line_triangle_intersection

regridding.geometry.line_triangle_intersection(line, tuv)

Compute the 3D point where a line intersects a triangle using the Parametric form described in the Line-plane intersection Wikipedia article.

Parameters:

• line (tuple[tuple[float, float, float], tuple[float, float, float]]) – Two 3D points representing a line segment.

• tuv (tuple[float, float, float]) – Intersection parameters computed using line_triangle_intersection_parameters().

Return type:

tuple[float, float, float]

See also

line_triangle_intersection_parameters()

the function used to compute tuv.

line_intersects_triangle()

A function which can be used to check if the intersection exists.

Examples

Compute the intercept between a line and a triangle and plot the result.

import numpy as np
import matplotlib.pyplot as plt
import regridding

# Define a line segment
line = (
    (1, 1, -1),
    (-1, -1, 1),
)

# Define a triangle
triangle = (
    (0, 1, 1),
    (1, -1, -1),
    (-1, -1, -1),
)

# Compute the intercept parameters between the line and triangle
tuv = regridding.geometry.line_triangle_intersection_parameters(
    line=line,
    triangle=triangle,
)

# Compute the actual intercept using the parameters
intercept = regridding.geometry.line_triangle_intersection(
    line=line,
    tuv=tuv,
)

# Plot the result
fig, ax = plt.subplots(subplot_kw=dict(projection="3d"))
ax.plot(
    *np.array(line).T
);
ax.plot(
    *np.array(triangle).T.take(np.arange(-1, 3), axis=1)
);
ax.scatter(
    *intercept
);