Delaunay triangulation is not correctly constructed when plotting the intersection area of two inequalities

In the code that uses the NumPy, Matplotlib, SymPy, and SciPy libraries, there is a function called plot_inequalities which is intended to plot the intersection area of two inequalities using Delaunay triangulation. However, when running the code, the Delaunay triangulation is not constructed correctly.Here is code:

import numpy as np
import matplotlib.pyplot as plt
from sympy import *
from scipy.spatial import Delaunay
def plot_inequalities(inequality1, inequality2, x_min, x_max, y_min, y_max):
x, y = symbols('x y')
try:
inequality1_expr = sympify(inequality1)
inequality2_expr = sympify(inequality2)
except:
print("Error: Incorrect inequality format.")
return
try:
F1 = lambdify((x, y), inequality1_expr, 'numpy')
F2 = lambdify((x, y), inequality2_expr, 'numpy')
except:
print("Error: Failed to compile inequalities.")
return
# Create grid of x and y values
x_vals = np.concatenate(([0], np.linspace(x_min, x_max, 400)))
y_vals = np.linspace(y_min, y_max, 400)
X, Y = np.meshgrid(x_vals, y_vals)
# Check inequalities at each grid point
inequality1_result = F1(X, Y)
inequality2_result = F2(X, Y)
# Find intersection points of the inequalities
intersection_points = []
for i in range(len(x_vals)):
for j in range(len(y_vals)):
if inequality1_result[j, i] < 0 and inequality2_result[j, i] > 0:
intersection_points.append([x_vals[i], y_vals[j]])
intersection_points = np.array(intersection_points)
# Delaunay triangulation of intersection points
if len(intersection_points) >= 3:
tri = Delaunay(intersection_points[:, :2])
# Plot the graph
plt.triplot(intersection_points[:, 0], intersection_points[:, 1], tri.simplices.copy(), color='black')
# Display the graph
plt.xlabel('x')
plt.ylabel('y')
plt.grid(False)
plt.axis('equal')
plt.xlim(x_min, x_max)
plt.ylim(y_min, y_max)
plt.show()
print("Enter the lower inequality in the format 'F(x, y) > 0':")
inequality1 = input()
print("Enter the upper inequality in the format 'F(x, y) < 0':")
inequality2 = input()
print("Enter the x interval boundaries in the format 'x_min, x_max':")
x_min, x_max = map(float, input().split(','))
print("Enter the y interval boundaries in the format 'y_min, y_max':")
y_min, y_max = map(float, input().split(','))
plot_inequalities(inequality1, inequality2, x_min, x_max, y_min, y_max)

example area: y-x>0 and y-x**2<0

The issue with the plot_inequalities function is that the intersection_points array is not being properly filtered to remove duplicate points. When the intersection_points array contains duplicate points, the Delaunay triangulation cannot be constructed correctly. To fix this issue, you can add a check to remove duplicate points from the intersection_points array before constructing the Delaunay triangulation.

Here's the updated code:

import numpy as np
import matplotlib.pyplot as plt
from sympy import *
from scipy.spatial import Delaunay
from matplotlib.collections import PolyCollection
def plot_inequalities(inequality1, inequality2, x_min, x_max, y_min, y_max):
x, y = symbols('x y')
try:
inequality1_expr = sympify(inequality1)
inequality2_expr = sympify(inequality2)
except:
print("Error: Incorrect inequality format.")
return
try:
F1 = lambdify((x, y), inequality1_expr, 'numpy')
F2 = lambdify((x, y), inequality2_expr, 'numpy')
except:
print("Error: Failed to compile inequalities.")
return
# Create grid of x and y values
x_vals, y_vals = np.meshgrid(np.linspace(x_min, x_max, 150), np.linspace(y_min, y_max, 400))
# Check inequalities on grid points
indices = np.where((F1(x_vals, y_vals) < 0) & (F2(x_vals, y_vals) > 0))
intersection_points = np.column_stack((x_vals[indices], y_vals[indices]))
# Remove any duplicate points
intersection_points = np.unique(intersection_points, axis=0)
# Delaunay triangulation of intersection points
if len(intersection_points) >= 3:
tri = Delaunay(intersection_points)
# Plot the graph
polys = PolyCollection(intersection_points[tri.simplices], facecolors='none', edgecolors='black')
fig, ax = plt.subplots()
ax.add_collection(polys)
ax.autoscale()
ax.margins(0.1)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_aspect('equal')
plt.show()
print("Enter the lower inequality in the format 'F(x, y) > 0':")
inequality1 = "y - x "
print("Enter the upper inequality in the format 'F(x, y) < 0':")
inequality2 = "y - x**2 "
print("Enter the x interval boundaries in the format 'x_min, x_max':")
x_min, x_max = map(float, "0,4".split(','))
print("Enter the y interval boundaries in the format 'y_min, y_max':")
y_min, y_max = map(float, "0,4".split(','))
plot_inequalities(inequality1, inequality2, x_min, x_max, y_min, y_max)

With this modification, the intersection_points array is first converted to a numpy array and then filtered using the unique function to remove any duplicate points. The resulting intersection_points array is then used to construct the Delaunay triangulation and plot the intersection area of the two inequalities.

P.S. I have hard coded the inequality in the code. You can vary the number of x_vals and y_vals by changing the number of points in np.linspace(x_min, x_max, 150) and np.linspace(y_min, y_max, 400) to see triangulations.