"""
Geometry Primitive Vertices
===========================
Defines various geometry primitive vertices generation methods:
- :func:`colour.geometry.primitive_vertices_quad_mpl`
- :func:`colour.geometry.primitive_vertices_grid_mpl`
- :func:`colour.geometry.primitive_vertices_cube_mpl`
- :func:`colour.geometry.primitive_vertices_sphere`
- :func:`colour.PRIMITIVE_VERTICES_METHODS`
- :func:`colour.primitive_vertices`
"""
from __future__ import annotations
import numpy as np
from colour.algebra import spherical_to_cartesian
from colour.geometry import MAPPING_PLANE_TO_AXIS
from colour.hints import Any, ArrayLike, Literal, NDArrayFloat
from colour.utilities import (
CanonicalMapping,
as_float_array,
filter_kwargs,
full,
ones,
tsplit,
tstack,
validate_method,
zeros,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"primitive_vertices_quad_mpl",
"primitive_vertices_grid_mpl",
"primitive_vertices_cube_mpl",
"primitive_vertices_sphere",
"PRIMITIVE_VERTICES_METHODS",
"primitive_vertices",
]
[docs]
def primitive_vertices_quad_mpl(
width: float = 1,
height: float = 1,
depth: float = 0,
origin: ArrayLike = np.array([0, 0]),
axis: Literal["+z", "+x", "+y", "yz", "xz", "xy"] | str = "+z",
) -> NDArrayFloat:
"""
Return the vertices of a quad primitive for use with *Matplotlib*
:class:`mpl_toolkits.mplot3d.art3d.Poly3DCollection` class.
Parameters
----------
width
Quad width.
height
Quad height.
depth
Quad depth.
origin
Quad origin on the construction plane.
axis
Axis the quad will be normal to, or plane the quad will be co-planar
with.
Returns
-------
:class:`numpy.ndarray`
Quad primitive vertices.
Examples
--------
>>> primitive_vertices_quad_mpl()
array([[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 1., 0.],
[ 0., 1., 0.]])
"""
axis = MAPPING_PLANE_TO_AXIS.get(axis, axis).lower()
axis = validate_method(
axis, ("+x", "+y", "+z"), '"{0}" axis invalid, it must be one of {1}!'
)
u, v = tsplit(origin)
if axis == "+z":
vertices = [
(u, v, depth),
(u + width, v, depth),
(u + width, v + height, depth),
(u, v + height, depth),
]
elif axis == "+y":
vertices = [
(u, depth, v),
(u + width, depth, v),
(u + width, depth, v + height),
(u, depth, v + height),
]
elif axis == "+x":
vertices = [
(depth, u, v),
(depth, u + width, v),
(depth, u + width, v + height),
(depth, u, v + height),
]
return as_float_array(vertices)
[docs]
def primitive_vertices_grid_mpl(
width: float = 1,
height: float = 1,
depth: float = 0,
width_segments: int = 1,
height_segments: int = 1,
origin: ArrayLike = np.array([0, 0]),
axis: Literal["+z", "+x", "+y", "yz", "xz", "xy"] | str = "+z",
) -> NDArrayFloat:
"""
Return the vertices of a grid primitive made of quad primitives for use
with *Matplotlib* :class:`mpl_toolkits.mplot3d.art3d.Poly3DCollection`
class.
Parameters
----------
width
Grid width.
height
Grid height.
depth
Grid depth.
width_segments:
Grid width segments, quad primitive counts along the width.
height_segments:
Grid height segments, quad primitive counts along the height.
origin
Grid origin on the construction plane.
axis
Axis the grid will be normal to, or plane the grid will be co-planar
with.
Returns
-------
:class:`numpy.ndarray`
Grid primitive vertices.
Examples
--------
>>> primitive_vertices_grid_mpl(width_segments=2, height_segments=2)
array([[[ 0. , 0. , 0. ],
[ 0.5, 0. , 0. ],
[ 0.5, 0.5, 0. ],
[ 0. , 0.5, 0. ]],
<BLANKLINE>
[[ 0. , 0.5, 0. ],
[ 0.5, 0.5, 0. ],
[ 0.5, 1. , 0. ],
[ 0. , 1. , 0. ]],
<BLANKLINE>
[[ 0.5, 0. , 0. ],
[ 1. , 0. , 0. ],
[ 1. , 0.5, 0. ],
[ 0.5, 0.5, 0. ]],
<BLANKLINE>
[[ 0.5, 0.5, 0. ],
[ 1. , 0.5, 0. ],
[ 1. , 1. , 0. ],
[ 0.5, 1. , 0. ]]])
"""
u, v = tsplit(origin)
w_x, h_y = width / width_segments, height / height_segments
quads = []
for i in range(width_segments):
for j in range(height_segments):
quads.append(
primitive_vertices_quad_mpl(
w_x, h_y, depth, (i * w_x + u, j * h_y + v), axis
)
)
return as_float_array(quads)
[docs]
def primitive_vertices_cube_mpl(
width: float = 1,
height: float = 1,
depth: float = 1,
width_segments: int = 1,
height_segments: int = 1,
depth_segments: int = 1,
origin: ArrayLike = np.array([0, 0, 0]),
planes: (
Literal[
"-x",
"+x",
"-y",
"+y",
"-z",
"+z",
"xy",
"xz",
"yz",
"yx",
"zx",
"zy",
]
| None
) = None,
) -> NDArrayFloat:
"""
Return the vertices of a cube primitive made of grid primitives for use
with *Matplotlib* :class:`mpl_toolkits.mplot3d.art3d.Poly3DCollection`
class.
Parameters
----------
width
Cube width.
height
Cube height.
depth
Cube depth.
width_segments
Cube segments count along the width.
height_segments
Cube segments count along the height.
depth_segments
Cube segments count along the depth.
origin
Cube origin.
planes
Grid primitives to include in the cube construction.
Returns
-------
:class:`numpy.ndarray`
Cube primitive vertices.
Examples
--------
>>> primitive_vertices_cube_mpl()
array([[[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 1., 0.],
[ 0., 1., 0.]],
<BLANKLINE>
[[ 0., 0., 1.],
[ 1., 0., 1.],
[ 1., 1., 1.],
[ 0., 1., 1.]],
<BLANKLINE>
[[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 0., 1.],
[ 0., 0., 1.]],
<BLANKLINE>
[[ 0., 1., 0.],
[ 1., 1., 0.],
[ 1., 1., 1.],
[ 0., 1., 1.]],
<BLANKLINE>
[[ 0., 0., 0.],
[ 0., 1., 0.],
[ 0., 1., 1.],
[ 0., 0., 1.]],
<BLANKLINE>
[[ 1., 0., 0.],
[ 1., 1., 0.],
[ 1., 1., 1.],
[ 1., 0., 1.]]])
"""
axis = (
sorted(MAPPING_PLANE_TO_AXIS.values())
if planes is None
else [MAPPING_PLANE_TO_AXIS.get(plane, plane).lower() for plane in planes]
)
u, v, w = tsplit(origin)
w_s, h_s, d_s = width_segments, height_segments, depth_segments
grids: list = []
if "-z" in axis:
grids.extend(
primitive_vertices_grid_mpl(width, depth, v, w_s, d_s, (u, w), "+z")
)
if "+z" in axis:
grids.extend(
primitive_vertices_grid_mpl(
width, depth, v + height, w_s, d_s, (u, w), "+z"
)
)
if "-y" in axis:
grids.extend(
primitive_vertices_grid_mpl(width, height, w, w_s, h_s, (u, v), "+y")
)
if "+y" in axis:
grids.extend(
primitive_vertices_grid_mpl(
width, height, w + depth, w_s, h_s, (u, v), "+y"
)
)
if "-x" in axis:
grids.extend(
primitive_vertices_grid_mpl(depth, height, u, d_s, h_s, (w, v), "+x")
)
if "+x" in axis:
grids.extend(
primitive_vertices_grid_mpl(
depth, height, u + width, d_s, h_s, (w, v), "+x"
)
)
return as_float_array(grids)
[docs]
def primitive_vertices_sphere(
radius: float = 0.5,
segments: int = 8,
intermediate: bool = False,
origin: ArrayLike = np.array([0, 0, 0]),
axis: Literal["+z", "+x", "+y", "yz", "xz", "xy"] | str = "+z",
) -> NDArrayFloat:
"""
Return the vertices of a latitude-longitude sphere primitive.
Parameters
----------
radius
Sphere radius.
segments
Latitude-longitude segments, if the ``intermediate`` argument is
*True*, then the sphere will have one less segment along its longitude.
intermediate
Whether to generate the sphere vertices at the center of the faces
outlined by the segments of a regular sphere generated without
the ``intermediate`` argument set to *True*. The resulting sphere is
inscribed on the regular sphere faces but possesses the same poles.
origin
Sphere origin on the construction plane.
axis
Axis (or normal of the plane) the poles of the sphere will be aligned
with.
Returns
-------
:class:`numpy.ndarray`
Sphere primitive vertices.
Notes
-----
- The sphere poles have latitude segments count - 1 co-located vertices.
Examples
--------
>>> primitive_vertices_sphere(segments=4) # doctest: +ELLIPSIS
array([[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ -3.5355339...e-01, -4.3297802...e-17, 3.5355339...e-01],
[ -5.0000000...e-01, -6.1232340...e-17, 3.0616170...e-17],
[ -3.5355339...e-01, -4.3297802...e-17, -3.5355339...e-01],
[ -6.1232340...e-17, -7.4987989...e-33, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 2.1648901...e-17, -3.5355339...e-01, 3.5355339...e-01],
[ 3.0616170...e-17, -5.0000000...e-01, 3.0616170...e-17],
[ 2.1648901...e-17, -3.5355339...e-01, -3.5355339...e-01],
[ 3.7493994...e-33, -6.1232340...e-17, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 3.5355339...e-01, 0.0000000...e+00, 3.5355339...e-01],
[ 5.0000000...e-01, 0.0000000...e+00, 3.0616170...e-17],
[ 3.5355339...e-01, 0.0000000...e+00, -3.5355339...e-01],
[ 6.1232340...e-17, 0.0000000...e+00, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 2.1648901...e-17, 3.5355339...e-01, 3.5355339...e-01],
[ 3.0616170...e-17, 5.0000000...e-01, 3.0616170...e-17],
[ 2.1648901...e-17, 3.5355339...e-01, -3.5355339...e-01],
[ 3.7493994...e-33, 6.1232340...e-17, -5.0000000...e-01]]])
"""
origin = as_float_array(origin)
axis = MAPPING_PLANE_TO_AXIS.get(axis, axis).lower()
axis = validate_method(
axis, ("+x", "+y", "+z"), '"{0}" axis invalid, it must be one of {1}!'
)
if not intermediate:
theta = np.tile(
np.radians(np.linspace(0, 180, segments + 1)),
(int(segments) + 1, 1),
)
phi = np.transpose(
np.tile(
np.radians(np.linspace(-180, 180, segments + 1)),
(int(segments) + 1, 1),
)
)
else:
theta = np.tile(
np.radians(np.linspace(0, 180, segments * 2 + 1)[1::2][1:-1]),
(int(segments) + 1, 1),
)
theta = np.hstack(
[
zeros((segments + 1, 1)),
theta,
full((segments + 1, 1), np.pi),
]
)
phi = np.transpose(
np.tile(
np.radians(np.linspace(-180, 180, segments + 1))
+ np.radians(360 / segments / 2),
(int(segments), 1),
)
)
rho = ones(phi.shape) * radius
rho_theta_phi = tstack([rho, theta, phi])
vertices = spherical_to_cartesian(rho_theta_phi)
# Removing extra longitude vertices.
vertices = vertices[:-1, :, :]
if axis == "+z":
pass
elif axis == "+y":
vertices = np.roll(vertices, 2, -1)
elif axis == "+x":
vertices = np.roll(vertices, 1, -1)
vertices += origin
return vertices
PRIMITIVE_VERTICES_METHODS: CanonicalMapping = CanonicalMapping(
{
"Quad MPL": primitive_vertices_quad_mpl,
"Grid MPL": primitive_vertices_grid_mpl,
"Cube MPL": primitive_vertices_cube_mpl,
"Sphere": primitive_vertices_sphere,
}
)
PRIMITIVE_VERTICES_METHODS.__doc__ = """
Supported geometry primitive vertices generation methods.
"""
[docs]
def primitive_vertices(
method: (Literal["Cube MPL", "Quad MPL", "Grid MPL", "Sphere"] | str) = "Cube MPL",
**kwargs: Any,
) -> NDArrayFloat:
"""
Return the vertices of a geometry primitive using given method.
Parameters
----------
method
Vertices generation method.
Other Parameters
----------------
axis
{:func:`colour.geometry.primitive_vertices_quad_mpl`,
:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_sphere`},
**{'+z', '+x', '+y', 'yz', 'xz', 'xy'}**,
Axis the primitive will be normal to, or plane the primitive will be
co-planar with.
depth
{:func:`colour.geometry.primitive_vertices_quad_mpl`,
:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive depth.
depth_segments
{:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive depth segments, quad primitive counts along the depth.
height
{:func:`colour.geometry.primitive_vertices_quad_mpl`,
:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive height.
height_segments
{:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive height segments, quad primitive counts along the height.
intermediate
{:func:`colour.geometry.primitive_vertices_sphere`},
Whether to generate the sphere vertices at the center of the faces
outlined by the segments of a regular sphere generated without
the ``intermediate`` argument set to *True*. The resulting sphere is
inscribed on the regular sphere faces but possesses the same poles.
origin
{:func:`colour.geometry.primitive_vertices_quad_mpl`,
:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`,
:func:`colour.geometry.primitive_vertices_sphere`},
Primitive origin on the construction plane.
planes
{:func:`colour.geometry.primitive_vertices_cube_mpl`},
**{'-x', '+x', '-y', '+y', '-z', '+z',
'xy', 'xz', 'yz', 'yx', 'zx', 'zy'}**,
Included grid primitives in the cube construction.
radius
{:func:`colour.geometry.primitive_vertices_sphere`},
Sphere radius.
segments
{:func:`colour.geometry.primitive_vertices_sphere`},
Latitude-longitude segments, if the ``intermediate`` argument is
*True*, then the sphere will have one less segment along its longitude.
width
{:func:`colour.geometry.primitive_vertices_quad_mpl`,
:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive width.
width_segments
{:func:`colour.geometry.primitive_vertices_grid_mpl`,
:func:`colour.geometry.primitive_vertices_cube_mpl`},
Primitive width segments, quad primitive counts along the width.
Returns
-------
:class:`numpy.ndarray`
Primitive vertices.
Examples
--------
>>> primitive_vertices()
array([[[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 1., 0.],
[ 0., 1., 0.]],
<BLANKLINE>
[[ 0., 0., 1.],
[ 1., 0., 1.],
[ 1., 1., 1.],
[ 0., 1., 1.]],
<BLANKLINE>
[[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 0., 1.],
[ 0., 0., 1.]],
<BLANKLINE>
[[ 0., 1., 0.],
[ 1., 1., 0.],
[ 1., 1., 1.],
[ 0., 1., 1.]],
<BLANKLINE>
[[ 0., 0., 0.],
[ 0., 1., 0.],
[ 0., 1., 1.],
[ 0., 0., 1.]],
<BLANKLINE>
[[ 1., 0., 0.],
[ 1., 1., 0.],
[ 1., 1., 1.],
[ 1., 0., 1.]]])
>>> primitive_vertices("Quad MPL")
array([[ 0., 0., 0.],
[ 1., 0., 0.],
[ 1., 1., 0.],
[ 0., 1., 0.]])
>>> primitive_vertices("Sphere", segments=4) # doctest: +ELLIPSIS
array([[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ -3.5355339...e-01, -4.3297802...e-17, 3.5355339...e-01],
[ -5.0000000...e-01, -6.1232340...e-17, 3.0616170...e-17],
[ -3.5355339...e-01, -4.3297802...e-17, -3.5355339...e-01],
[ -6.1232340...e-17, -7.4987989...e-33, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 2.1648901...e-17, -3.5355339...e-01, 3.5355339...e-01],
[ 3.0616170...e-17, -5.0000000...e-01, 3.0616170...e-17],
[ 2.1648901...e-17, -3.5355339...e-01, -3.5355339...e-01],
[ 3.7493994...e-33, -6.1232340...e-17, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 3.5355339...e-01, 0.0000000...e+00, 3.5355339...e-01],
[ 5.0000000...e-01, 0.0000000...e+00, 3.0616170...e-17],
[ 3.5355339...e-01, 0.0000000...e+00, -3.5355339...e-01],
[ 6.1232340...e-17, 0.0000000...e+00, -5.0000000...e-01]],
<BLANKLINE>
[[ 0.0000000...e+00, 0.0000000...e+00, 5.0000000...e-01],
[ 2.1648901...e-17, 3.5355339...e-01, 3.5355339...e-01],
[ 3.0616170...e-17, 5.0000000...e-01, 3.0616170...e-17],
[ 2.1648901...e-17, 3.5355339...e-01, -3.5355339...e-01],
[ 3.7493994...e-33, 6.1232340...e-17, -5.0000000...e-01]]])
"""
method = validate_method(method, tuple(PRIMITIVE_VERTICES_METHODS))
function = PRIMITIVE_VERTICES_METHODS[method]
return function(**filter_kwargs(function, **kwargs))