Matplotlib中3D热力图（XY,C）插值结果异常，求助排查

我在2D极坐标图中绘制了带第三维度强度值的XY坐标点，尝试实现圆形插值热力图，但结果不符合预期：左侧散点图能正确呈现三层环形强度分布（外层值100、中层50、内层1），但右侧插值后的热力图完全无法匹配该分布，更换插值方法也未解决问题。

原始代码 #

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

### INTENSITY VALUES FOR HEATMAP ###

T1 = 100,100,100,100,100,100,50,50,50,50,50,50,1,1,1,1,1,1,

### CO-ORDINATES ###

a=0
b=0
rO = 7.5
rM = 5
rI = 2.5
heights =  1,2,3,4,5

### RADIAL POINTS ###

def XCoords(a,rO,rM,rI):
    XsX = []
    O = np.linspace(0,2*np.pi,6,endpoint=False)
    for i in O:
        xx = a+rO*np.cos(i),a+rM*np.cos(i),a+rI*np.cos(i)
        XsX.append(xx)
    return XsX

Xs1,Xs2,Xs3 = np.column_stack(XCoords(a,rO,rM,rI))
        
def YCoords(b,rO,rM,rI):
    YsY = []
    O = np.linspace(0,2*np.pi,6,endpoint=False)
    for i in O:
        yy = a+rO*np.sin(i),a+rM*np.sin(i),a+rI*np.sin(i)
        YsY.append(yy)
    return YsY

Ys1,Ys2,Ys3 = np.column_stack(YCoords(b,rO,rM,rI))

def cart2pol(x,y):
    rho = np.sqrt(x**2 + y**2)
    phi = np.arctan2(y,x)
    return (rho,phi)

PolarR1, PolarT1 = cart2pol(Xs1,Ys1)
PolarR2, PolarT2 = cart2pol(Xs2,Ys2)
PolarR3, PolarT3 = cart2pol(Xs3,Ys3)

PolarRF = PolarR1,PolarR2,PolarR3
PolarTF = PolarT1,PolarT2,PolarT3

### INTERPOLATION ATTEMPT ###

max_r = 7.5
max_theta = 2*np.pi
theta = np.linspace(0,max_theta,200)
r = np.linspace(0,max_r,200)
grid_r,grid_theta = np.meshgrid(r,theta)

X,Y = np.meshgrid(PolarRF,PolarTF)

points = np.column_stack((X.flatten(),Y.flatten()))  
values = np.linspace(np.min(T1),np.max(T1),324)

data = griddata(points,values,(grid_r,grid_theta),method='nearest',fill_value=0,rescale=False)

### HEAT MAP COLORS ###

grad = 'viridis'

cA = T1
mB = plt.cm.ScalarMappable(cmap=grad)
fAcolors = mB.to_rgba(cA)

### PLOT ###

fig = plt.figure(figsize=(15,15), dpi=300)
ax = fig.add_subplot(121,projection='polar')
ax.scatter(PolarTF,PolarRF,s=200,c=fAcolors,alpha=0.5)

fig2 = plt.figure(figsize=(15,15),dpi=300)
ax2 = fig.add_subplot(122,projection='polar')
ax2.pcolormesh(grid_theta,grid_r,data,alpha=0.5)


plt.show()

问题根源与修正方案 #

核心问题 #

1. 点-值对应关系错误：用np.linspace生成的values完全脱离了原始T1的强度分配，每个坐标点没有匹配到正确的强度值。
2. 原始点构建冗余：np.meshgrid(PolarRF,PolarTF)生成了多余的点组合，导致points数组维度错误。
3. 插值网格维度不匹配：griddata的输入网格与points的维度对应错误，导致插值结果混乱。
4. 函数笔误：YCoords函数中误用了变量a，应该使用b。

修正后的代码 #

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

### INTENSITY VALUES FOR HEATMAP ###
T1 = np.array([100]*6 + [50]*6 + [1]*6)  # 明确外层6个100，中层6个50，内层6个1

### CO-ORDINATES ###
a=0
b=0
rO = 7.5
rM = 5
rI = 2.5

### RADIAL POINTS ###
def XCoords(a,rO,rM,rI):
    XsX = []
    O = np.linspace(0,2*np.pi,6,endpoint=False)
    for i in O:
        xx = (a+rO*np.cos(i), a+rM*np.cos(i), a+rI*np.cos(i))
        XsX.append(xx)
    return XsX

Xs1,Xs2,Xs3 = np.column_stack(XCoords(a,rO,rM,rI))
        
def YCoords(b,rO,rM,rI):
    YsY = []
    O = np.linspace(0,2*np.pi,6,endpoint=False)
    for i in O:
        yy = (b+rO*np.sin(i), b+rM*np.sin(i), b+rI*np.sin(i))  # 修复笔误：a改为b
        YsY.append(yy)
    return YsY

Ys1,Ys2,Ys3 = np.column_stack(YCoords(b,rO,rM,rI))

def cart2pol(x,y):
    rho = np.sqrt(x**2 + y**2)
    phi = np.arctan2(y,x)
    return (rho,phi)

PolarR1, PolarT1 = cart2pol(Xs1,Ys1)
PolarR2, PolarT2 = cart2pol(Xs2,Ys2)
PolarR3, PolarT3 = cart2pol(Xs3,Ys3)

# 合并原始极坐标点，确保每个点对应正确的T1值
PolarR = np.concatenate([PolarR1, PolarR2, PolarR3])
PolarT = np.concatenate([PolarT1, PolarT2, PolarT3])

### INTERPOLATION ATTEMPT ###
max_r = 7.5
max_theta = 2*np.pi
theta = np.linspace(0, max_theta, 200)
r = np.linspace(0, max_r, 200)
grid_theta, grid_r = np.meshgrid(theta, r)  # 调整顺序，匹配griddata输入要求

# 构建正确的点数组：每个点是(theta, r)
points = np.column_stack((PolarT, PolarR))
values = T1  # 直接用原始强度值，确保一一对应

# 插值：使用cubic获得更平滑的效果，也可切换为linear/nearest
data = griddata(points, values, (grid_theta, grid_r), method='cubic', fill_value=0)

### HEAT MAP COLORS ###
grad = 'viridis'
mB = plt.cm.ScalarMappable(cmap=grad)
mB.set_array(T1)  # 设置颜色映射的范围

### PLOT ###
fig = plt.figure(figsize=(12,6), dpi=100)
# 左侧散点图
ax1 = fig.add_subplot(121, projection='polar')
ax1.scatter(PolarT, PolarR, s=200, c=T1, cmap=grad, alpha=0.5)
ax1.set_title('原始散点图')

# 右侧插值热力图
ax2 = fig.add_subplot(122, projection='polar')
im = ax2.pcolormesh(grid_theta, grid_r, data, cmap=grad, alpha=0.8)
ax2.set_title('插值热力图')
fig.colorbar(mB, ax=[ax1, ax2], shrink=0.8)

plt.tight_layout()
plt.show()

关键改动说明 #

• 明确T1的数组结构，确保每个环形的点对应正确的强度值
• 合并原始极坐标点时直接拼接，避免冗余的网格点生成
• 调整插值网格的生成顺序，匹配griddata的输入要求
• 修复了YCoords函数中误用a的笔误
• 统一颜色映射，添加色标方便对比

内容的提问来源于stack exchange，提问作者IrwinJ