有没有办法强制 ContourPlot 重新检查其递归算法每个阶段的所有点？
感谢对情节的出色分析 Yaroslav Bulatov 的算法，我现在明白了 Plot3D 和 ContourPlot 无法绘制具有中断和不连续性的平滑函数的原因。
例如，在以下情况下，ContourPlot 根本无法绘制轮廓 x^2 + y^2 = 1：
ContourPlot[Abs[x^2 + y^2 - 1], {x, -1, 1}, {y, -1, 1}, Contours -> {0}]
这是因为算法没有深入到 x^2 + y^2 = 1 附近的区域。它“下降” “该地区还处于初级阶段，不会尝试进一步调查。从这个意义上说，增加 MaxRecursion 没有任何作用。甚至未记录的选项 Method -> {细化-> {控制值-> .01 \[Degree]}} 没有帮助（但使 Plot3D 更平滑一些）。
上面的函数只是一个简单的例子。在现实生活中，我正在处理非常复杂的隐式函数，无法通过分析解决。
有没有办法让 ContourPlot 深入到断裂和不连续附近的区域？
Thanks to this excellent analysis of the Plot algorithm by Yaroslav Bulatov, I now understand the reason why Plot3D and ContourPlot fail to draw smoothly functions with breaks and discontinuities.
For example, in the following case ContourPlot fails to draw contour x^2 + y^2 = 1 at all:
ContourPlot[Abs[x^2 + y^2 - 1], {x, -1, 1}, {y, -1, 1}, Contours -> {0}]
It is because the algorithm does not go deeply into the region near x^2 + y^2 = 1. It "drops" this region on an initial stage and does not try to investigate it further. Increasing MaxRecursion does nothing in this sense. And even undocumented option Method -> {Refinement -> {ControlValue -> .01 \[Degree]}} does not help (but makes Plot3D a little bit smoother).
The above function is just a simple example. In real life I'm working with very complicated implicit functions that cannot be solved analytically.
Is there a way to get ContourPlot to go deeply into such regions near breaks and discontinuities?
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这些是标准图。
以及 10^-20 处的轮廓
它们对我来说非常清楚。
您期望更准确的信息吗？
编辑
如果您想使用轮廓->{0}选项，您可以使用：
These are the standard Plots .
And the Contour at 10^-20
They are pretty clear for me.
Do you expect something more accurate?
Edit
If you want to use the Contours->{0} Option, you may use: