Timeline for Plot the boundaries of each piece of a piecewise function
Current License: CC BY-SA 3.0
18 events
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| Jul 19, 2013 at 9:09 | comment | added | Ailurus | @Kuba The second image on vectorizer.org/boar/gallery.html shows the ZP function/element. It consists of 28 pieces. These pieces should be outlined in the same fashion as your latest solution for the hexagonal hat function (which is in fact the Courant function/element). Thanks :) | |
| Jul 19, 2013 at 9:02 | comment | added | Kuba | @Ailurus I will take a closer look later, I do not have time now, sorry. | |
| Jul 19, 2013 at 9:00 | comment | added | Ailurus |
@Kuba Well, there are no warnings anymore, but the plot seems to be empty. Yes, the x + t should be in that integration, the resulting function $B_{1111}(x,y)$ is called the Zwart-Powell function.
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| Jul 19, 2013 at 8:52 | comment | added | Kuba |
@Ailurus You can try something like f[x_, y_] = Piecewise[First[List @@ #], None]&/@B1111[x, y] since it is sum of piecewise functions. however it looks quite smooth so you will get only the domain boundary on the plot. Tell im if this is helpful. (should there be x+t in second integration?)
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| Jul 19, 2013 at 7:13 | vote | accept | Ailurus | ||
| Jul 19, 2013 at 7:13 | comment | added | Ailurus |
@Kuba Yes this looks good, thanks for all the effort! However, it doesn't seem to work for $B_{1111}(x,y)$ as defined in my comment above. Mathematica mentions The first argument of Piecewise is not a list of pairs. Is this easily fixed?
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| Jul 18, 2013 at 22:57 | comment | added | Kuba | @Ailurus I've made an edit :) tell me if it is what you are looking for. | |
| Jul 18, 2013 at 22:51 | history | edited | Kuba | CC BY-SA 3.0 |
response to op's last edit
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| Jul 18, 2013 at 21:16 | comment | added | Ailurus | @Kuba Now that I think of it, the result is actually the projection of the outlined supports of the regions onto the curve. | |
| Jul 18, 2013 at 21:15 | comment | added | Ailurus | @Kuba I just updated my question with the result I have in mind. The boundaries of all regions should be marked with a relatively thick black line. It is not necessary to highlight the supports of the regions as in your colourful example above :). If possible, it should be applicable without manually providing a set of coordinates. | |
| Jul 18, 2013 at 19:09 | comment | added | Kuba | @Ailurus I can try to make someghing more general and useful but you have not respond to my question about edges in comment. Also I need to know what result you want to have, just a plot of smaller regions? Maybe all the edges like now? Do you need to know the coordinates or the plot is enough? :) | |
| Jul 18, 2013 at 15:11 | comment | added | Ailurus |
@Kuba Thanks for your solution! This goes way above my knowledge of Mathematica however, so what would I need to change to do the same thing for the function $B_{1111}(u,v)$ defined as B1111[x_, y_] = Integrate[B111[x + t, y - t], {t, 0, 1}]?
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| Jul 18, 2013 at 8:44 | comment | added | Kuba |
@RahulNarain Yes, I like it too :). I also like that Mathematica gives us easy access to the data produced inside Plot Piecewise etc.
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| Jul 18, 2013 at 0:35 | history | edited | Kuba | CC BY-SA 3.0 |
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| Jul 18, 2013 at 0:28 | history | edited | Kuba | CC BY-SA 3.0 |
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| Jul 18, 2013 at 0:04 | history | edited | Kuba | CC BY-SA 3.0 |
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| Jul 17, 2013 at 20:35 | comment | added | user484 |
+1; I was just about to post something like this. It's worth pointing out that this solution relies on the fact that B111[x, y] is actually a Piecewise function that we can "look inside" (and not something involving Abs or Max or the like).
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| Jul 17, 2013 at 20:32 | history | answered | Kuba | CC BY-SA 3.0 |