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=this can be solved exactly for the thickness functionThis is a 3rd degree polynomial equation in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGQQ== so it can be solved exactly for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGQQ== and then the square root will give LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYnLUYjNiUtSSNtaUdGJDYmUSJZRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGN0Y9LyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRkFGN0Y9.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Hmm, there is a problem since our solved expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn should be 0 at 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. Seems to be some numerical difficulties at the vertex on the vertical axis. Perhaps the tangent plane is going vertical as it approaches at the vertex.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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This gives a really smooth surface except at the thickness symmetry plane. Perhaps this could be joined to a narrow thickness implicitplot3d in between the two surfaces.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Success!