""" Samples a point on a 1-sphere (circle), or on a 2-ball (disk, i.e. circle + interior space) """
from typing import Union, List, Optional
import mathutils
import numpy as np
from mathutils import Vector
[docs]
def disk(center: Union[Vector, np.ndarray, List[float]], radius: float,
rotation: Optional[Union[Vector, np.ndarray, List[float]]] = None,
sample_from: str = "disk", start_angle: float = 0, end_angle: float = 180) -> np.ndarray:
""" Samples a point on a 1-sphere (circle), or on a 2-ball (disk, i.e. circle + interior space), or on an arc/sector
with an inner angle less or equal than 180 degrees. Returns a 3d mathutils.Vector sampled point.
Example 1: Sample a point from a 1-sphere.
.. code-block:: python
Disk.sample(
center=[0, 0, 4],
radius=7,
sample_from="circle"
)
Example 2: Sample a point from a sector.
.. code-block:: python
Disk.sample(
center=[0, 0, 4],
radius=7,
sample_from="sector",
start_angle=0,
end_angle=90
)
:param center: Center (in 3d space) of a 2d geometrical shape to sample from.
:param radius: The radius of the disk.
:param rotation: List of three (XYZ) Euler angles that represent the rotation of the 2d geometrical structure
used for sampling in 3d space.
:param sample_from: Mode of sampling. Defines the geometrical structure used for sampling, i.e. the shape to
sample from.
:param start_angle: Start angle in degrees that is used to define a sector/arc to sample from. Must be smaller than
end_angle. Arc's/sector's inner angle (between start and end) must be less or equal than
180 degrees. Angle increases in the counterclockwise direction from the positive direction
of X axis.
:param end_angle: End angle in degrees that is used to define a sector/arc to sample from. Must be bigger than
start_angle. Arc's/sector's inner angle (between start and end) must be less or equal
than 180 degrees. Angle increases in the counterclockwise direction from the positive
direction of X axis.
:return: A random point sampled point on a circle/disk/arc/sector.
"""
if rotation is None:
rotation = [0, 0, 0]
# check if the mode/sampling structure is supported
if sample_from not in ["disk", "circle", "sector", "arc"]:
raise Exception("Unknown mode of operation: " + sample_from)
# if mode is sampling from sector or arc
if sample_from in ["arc", "sector"]:
# check if start and end angles comply to boundaries
if not all([start_angle < end_angle, abs(start_angle - end_angle) <= 180]):
raise Exception("Sector's/arch's start and end points are defined wrong! Boundaries to comply with:"
"1. start_angle < end_angle; 2. abs(start_angle - end_angle) <= 180.")
# transform to 2d vectors
start_vec = [np.cos(np.deg2rad(start_angle)), np.sin(np.deg2rad(start_angle))]
end_vec = [np.cos(np.deg2rad(end_angle)), np.sin(np.deg2rad(end_angle))]
# if sampling from the circle or arc set magnitude to radius, if not - to the scaled radius
if sample_from.lower() in ["circle", "arc"]:
magnitude = radius
elif sample_from.lower() in ["disk", "sector"]:
magnitude = radius * np.sqrt(np.random.uniform())
else:
raise Exception("Unknown mode of operation: " + sample_from)
sampled_point = _Disk.sample_point(magnitude)
# sample a point until it falls into the defined sector/arc
if sample_from in ["arc", "sector"]:
while not all([not _Disk.is_clockwise(start_vec, sampled_point), _Disk.is_clockwise(end_vec, sampled_point)]):
sampled_point = _Disk.sample_point(magnitude)
# get rotation
rot_mat = mathutils.Euler(rotation, 'XYZ').to_matrix()
# apply rotation and add center
location = np.array(rot_mat) @ sampled_point + np.array(center)
return location
[docs]
class _Disk:
[docs]
@staticmethod
def sample_point(magnitude: float) -> np.ndarray:
""" Samples a 3d point from a two-dimensional normal distribution with the third dim equal to 0.
:param magnitude: Scaling factor of a radius.
:return: Sampled 3d point. Type: numpy.array.
"""
direction = np.random.normal(loc=0.0, scale=1.0, size=2)
if np.count_nonzero(direction) == 0:
direction[0] = 1e-5
norm = np.sqrt(direction.dot(direction))
sampled_point = np.append(list(map(lambda x: magnitude * x / norm, direction)), 0)
return sampled_point
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@staticmethod
def is_clockwise(rel_point: Union[Vector, np.ndarray, List[float]],
sampled_point: Union[Vector, np.ndarray, List[float]]) -> bool:
""" Checks if the sampled_point is in the clockwise direction in relation to the rel_point.
:param rel_point: Point relative to which the test is performed.
:param sampled_point: Point for which test is performed.
:return: True if the sampled_point lies in the clockwise direction in relation to the rel_point, False if not.
"""
return (-rel_point[0] * sampled_point[1] + rel_point[1] * sampled_point[0]) > 0