maths.line_intersection

Functions

determinant(→ float)	Calculates the determinant of a 2x2 matrix:
line_coefficients(→ tuple)	Computes the coefficients A, B, C of the line equation Ax + By + C = 0
segment_intersection(→ list[float] | None)	Finds the intersection point of two line segments or lines, if it exists.

Module Contents

maths.line_intersection.determinant(m00: float, m01: float, m10: float, m11: float) → float

Calculates the determinant of a 2x2 matrix:

m00 m01 |

m10 m11 |

Args:

m00 (float): Element in the first row, first column. m01 (float): Element in the first row, second column. m10 (float): Element in the second row, first column. m11 (float): Element in the second row, second column.

Returns:

float: The determinant of the matrix.

Examples:

# Determinant of the identity matrix (should be 1) >>> determinant(1, 0, 0, 1) 1

# Determinant of a matrix with two equal rows (should be 0) >>> determinant(1, 2, 1, 2) 0

# Determinant of a matrix with a negative determinant >>> determinant(1, 2, 3, 4) -2

# Determinant of a matrix with larger numbers >>> determinant(10, 20, 30, 40) -200

maths.line_intersection.line_coefficients(p1: list[float] | tuple, p2: list[float] | tuple) → tuple

Computes the coefficients A, B, C of the line equation Ax + By + C = 0 from two points.

Args:

p1 (List[float] | tuple): First point (x, y). p2 (List[float] | tuple): Second point (x, y).

Returns:

tuple: Coefficients (A, B, C) of the line equation.

Examples:

# Vertical line (x = constant) >>> line_coefficients([1, 0], [1, 2]) (1, 0, 1)

# Horizontal line (y = constant) >>> line_coefficients([0, 1], [2, 1]) (0.0, -1, 1.0)

# Diagonal line (positive slope) >>> line_coefficients([0, 0], [1, 1]) (1.0, -1, 0.0)

# Diagonal line (negative slope) >>> line_coefficients([0, 1], [1, 0]) (-1.0, -1, 1.0)

maths.line_intersection.segment_intersection(v1: list[float] | tuple, v2: list[float] | tuple, v1_prime: list[float] | tuple, v2_prime: list[float] | tuple, as_segments: bool = True) → list[float] | None

Finds the intersection point of two line segments or lines, if it exists.

Args:

v1 (List[float] | tuple): First point of the first segment (x, y). v2 (List[float] | tuple): Second point of the first segment (x, y). v1_prime (List[float] | tuple): First point of the second segment (x, y). v2_prime (List[float] | tuple): Second point of the second segment (x, y). as_segments (bool):

treat the inputs as line segments (True) or as infinite lines (False).

Returns:

List[float] | None:

Returns the intersection point [x, y] if existent, otherwise None.

References:

Cramer’s rule: https://en.wikipedia.org/wiki/Cramer%27s_rule

Examples:

>>> segment_intersection([0, 0], [1, 1], [1, 0], [0, 1])
[0.5, 0.5]

# No intersection >>> segment_intersection([0, 0], [1, 1], [2, 2], [3, 3]) is None True

# Parallel lines >>> segment_intersection([0, 0], [0, 1], [1, 0], [1, 1]) is None True

# Intersecting infinite lines >>> segment_intersection([0, 0], [1, 1], [1, 0], [0, 1], as_segments=False) [0.5, 0.5]

# Parallel infinite lines (ignoring segment boundaries) >>> segment_intersection([0, 0], [1, 1], [2, 2], [3, 3], False) is None True