Module pavpen.geometry_calculator.orthonormal_basis_calculator

class pavpen.geometry_calculator.orthonormal_basis_calculator.OrthonormalBasisCalculator[Vector](vector_field_operations: FloatVectorFieldOperations, points: list[Vector], float_tolerance: float = 1e-09)

Bases: Generic

Calculates an orthonormal basis of a space that spans a given set of points

Example:

>>> import math
>>> from pavpen.geometry_calculator import OrthonormalBasisCalculator
>>> from pavpen.geometry_calculator.vector_field_implementations import (
...     TupleFloatVectorFieldOperations,
... )
>>>
>>> OrthonormalBasisCalculator(
...     vector_field_operations=TupleFloatVectorFieldOperations.for_3d(),
...     float_tolerance=1e-8,
...     points=((0, 0, 0), (0, 2, 0), (0, 0, -2)),
... ).calculate().basis_vectors
[(0.0, 1.0, 0.0), (0.0, 0.0, -1.0)]

calculate(*, require_points_are_non_redundant: bool = False) → Self

Calculates, and sets self.basis_vectors: List[Vector]

The values in basis_vectors are orthonormal vectors spanning the space that contains the points passed in during construction. Two non-redundant points define a line, three points define a plane, etc.

Setting require_points_are_non_redundant to True makes it an exception for points to be spanned by less than len(points) - 1 basis vectors. In this case [CalculationPrecisionExceededError] is raised, if two points are too close to each other, or if two different pairs of points define directions that are close to colinear, or if a computation’s maximum tolerance exceeds float_tolerance (specified during object construction) for any other reason.