python - 使用线性方程创建径向插值圆

Question

给定一个线性方程，我想使用斜率围绕给定点创建一个值圆，如果可能，由线性方程的斜率定义

我目前有点远 - 只能制作径向图但不知道如何将其与输入方程联系起来。我的第一个想法是使用 import matplotlib.animation as animation 和循环 matplotlib 的 alpha 参数来改变不透明度，使其逐渐变得越来越不透明。然而，alpha 似乎并没有改变不透明度。

代码:

# lenth of radius
distance = 200

# create radius 
radialVals = np.linspace(0,distance)

# 2 pi radians = full circle
azm = np.linspace(0, 2 * np.pi)
r, th = np.meshgrid(radialVals, azm)
z = (r ** 2.0) / 4.0

# creates circle
plt.subplot(projection="polar")

# add color gradient
plt.pcolormesh(th, r, z)

plt.plot(azm, r,alpha=1, ls='', drawstyle = 'steps') 

#gridlines
# plt.grid()

plt.show()

Answer 1

这是解决它的一种方法，想法是创建一个网格，使用函数计算颜色，然后使用 imshow 可视化网格。

from matplotlib import pyplot as plt 
import numpy as np


def create_mesh(slope,center,radius,t_x,t_y,ax,xlim,ylim):
    """
    slope: the slope of the linear function
    center: the center of the circle
    raadius: the radius of the circle 
    t_x: the number of grids in x direction 
    t_y: the number of grids in y direction 
    ax: the canvas 
    xlim,ylim: the lims of the ax
    """
    def cart2pol(x,y):
        rho = np.sqrt(x**2 + y**2)
        phi = np.arctan2(y,x)
        return rho,phi
    
    def linear_func(slope):
        # initialize a patch and grids  
        patch = np.empty((t_x,t_y))
        patch[:,:] = np.nan
        x = np.linspace(xlim[0],xlim[1],t_x)
        y = np.linspace(ylim[0],ylim[1],t_y)
        x_grid,y_grid = np.meshgrid(x, y)
        
        # centered grid
        xc = np.linspace(xlim[0]-center[0],xlim[1]-center[0],t_x)
        yc = np.linspace(ylim[0]-center[1],ylim[1]-center[1],t_y)
        xc_grid,yc_grid = np.meshgrid(xc, yc)
        rho,phi = cart2pol(xc_grid,yc_grid)
        linear_values = slope * rho
        
        # threshold controls the size of the gaussian 
        circle_mask = (x_grid-center[0])**2 + (y_grid-center[1])**2 < radius
        patch[circle_mask] = linear_values[circle_mask]
    
        return patch

    # modify the patch
    patch = linear_func(slope)
    extent = xlim[0],xlim[1],ylim[0],ylim[1]
    ax.imshow(patch,alpha=.6,interpolation='bilinear',extent=extent,
              cmap=plt.cm.YlGn,vmin=v_min,vmax=v_max)
        
        
fig,ax = plt.subplots(nrows=1,ncols=2,figsize=(12,6))
slopes = [40,30]
centroids = [[2,2],[4,3]]
radii = [1,4]

for item in ax:item.set_xlim(0,8);item.set_ylim(0,8)
v_max,v_min = max(slopes),0

create_mesh(slopes[0],centroids[0],radii[0],t_x=300,t_y=300,ax=ax[0],xlim=(0,8),ylim=(0,8))
create_mesh(slopes[1],centroids[1],radii[1],t_x=300,t_y=300,ax=ax[1],xlim=(0,8),ylim=(0,8))

plt.show()

这段代码的输出是

如您所见，由于坡度不同 ([40,30])，左侧图形的颜色渐变不如右侧图形清晰。

还要注意，这两行代码

v_max,v_min = max(slopes),0

ax.imshow(patch,alpha=.6,interpolation='bilinear',extent=extent,
          cmap=plt.cm.YlGn,vmin=v_min,vmax=v_max)

添加是为了让两个子图共享相同的颜色图。