# Source code for pyleecan.Functions.Geometry.inter_line_line

```# -*- coding: utf-8 -*-

[docs]def inter_line_line(Z1, Z2, Z3, Z4):
"""INTER_LINE_LINE find the intersection between two lines defined by two
complex

Parameters
----------
Z1 : complex
Complex coordinate of a point on the first line
Z2 : complex
Complex coordinate of another point on the first line
Z3 : complex
Complex coordinate of a point on the second line
Z4 : complex
Complex coordinate of another point on the second line

Returns
-------
Zlist: list
List of the complex coordinates of the intersection
return [Z1, Z2] if the 4 points are aligned
"""

# Check if the points are aligned
Z12 = Z1 - Z2
Z13 = Z1 - Z3
Z14 = Z1 - Z4
if (
Z12.real * Z13.imag - Z12.imag * Z13.real == 0
and Z12.real * Z14.imag - Z12.imag * Z14.real == 0
):
return [Z1, Z2]

# Compute the line equation
(A1, B1, C1) = find_line_eq(Z1, Z2)
(A2, B2, C2) = find_line_eq(Z3, Z4)
# Compute the intersection
D = A1 * B2 - B1 * A2
Dx = C1 * B2 - B1 * C2
Dy = A1 * C2 - C1 * A2
if D != 0:
x = Dx / D
y = Dy / D
return [x + 1j * y]
else:
return []

[docs]def find_line_eq(Z1, Z2):
"""Find the line equation (Ax+By=C)

Parameters
----------
Z1 : complex
Complex coordinate of a point on the line
Z2 : complex
Complex coordinate of another point on the line

Returns
-------
A, B, C : (float, float, float)
Line equation parameters
"""
A = Z1.imag - Z2.imag
B = Z2.real - Z1.real
C = Z1.real * Z2.imag - Z2.real * Z1.imag
return (A, B, -C)
```