当我给出更多数据点时，matplotlib tricontourf会遇到问题

Question

当我试图描绘压力时，我遇到了一个问题。在

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.tri as mtri
import matplotlib.cm as cm

def plot(x_plot, y_plot, a_plot):
    x = np.array(x_plot)
    y = np.array(y_plot)
    a = np.array(a_plot)

    triang = mtri.Triangulation(x, y)
    refiner = mtri.UniformTriRefiner(triang)
    tri_refi, z_test_refi = refiner.refine_field(a, subdiv=4)

    plt.figure(figsize=(18, 9))
    plt.gca().set_aspect('equal')
    #     levels = np.arange(23.4, 23.7, 0.025)
    levels = np.linspace(a.min(), a.max(), num=1000)
    cmap = cm.get_cmap(name='jet')
    plt.tricontourf(tri_refi, z_test_refi, levels=levels, cmap=cmap)
    plt.scatter(x, y, c=a, cmap=cmap)
    plt.colorbar()

    plt.title('stress plot')
    plt.show()

首先，我只使用8个点绘制：

^{pr2}$

然后我试图给出一个关于矩形边界的信息：

x = [2.3384750000000003, 1.983549, 3.018193, 2.013683, 3.671702, 3.978008, 4.018905, 0.3356813, 0.0, 0.0, 1.0070439, 3.325298666666667, 2.979695, 2.660479, 1.3271675666666667, 0.9909098, 1.6680919666666665, 0.6659845666666667]
y = [0.614176, -0.038322, 0.922264, 0.958586, 0.5590579999999999, -0.1229, 0.87781, 0.663329, 1.0, 0.0, 0.989987, 0.24002166666666666, -0.079299, 0.26821433333333333, 0.31229233333333334, -0.014787999999999999, 0.6367503333333334, 0.3250663333333333]
a = [2.572, 2.572, 2.572, 2.572, 0.8214, 0.8214, 0.8214, 5.689, 5.689, 5.689, 5.689, -0.8214, -0.8214, -2.572, -4.292, -4.292, 4.292, -5.689]
plot(x, y, a)

我不知道怎么解决，为什么会这样。 我想要的数字是：

我做了散点图的每一个点在第二个数字，有正确的，但为什么颜色不是轮廓。在

非常感谢。在

Answer 1

在附加点的情况下，UniformTriRefiner返回的字段不能很好地插值。相反，它引入了新的最小值和最大值，其值比原始点大20倍。在

下面的情节显示了正在发生的事情。在

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.tri as mtri
import matplotlib.cm as cm

def plot(x_plot, y_plot, a_plot, ax=None):
    if ax == None: ax = plt.gca()
    x = np.array(x_plot)
    y = np.array(y_plot)
    a = np.array(a_plot)

    triang = mtri.Triangulation(x, y)
    refiner = mtri.UniformTriRefiner(triang)
    tri_refi, z_test_refi = refiner.refine_field(a, subdiv=2)

    levels = np.linspace(z_test_refi.min(), z_test_refi.max(), num=100)
    cmap = cm.get_cmap(name='jet')

    tric = ax.tricontourf(tri_refi, z_test_refi, levels=levels, cmap=cmap)
    ax.scatter(x, y, c=a, cmap=cmap, vmin= z_test_refi.min(),vmax= z_test_refi.max())
    fig.colorbar(tric, ax=ax)

    ax.set_title('stress plot')

fig, (ax, ax2) = plt.subplots(nrows=2, sharey=True,sharex=True, subplot_kw={"aspect":"equal"} )

x = [2.3384750000000003, 3.671702, 0.3356813, 3.325298666666667, 2.660479, 1.3271675666666667, 1.6680919666666665, 0.6659845666666667]
y = [0.614176, 0.5590579999999999, 0.663329, 0.24002166666666666, 0.26821433333333333, 0.31229233333333334, 0.6367503333333334, 0.3250663333333333]
a = [2.572, 0.8214, 5.689, -0.8214, -2.572, -4.292, 4.292, -5.689]
plot(x, y, a, ax)


x = [2.3384750000000003, 1.983549, 3.018193, 2.013683, 3.671702, 3.978008, 4.018905, 0.3356813, 0.0, 0.0, 1.0070439, 3.325298666666667, 2.979695, 2.660479, 1.3271675666666667, 0.9909098, 1.6680919666666665, 0.6659845666666667]
y = [0.614176, -0.038322, 0.922264, 0.958586, 0.5590579999999999, -0.1229, 0.87781, 0.663329, 1.0, 0.0, 0.989987, 0.24002166666666666, -0.079299, 0.26821433333333333, 0.31229233333333334, -0.014787999999999999, 0.6367503333333334, 0.3250663333333333]
a = [2.572, 2.572, 2.572, 2.572, 0.8214, 0.8214, 0.8214, 5.689, 5.689, 5.689, 5.689, -0.8214, -0.8214, -2.572, -4.292, -4.292, 4.292, -5.689]
plot(x, y, a, ax2)

plt.show()

可以看出，“插值”字段的值超出了原始值很大一部分。
原因是默认情况下，UniformTriRefiner.refine_field使用三次插值（a^{}）。文件规定

The interpolation is based on a Clough-Tocher subdivision scheme of the triangulation mesh (to make it clearer, each triangle of the grid will be divided in 3 child-triangles, and on each child triangle the interpolated function is a cubic polynomial of the 2 coordinates). This technique originates from FEM (Finite Element Method) analysis; the element used is a reduced Hsieh-Clough-Tocher (HCT) element. Its shape functions are described in 1. The assembled function is guaranteed to be C1-smooth, i.e. it is continuous and its first derivatives are also continuous (this is easy to show inside the triangles but is also true when crossing the edges).

In the default case (kind ='min_E'), the interpolant minimizes a curvature energy on the functional space generated by the HCT element shape functions - with imposed values but arbitrary derivatives at each node.

虽然这确实是非常技术性的，但我强调了一些重要的方面，即插值是平滑的，并且具有定义的导数连续。为了保证这种行为，当数据非常稀疏但振幅波动很大时，超调是不可避免的。在

这里的数据根本不适合三次插值。人们要么试图获取更密集的数据，要么使用线性插值法。在