如何确定 PlotRange 以包含所有图形?

问题描述

给定 Graphics 对象，我如何确定包含所有图形所需的坐标范围?基本上我需要像 Show 默认情况下所做的事情，但我想明确指定 PlotRange、PlotRangePadding 和 ImagePadding.

Given Graphics object, how do I determine the range of coordinates needed to include all of graphics? Basically I need something like what Show does by default, but I want to specify PlotRange,PlotRangePadding and ImagePadding explicitly.

例如，下面的两个Show应该呈现相同的

Example, two Shows below should render the same

g = Graphics[{Thickness[1], CapForm["Round"], Line[{{0, 0}, {1, 1}}]}];
Show[g]
Show[g, PlotRange -> getPlotRange[g], PlotRangePadding->getPlotRangePadding[g], ImagePadding->getImagePadding[g]]

动机:修复这个问题

更新:AbsoluteOptions 给了我 PlotRange 而不是其他两个选项.显式指定 ImagePadding->Automatic 会改变外观，尽管默认情况下它应该是 Automatic.

Update:AbsoluteOptions gives me PlotRange but not the other two options. Explicitly specifying ImagePadding->Automatic changes appearance though it's supposedly Automatic by default.

下面两张图片显示不同，我不明白为什么

Two images below show differently and I don't understand why

g = Graphics[{Thickness[1], CapForm["Round"], Line[{{0, 0}, {1, 1}}]}];
Show[g]
Show[g, Sequence @@ AbsoluteOptions[Show[g]]]

更新 2:类似的问题是 一年前提出的，没有提出的解决方案，但自 Mathematica 8.0 起未修复.总结

Update 2:A similar problem was brought up a year ago, with no solutions proposed, and not fixed as of Mathematica 8.0. To summarize

1. 没有办法通过PlotRange
的显式设置来重现上面的Show[g]
2. 无法获得 Show[g]
使用的绝对 ImagePadding
3. Show[g,PlotRange->Automatic] 看起来与 Show[g]
不同
4. AbsoluteOptions 可以给出错误的结果 用于 PlotRange

1. There's no way to reproduce Show[g] above with explicit setting of PlotRange
2. There's no way to get absolute ImagePadding used by Show[g]
3. Show[g,PlotRange->Automatic] looks different from Show[g]
4. AbsoluteOptions can give the wrong result for PlotRange

推荐答案

我可以建议以下 Ticks hack:

I can suggest the following Ticks hack:

pl = Plot[Sin[x], {x, 0, 10}];
Reap[Rasterize[Show[pl, Ticks -> {Sow[{##}] &, Sow[{##}] &}, ImageSize -> 0], 
   ImageResolution -> 1]][[2, 1]]

=> {{-0.208333, 10.2083}, {-1.04167, 1.04167}} 

诀窍是真正的PlotRange 是由前端决定的，而不是由内核决定的.因此，我们必须强制前端渲染图形，以便评估刻度函数.这个 hack 给出了完整的 PlotRange，并添加了 PlotRangePadding 的显式值.

The trick is that real PlotRange is determined by the FrontEnd, not by the Kernel. So we must force the FrontEnd to render the graphics in order to get tick functions evaluated. This hack gives the complete PlotRange with explicit value of PlotRangePadding added.

更通用的解决方案，考虑到 pl 具有 DisplayFinction 选项的非标准值并且可能设置了 Axes 选项的可能性假:

More general solution taking into account a possibility that pl has non-standard value of DisplayFinction option and that it may have Axes option set to False:

completePlotRange[plot:(_Graphics|_Graphics3D|_Graph)] := 
 Quiet@Last@
   Last@Reap[
     Rasterize[
      Show[plot, Axes -> True, Frame -> False, Ticks -> (Sow[{##}] &), 
       DisplayFunction -> Identity, ImageSize -> 0], ImageResolution -> 1]]

使用以下函数可以获得准确的PlotRange(不添加PlotRangePadding):

One can get the exact PlotRange (without the PlotRangePadding added) with the following function:

plotRange[plot : (_Graphics | _Graphics3D | _Graph)] := 
 Quiet@Last@
   Last@Reap[
     Rasterize[
      Show[plot, PlotRangePadding -> None, Axes -> True, Frame -> False, 
       Ticks -> (Sow[{##}] &), DisplayFunction -> Identity, ImageSize -> 0], 
      ImageResolution -> 1]]

附言在PlotRange 的文档页面上的更多信息"下，可以阅读:AbsoluteOptions 给出了 Mathematica 内部使用的选项的实际设置当给定的设置为 Automatic 或 All 时."(强调我的).因此，文档似乎甚至不能保证 AbsoluteOptions 在不是 Automatic 或 AllPlotRange 提供正确的值/代码>.

---

P.S. On the Documentation page for PlotRange under the "More information" one can read: "AbsoluteOptions gives the actual settings for options used internally by Mathematica when the setting given is Automatic or All. " (emphasis mine). So it seems that the Documentation does not even guarantee that AbsoluteOptions will give correct values for PlotRange when it is not Automatic or All.

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