Hatched shading?
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From: annetts729 on 22 Jul 2010 05:44 On Jul 21, 7:10 pm, "Alexey Popkov" <lehi...(a)gmail.com> wrote: > Hello, > > I confirm this behavior on Windows XP SP3 with Mathematica 7.0.1. All the > red lines get out of the region defined by RegionFunction. > > "ADL" <alberto.dilu...(a)tiscali.it> news:i23k1u$eqc$1(a)smc.vnet.net... > > > Following what Bob brilliantly suggested, I found a possible bug in > > Mathematica 7.0.1 for Windows. > > If you type the following, you will get a couple of red lines getting > > out of their boundary: > > > f[x_] := Sin[x]; > > > Plot[ > > {Table[(x - k)/3, {k, -3, 3, .10}], f[3x]}, > > {x, 0, 3}, > > PlotRange -> {0, 1}, > > RegionFunction -> Function[{x, y}, 0 < y <= f[3x]], > > PlotStyle -> { > > Directive[ AbsoluteThickness[4], Red], > > Directive[ Thick, Blue] > > } > > ] > > > Does anybody else confirms this? > > > ADL Yeah -- there are red lines. But I'd suggest it's an artifact of plotting rather than a bug per se. Look at f[x_] := Sin[x]; Plot[{Table[(x - k)/3, {k, -3, 3, .10}], f[3 x]}, {x, 0, 3}, PlotRange -> {0, 1}, RegionFunction -> Function[{x, y}, 0 < y <= f[3 x]], PlotStyle -> {Directive[AbsoluteThickness[4], Red], Directive[Thick, Blue]}, PlotPoints -> #, ImageSize -> 500] & /@ {25, 50, 75, 100} Regards, Dave.
From: E. Martin-Serrano on 23 Jul 2010 07:07 In my XP SP3 it the DPark's solution works perfect. Beside, I tried several PlotPoints settings and see that below 150 points the hatching starts to go uneven. With 100 points it becomes pretty unusable. And, I have had similar problems with *RegionFunction* when applied to some rotated and translated functions plots. The corresponding (rotated/translated) *RegionFunction* specification sometimes works and sometimes does not when applied to the same (rotated/translated) functions. I solved the problem by applying the corresponding 'rotation/translation' to the original 'PlotRangle rectangle' and then plotting by hand only the points of the shifted functions lying within the rotated/translated PlotRangle rectangle. My problem seems to be related with the computation of the intersections with of the converted functions with the corresponding new *PlotRange* limits. The examples I have are too large, and perhaps tricky, to be posted here. I will try to isolate some simpler example to post it. E. Martin-Serrano ___________________________________________________ -----Original Message----- From: Themis Matsoukas [mailto:tmatsoukas(a)me.com] Sent: Thursday, July 22, 2010 11:43 AM Subject: Re: Hatched shading? I get an error. What am I missing? Get::noopen: Cannot open Presentations`Master`. >> Needs::nocont: Context Presentations`Master` was not created when Needs was evaluated. >> $Failed Themis
From: Bill Rowe on 23 Jul 2010 07:10 On 7/22/10 at 5:43 AM, tmatsoukas(a)me.com (Themis Matsoukas) wrote: >I get an error. What am I missing? >Get::noopen: Cannot open Presentations`Master`. >> >Needs::nocont: Context Presentations`Master` was not created when >Needs was evaluated. >> >$Failed Presentations is a package written by David Park available from him for a fee. It is not a package distributed with Mathematica. The message you got above is consistent with not having the package installed. The other possibility is the package is installed but installed incorrectly, i.e., not in one of the directories returned by evaluating $Path
From: Murray Eisenberg on 23 Jul 2010 07:12 You need to have David Park's Presentations application: http://home.comcast.net/~djmpark/DrawGraphicsPage.html On 7/22/2010 5:43 AM, Themis Matsoukas wrote: > I get an error. What am I missing? > > Get::noopen: Cannot open Presentations`Master`.>> > > Needs::nocont: Context Presentations`Master` was not created when Needs was evaluated.>> > > $Failed > > Themis > -- Murray Eisenberg murray(a)math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
From: David Park on 23 Jul 2010 07:14
Here is a better method for hatching. The problem with using RegionFunction is that Mathematica uses even spacing of points and then determines if they are in the predicate region. This produces poor results unless we use brute force with many PlotPoints and do extra trimming on the lines. An alternative method is to define hatching lines so that the y value is real within the region and imaginary outside the region. The Mathematica algorithm then uses recursion near the boundary line to obtain better defined lines. We no longer have to use brute force or trim the lines. Needs["Presentations`Master`"] f[x_] := Sin[x]; hatch[k_][x_] := If[0 < x < 3 \[And] 0 <= (x - k)/3 <= f[3 x], (x - k)/3, I]; Draw2D[ {(* Draw hatch lines first *) Red, AbsoluteThickness[1], Table[ ParametricDraw[{x, hatch[k][x]}, {x, 0, 3}, PlotPoints -> Automatic, MaxRecursion -> Automatic], {k, -3, 3.0, .1}], (* Draw the curve without a fill *) Blue, AbsoluteThickness[2], Draw[f[3 x], {x, 0, 3}, PlotRange -> {0, 1}] }, AspectRatio -> .6, PlotRange -> {{0, 3}, {0, 1}}, PlotRangePadding -> {.1, .05}, Axes -> True, ImageSize -> 400] David Park djmpark(a)comcast.net http://home.comcast.net/~djmpark/ From: David Park [mailto:djmpark(a)comcast.net] The problem with RegionFunction is how many points does Mathematica use, especially with a straight line, and how does the algorithm determine where the boundary should be. Suppose one point is well within the region and the next point is well without. I'm sure that Mathematica doesn't calculate the exact intersections with boundaries. So I think the only reliable method is to use some brute force and trim the lines if they extend outside the region. Again, here is a Presentations solution where it is convenient to treat the hatching and the curve separately. Needs["Presentations`Master`"] f[x_] := Sin[x]; Draw2D[ {(* Draw hatch lines first *) Table[ Draw[(x - k)/3, {x, -1.5, 3}, RegionFunction -> Function[{x, y}, 0 < x < 3 \[And] 0 <= y <= f[3 x]], PlotRange -> {{1, 3}, {0, 1}}, PlotPoints -> 200, PlotStyle -> Directive[AbsoluteThickness[2], Red]] /. {x_?NumberQ, y_?NumberQ} :> If[0 < x < 3 \[And] 0 <= y <= f[3 x], {x, y}, Unevaluated[Sequence[]]], {k, -3, 3, .1}], (* Draw the curve without a fill *) Blue, AbsoluteThickness[2], Draw[f[3 x], {x, 0, 3}, PlotRange -> {0, 1}] }, AspectRatio -> .6, PlotRange -> {{0, 3}, {0, 1}}, PlotRangePadding -> {.1, .05}, Axes -> True, ImageSize -> 400] If you do the same graphic with say 25 points you will see that Mathematica did not always use points very close to the boundary. David Park djmpark(a)comcast.net http://home.comcast.net/~djmpark/ From: ADL [mailto:alberto.dilullo(a)tiscali.it] Following what Bob brilliantly suggested, I found a possible bug in Mathematica 7.0.1 for Windows. If you type the following, you will get a couple of red lines getting out of their boundary: f[x_] := Sin[x]; Plot[ {Table[(x - k)/3, {k, -3, 3, .10}], f[3x]}, {x, 0, 3}, PlotRange -> {0, 1}, RegionFunction -> Function[{x, y}, 0 < y <= f[3x]], PlotStyle -> { Directive[ AbsoluteThickness[4], Red], Directive[ Thick, Blue] } ] Does anybody else confirms this? ADL On 18 Lug, 07:06, Bob Hanlon <hanl...(a)cox.net> wrote: > I forget to copy the definition of f[x] that I was using as an example > > f[x_] = Exp[-x] > > Bob Hanlon |