pohlke.utils.geometry_math

Contains all usefull mathematical functions for the add-on

Attributes

logger

Functions

calculate_oblique_attributes(→ float)	Calculates the second attribute of an oblique projection (beta or alpha) from the first one (alpha or beta). If the input parameter is alpha, the function returns beta, and vice versa.
calculate_oblique_z_axis(→ float)	Calculate the Z-axis reduction factor of an oblique projection using it alpha parameter
calculate_altitude_with_z_value(→ float)	Calculate the projection's altitude using it Z-axis reduction factor
compute_scales(→ tuple[float, float, float])	Calculate scale factors for given axonometry inclination angles.
tilt(→ tuple[float, float])	Coordinate plane tilt.
get_tilted_angles(→ list[tuple[float]])	Order by coordinate plane is XY, ZY, ZX.
calculate_axonometric_rotation(→ float)	Calculate the rotation of an axonometric projection with its alpha and beta parameters
calculate_axonometric_altitude(beta_rad, alpha_rad)	Calculate the altitude of an axonometric projection with its alpha and beta parameters
normalize_factors(x, y, z)	Normalize axonometric reduction factors so that the largest factor is 1.0

Module Contents

pohlke.utils.geometry_math.logger

pohlke.utils.geometry_math.calculate_oblique_attributes(attribute: float) → float

Calculates the second attribute of an oblique projection (beta or alpha) from the first one (alpha or beta). If the input parameter is alpha, the function returns beta, and vice versa.

Parameters

attributefloat

One of the projection attributes (alpha or beta)

Returns

float

The second attribute depending on the param (alpha if attribue param is beta, and vice versa)

Examples

>>> from math import radians, degrees
>>> from utils.geometry_math import calculate_oblique_attributes
>>> oblique_beta = radians(45)
>>> oblique_alpha = calculate_oblique_attributes(oblique_beta)
>>> print(degrees(oblique_alpha))
45

>>> oblique_alpha = radians(30)
>>> oblique_beta = calculate_oblique_attributes(oblique_alpha)
>>> print(degrees(oblique_beta))
60

pohlke.utils.geometry_math.calculate_oblique_z_axis(alpha: float) → float

Calculate the Z-axis reduction factor of an oblique projection using it alpha parameter

Parameters

alphafloat

The alpha parameter of the projection

Returns

float

The Z-axis reduction factor (between 0 and 1)

Examples

>>> from math import radians
>>> from utils.geometry_math import calculate_oblique_z_axis
>>> oblique_alpha = radians(45)
>>> z = calculate_oblique_z_axis(oblique_alpha)
>>> print(z)
1.0

pohlke.utils.geometry_math.calculate_altitude_with_z_value(z_value: float) → float

Calculate the projection’s altitude using it Z-axis reduction factor

Parameters

z_valuefloat

Z-axis reduction factor of the projection (between 0 ans 1)

Returns

float

Altitude of the projection (in radians)

Examples

>>> from math import degrees
>>> from utils.geometry_math import calculate_altitude_with_z_value
>>> z = 1.0
>>> oblique_altitude = calculate_altitude_with_z_value(z)
>>> print(degrees(oblique_altitude))
45

pohlke.utils.geometry_math.compute_scales(beta_rad: float, alpha_rad: float) → tuple[float, float, float]

Calculate scale factors for given axonometry inclination angles.

Source

Lien de référence : <https://axonometry.readthedocs.io/en/beta/>

Parameters

beta_radfloat

The beta angle of the plan (in radians)

alpha_radfloat

The beta angle of the plan (in radians)

Returns

tuple[float, float, float]

Axes scales

Examples

>>> from math import degrees, radians
>>> from utils.geometry_math import compute_scales
>>> # Test with isometric projection
>>> alpha_rad = radians(30)
>>> beta_rad = radians(30)
>>> y, z, x = compute_scales(beta_rad, alpha_rad)
>>> print(x, y, z)
0.82, 0.82, 0.82

pohlke.utils.geometry_math.tilt(angles: tuple[float, float]) → tuple[float, float]

Coordinate plane tilt.

Source

Lien de référence : <https://axonometry.readthedocs.io/en/beta/>

pohlke.utils.geometry_math.get_tilted_angles(beta_rad, alpha_rad) → list[tuple[float]]

Order by coordinate plane is XY, ZY, ZX.

Source

Lien de référence : <https://axonometry.readthedocs.io/en/beta/>

pohlke.utils.geometry_math.calculate_axonometric_rotation(beta_rad: float, alpha_rad: float) → float

Calculate the rotation of an axonometric projection with its alpha and beta parameters

Parameters

beta_radfloat

The beta angle of the plan (in radians)

alpha_radfloat

The alpha angle of the plan (in radians)

Returns

float

The rotation of the projection (in radians)

Examples

>>> from math import radians, degrees
>>> from utils.geometry_math import calculate_axonometric_rotation
>>> alpha_rad = radians(30)
>>> beta_rad = radians(30)
>>> axonometric_rotation = calculate_axonometric_rotation(beta_rad, alpha_rad)
>>> print(degrees(axonometric_rotation))
45

pohlke.utils.geometry_math.calculate_axonometric_altitude(beta_rad, alpha_rad)

Calculate the altitude of an axonometric projection with its alpha and beta parameters

Parameters

beta_radfloat

The beta angle of the plan (in radians)

alpha_radfloat

The alpha angle of the plan (in radians)

Returns

float

The altitude of the projection (in radians)

Examples

>>> from math import radians, degrees
>>> from utils.geometry_math import calculate_axonometric_altitude
>>> alpha_rad = radians(30)
>>> beta_rad = radians(30)
>>> axonometric_rotation = calculate_axonometric_altitude(beta_rad, alpha_rad)
>>> print(degrees(axonometric_rotation))
35.26

pohlke.utils.geometry_math.normalize_factors(x, y, z)

Normalize axonometric reduction factors so that the largest factor is 1.0 and others are scaled proportionally.

Parameters

xfloat

The reduction factor for the X axis.

yfloat

The reduction factor for the Y axis.

zfloat

The reduction factor for the Z axis.

Returns

tuple[float, float, float]

A tuple containing (norm_x, norm_y, norm_z) where the maximum value is 1.0. Returns (0.0, 0.0, 0.0) if all input parameters are zero.

Examples

>>> from utils.geometry_math import normalize_reduction_factors
>>> x, y, z = 10.0, 5.0, 2.0
>>> nx, ny, nz = normalize_reduction_factors(x, y, z)
>>> print(nx, ny, nz)
1.0, 0.5, 0.2

>>> # Case with equal factors
>>> normalize_reduction_factors(0.5, 0.5, 0.5)
(1.0, 1.0, 1.0)