Mesh Quality Visualization

Visualize element quality metrics to identify problematic areas in an IWFM mesh.

Aspect Ratio Map

Color elements by aspect ratio to find elongated cells:

import matplotlib.pyplot as plt
import numpy as np
from pyiwfm.sample_models import create_sample_mesh
from pyiwfm.core.mesh_quality import compute_mesh_quality
from pyiwfm.visualization.plotting import plot_scalar_field

mesh = create_sample_mesh(nx=12, ny=12, n_subregions=4)
report = compute_mesh_quality(mesh)

aspect_ratios = np.array([eq.aspect_ratio for eq in report.element_qualities])

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 6))

# Spatial map
plot_scalar_field(mesh, aspect_ratios, field_type='cell',
                  ax=ax1, cmap='YlOrRd', show_mesh=True,
                  edge_color='gray', edge_width=0.3)
ax1.set_title(f'Aspect Ratio (mean={report.aspect_ratio_mean:.2f})')
ax1.set_xlabel('X (feet)')
ax1.set_ylabel('Y (feet)')

# Histogram
ax2.hist(aspect_ratios, bins=30, edgecolor='black', alpha=0.7, color='steelblue')
ax2.axvline(5.0, color='red', linestyle='--', linewidth=1.5, label='Threshold (AR=5)')
ax2.set_xlabel('Aspect Ratio')
ax2.set_ylabel('Count')
ax2.set_title('Aspect Ratio Distribution')
ax2.legend()

plt.show()

(Source code)

Skewness Map

Skewness measures deviation from ideal element shape (0 = perfect, 1 = degenerate):

import matplotlib.pyplot as plt
import numpy as np
from pyiwfm.sample_models import create_sample_mesh
from pyiwfm.core.mesh_quality import compute_mesh_quality
from pyiwfm.visualization.plotting import plot_scalar_field

mesh = create_sample_mesh(nx=15, ny=15, n_subregions=4)
report = compute_mesh_quality(mesh)

skewness = np.array([eq.skewness for eq in report.element_qualities])

fig, ax = plot_scalar_field(mesh, skewness, field_type='cell',
                            cmap='RdYlGn_r', show_mesh=True,
                            edge_color='gray', edge_width=0.3)
ax.set_title(f'Element Skewness (mean={report.skewness_mean:.3f})')
ax.set_xlabel('X (feet)')
ax.set_ylabel('Y (feet)')
plt.show()

(Source code)

Minimum Angle Distribution

Elements with very small angles can cause numerical instability:

import matplotlib.pyplot as plt
import numpy as np
from pyiwfm.sample_models import create_sample_mesh
from pyiwfm.core.mesh_quality import compute_mesh_quality

mesh = create_sample_mesh(nx=20, ny=20, n_subregions=4)
report = compute_mesh_quality(mesh)

min_angles = [eq.min_angle for eq in report.element_qualities]
max_angles = [eq.max_angle for eq in report.element_qualities]

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))

ax1.hist(min_angles, bins=30, edgecolor='black', alpha=0.7, color='coral')
ax1.axvline(15.0, color='red', linestyle='--', label='Min threshold (15°)')
ax1.set_xlabel('Minimum Angle (degrees)')
ax1.set_ylabel('Count')
ax1.set_title(f'Minimum Angles (global min={report.min_angle_global:.1f}°)')
ax1.legend()

ax2.hist(max_angles, bins=30, edgecolor='black', alpha=0.7, color='skyblue')
ax2.axvline(165.0, color='red', linestyle='--', label='Max threshold (165°)')
ax2.set_xlabel('Maximum Angle (degrees)')
ax2.set_ylabel('Count')
ax2.set_title(f'Maximum Angles (global max={report.max_angle_global:.1f}°)')
ax2.legend()

plt.show()

(Source code)