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There is now a built-in version of an algorithm in v10.1: WordCloud. I wonder whether any of your nice algorithms introduced here had any influence on the built-in function... Individual words can be styled, annotated, rotated, etc., so I must assume that there is a polygon-intersection checking algorithm running under the hood. Would be useful to know ...


4

This is documented behavior. The parametric forms of ArcLength, Area, and Volume take the parametrization as fundamental, and compute the area including multiple coverings. The region forms of the functions take the image as fundamental, and compute the area of the embedding into R^n. If you want the latter, you should use ParametricRegion. From the ...


3

I think you should step back and think carefully about the expression you're using. Why are you using Sin[p] to represent the height? Also, if the height is 2, then it is not 2π. expr = {Sin[t], Cos[t], p}; ParametricPlot3D[ expr, {t, 0, 2 \[Pi]}, {p, 0, 2}, AxesLabel -> (Style[#, 18, "Label", Blue] & /@ {"x", "y", "p"}) ] Area[expr, {t, 0, 2 ...


6

Let mi visualize this mistake. Instead of constant radius we will use radius that depends of p: expr = {1 + .1 p, 1 + .1 p, 1} { Sin[t], Cos[t], Sin[p]}; ParametricPlot3D[expr, {t, 0, 3 Pi/2}, {p, 0, 2 \[Pi]}] As you can see, for p limits: {0, 2Pi} you are plotting your surface twice. Try with Cos[p] and p in {0,Pi} or whatever monotonic function for ...


6

For this particular example versio 10 functionality is helpful: list = {{0, 13}, {8, 10}, {13, 6}, {10, 0}}; pg = {{0, 0}}~Join~list; rm[x_, y_] := RegionMember[Polygon[pg], {x, y}] You can see criteria: Reduce[rm[x, y]] yielding: (0 <= y <= 6 && 0 <= x <= (20 + y)/2) || (6 < y <= 10 && 0 <= x <= 1/4 (82 - 5 ...


4

Try this: list = {{0, 13}, {8, 10}, {13, 6}, {10, 0}}; A = {5, 3}; f = Interpolation[list, InterpolationOrder -> 1]; If[f[A[[1]]] < A[[2]], "Over the curve", "Under The curve"] (*"Under The curve"*) Based on your comment, you are looking to check if the point is enclosed within the curve and the line y = 0. You can try this: list2 = Join[{{0, ...



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