geoclide.mathope module#

Basic mathematical utilities.

This module gathers the scalar/array helper functions used by the geoclide shapes: clamping of a value into a range, solving of quadratic equations, and the gamma terms bounding the floating-point rounding errors (in simple and double precision) used by the ray-shape intersection tests.

geoclide.mathope.clamp(val: float, val_min: float, val_max: float) → float[source]#

Clamps val into the range [val_min, val_max]

Parameters:

valfloat: The scalar to be clamped
val_minfloat: The minimum value
val_maxfloat: The maximum value

Returns:

float: The result of the clamp

Examples

>>> import geoclide as gc
>>> gc.clamp(4, val_min=5, val_max=11)
5

geoclide.mathope.quadratic(a: ndarray, b: ndarray, c: ndarray) → tuple[ndarray, ndarray, ndarray][source]#

geoclide.mathope.quadratic(a: float, b: float, c: float) → tuple[bool, float | None, float | None]

Resolve the quadratic polynomial: ax**2 + bx + c

where x is the quadratic polynomial variable and a, b and c the coefficients

Parameters:

afloat or ndarray: The first coefficient(s) of the quadratic polynomial. In case of an ndarray, it must be 1-D
bfloat or ndarray: The second coefficient(s) of the quadratic polynomial. In case of an ndarray, it must be 1-D
cfloat or ndarray: The third coefficient(s) of the quadratic polynomial. In case of an ndarray, it must be 1-D

Returns:

bbool or ndarray: If the quadratic can be solved return True, else False. In case of an ndarray, it is a 1-D ndarray of booleans
x0float or None or ndarray: The first solution(s). In case of an ndarray, it is 1-D
x1float or None or ndarray: The second solution(s). In case of an ndarray, it is 1-D

Notes

If There are 2 solutions x0 < x1. And if there is only one solution x0 = x1.

Examples

>>> import geoclide as gc
>>> a = 2
>>> b = -5
>>> c = 0
>>> gc.quadratic(a, b, c)
(True, 0.0, 2.5)