WOLFRAM

Wolfram 语言与系统参考资料中心

等高线的法线

函数等高线的法向量等于函数的归一化梯度.

    
Wolfram Language code: f[x_, y_] := (x ^ 2/4) - 2x ^ 2 y - 3x y + y ^ 4 / 16
Wolfram Language code: grad[x_, y_] = Grad[f[x, y], {x, y}]
Wolfram Language code: normal[x_, y_] = Simplify[(grad[x, y]/Sqrt[grad[x, y].grad[x, y]])]
Wolfram Language code: Manipulate[ContourPlot[f[x, y], {x, -2, 2}, {y, -2, 2}, Epilog -> Arrow[{pt, pt + normal@@pt}], PerformanceGoal -> "Quality", Contours -> 20, PlotRange -> {{-2, 2}, {-2, 2}, {-30, 30}}], {{pt, {.01, -.1}}, Locator}, FrameLabel -> "Click a point to see its normal", SaveDefinitions -> True]