"""
Geometry Primitives
===================
Defines various geometry primitives and their generation methods:
- :attr:`colour.geometry.MAPPING_PLANE_TO_AXIS`
- :func:`colour.geometry.primitive_grid`
- :func:`colour.geometry.primitive_cube`
- :func:`colour.PRIMITIVE_METHODS`
- :func:`colour.primitive`
References
----------
- :cite:`Cabello2015` : Cabello, R. (n.d.). PlaneGeometry.js. Retrieved May
12, 2015, from
https://github.com/mrdoob/three.js/blob/dev/src/geometries/PlaneGeometry.js
"""
from __future__ import annotations
import numpy as np
from colour.constants import DEFAULT_INT_DTYPE, DEFAULT_FLOAT_DTYPE
from colour.hints import (
Any,
DTypeFloating,
DTypeInteger,
Floating,
Integer,
Literal,
NDArray,
Optional,
Tuple,
Type,
Union,
cast,
)
from colour.utilities import (
CaseInsensitiveMapping,
as_int_array,
filter_kwargs,
ones,
optional,
zeros,
validate_method,
)
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"MAPPING_PLANE_TO_AXIS",
"primitive_grid",
"primitive_cube",
"PRIMITIVE_METHODS",
"primitive",
]
MAPPING_PLANE_TO_AXIS: CaseInsensitiveMapping = CaseInsensitiveMapping(
{
"yz": "+x",
"zy": "-x",
"xz": "+y",
"zx": "-y",
"xy": "+z",
"yx": "-z",
}
)
MAPPING_PLANE_TO_AXIS.__doc__ = """Plane to axis mapping."""
[docs]def primitive_grid(
width: Floating = 1,
height: Floating = 1,
width_segments: Integer = 1,
height_segments: Integer = 1,
axis: Literal[
"-x", "+x", "-y", "+y", "-z", "+z", "xy", "xz", "yz", "yx", "zx", "zy"
] = "+z",
dtype_vertices: Optional[Type[DTypeFloating]] = None,
dtype_indexes: Optional[Type[DTypeInteger]] = None,
) -> Tuple[NDArray, NDArray, NDArray]:
"""
Generate vertices and indexes for a filled and outlined grid primitive.
Parameters
----------
width
Grid width.
height
Grid height.
width_segments
Grid segments count along the width.
height_segments
Grid segments count along the height.
axis
Axis the primitive will be normal to, or plane the primitive will be
co-planar with.
dtype_vertices
:class:`numpy.dtype` to use for the grid vertices, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_FLOAT_DTYPE` attribute.
dtype_indexes
:class:`numpy.dtype` to use for the grid indexes, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_INT_DTYPE` attribute.
Returns
-------
:class:`tuple`
Tuple of grid vertices, face indexes to produce a filled grid and
outline indexes to produce an outline of the faces of the grid.
References
----------
:cite:`Cabello2015`
Examples
--------
>>> vertices, faces, outline = primitive_grid()
>>> print(vertices)
[([-0.5, 0.5, 0. ], [ 0., 1.], [ 0., 0., 1.], [ 0., 1., 0., 1.])
([ 0.5, 0.5, 0. ], [ 1., 1.], [ 0., 0., 1.], [ 1., 1., 0., 1.])
([-0.5, -0.5, 0. ], [ 0., 0.], [ 0., 0., 1.], [ 0., 0., 0., 1.])
([ 0.5, -0.5, 0. ], [ 1., 0.], [ 0., 0., 1.], [ 1., 0., 0., 1.])]
>>> print(faces)
[[0 2 1]
[2 3 1]]
>>> print(outline)
[[0 2]
[2 3]
[3 1]
[1 0]]
"""
axis = MAPPING_PLANE_TO_AXIS.get(axis, axis).lower()
dtype_vertices = cast(
Type[DTypeFloating], optional(dtype_vertices, DEFAULT_FLOAT_DTYPE)
)
dtype_indexes = cast(
Type[DTypeInteger], optional(dtype_indexes, DEFAULT_INT_DTYPE)
)
x_grid = width_segments
y_grid = height_segments
x_grid1 = int(x_grid + 1)
y_grid1 = int(y_grid + 1)
# Positions, normals and uvs.
positions = zeros(x_grid1 * y_grid1 * 3)
normals = zeros(x_grid1 * y_grid1 * 3)
uvs = zeros(x_grid1 * y_grid1 * 2)
y = np.arange(y_grid1) * height / y_grid - height / 2
x = np.arange(x_grid1) * width / x_grid - width / 2
positions[::3] = np.tile(x, y_grid1)
positions[1::3] = -np.repeat(y, x_grid1)
normals[2::3] = 1
uvs[::2] = np.tile(np.arange(x_grid1) / x_grid, y_grid1)
uvs[1::2] = np.repeat(1 - np.arange(y_grid1) / y_grid, x_grid1)
# Faces and outline.
faces_indexes = []
outline_indexes = []
for i_y in range(y_grid):
for i_x in range(x_grid):
a = i_x + x_grid1 * i_y
b = i_x + x_grid1 * (i_y + 1)
c = (i_x + 1) + x_grid1 * (i_y + 1)
d = (i_x + 1) + x_grid1 * i_y
faces_indexes.extend([(a, b, d), (b, c, d)])
outline_indexes.extend([(a, b), (b, c), (c, d), (d, a)])
faces = np.reshape(as_int_array(faces_indexes, dtype_indexes), (-1, 3))
outline = np.reshape(as_int_array(outline_indexes, dtype_indexes), (-1, 2))
positions = np.reshape(positions, (-1, 3))
uvs = np.reshape(uvs, (-1, 2))
normals = np.reshape(normals, (-1, 3))
if axis in ("-x", "+x"):
shift, zero_axis = 1, 0
elif axis in ("-y", "+y"):
shift, zero_axis = -1, 1
elif axis in ("-z", "+z"):
shift, zero_axis = 0, 2
sign = -1 if "-" in axis else 1
positions = np.roll(positions, shift, -1)
normals = np.roll(normals, shift, -1) * sign
vertex_colours = np.ravel(positions)
vertex_colours = np.hstack(
[
np.reshape(
np.interp(
vertex_colours,
(np.min(vertex_colours), np.max(vertex_colours)),
(0, 1),
),
positions.shape,
),
ones((positions.shape[0], 1)),
]
)
vertex_colours[..., zero_axis] = 0
vertices = zeros(
positions.shape[0],
[
("position", dtype_vertices, 3),
("uv", dtype_vertices, 2),
("normal", dtype_vertices, 3),
("colour", dtype_vertices, 4),
], # type: ignore[arg-type]
)
vertices["position"] = positions
vertices["uv"] = uvs
vertices["normal"] = normals
vertices["colour"] = vertex_colours
return vertices, faces, outline
[docs]def primitive_cube(
width: Floating = 1,
height: Floating = 1,
depth: Floating = 1,
width_segments: Integer = 1,
height_segments: Integer = 1,
depth_segments: Integer = 1,
planes: Optional[
Literal[
"-x",
"+x",
"-y",
"+y",
"-z",
"+z",
"xy",
"xz",
"yz",
"yx",
"zx",
"zy",
]
] = None,
dtype_vertices: Optional[Type[DTypeFloating]] = None,
dtype_indexes: Optional[Type[DTypeInteger]] = None,
) -> Tuple[NDArray, NDArray, NDArray]:
"""
Generate vertices and indexes for a filled and outlined cube primitive.
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.
planes
Grid primitives to include in the cube construction.
dtype_vertices
:class:`numpy.dtype` to use for the grid vertices, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_FLOAT_DTYPE` attribute.
dtype_indexes
:class:`numpy.dtype` to use for the grid indexes, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_INT_DTYPE` attribute.
Returns
-------
:class:`tuple`
Tuple of cube vertices, face indexes to produce a filled cube and
outline indexes to produce an outline of the faces of the cube.
Examples
--------
>>> vertices, faces, outline = primitive_cube()
>>> print(vertices)
[([-0.5, 0.5, -0.5], [ 0., 1.], [-0., -0., -1.], [ 0., 1., 0., 1.])
([ 0.5, 0.5, -0.5], [ 1., 1.], [-0., -0., -1.], [ 1., 1., 0., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-0., -0., -1.], [ 0., 0., 0., 1.])
([ 0.5, -0.5, -0.5], [ 1., 0.], [-0., -0., -1.], [ 1., 0., 0., 1.])
([-0.5, 0.5, 0.5], [ 0., 1.], [ 0., 0., 1.], [ 0., 1., 1., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 0., 0., 1.], [ 1., 1., 1., 1.])
([-0.5, -0.5, 0.5], [ 0., 0.], [ 0., 0., 1.], [ 0., 0., 1., 1.])
([ 0.5, -0.5, 0.5], [ 1., 0.], [ 0., 0., 1.], [ 1., 0., 1., 1.])
([ 0.5, -0.5, -0.5], [ 0., 1.], [-0., -1., -0.], [ 1., 0., 0., 1.])
([ 0.5, -0.5, 0.5], [ 1., 1.], [-0., -1., -0.], [ 1., 0., 1., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-0., -1., -0.], [ 0., 0., 0., 1.])
([-0.5, -0.5, 0.5], [ 1., 0.], [-0., -1., -0.], [ 0., 0., 1., 1.])
([ 0.5, 0.5, -0.5], [ 0., 1.], [ 0., 1., 0.], [ 1., 1., 0., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 0., 1., 0.], [ 1., 1., 1., 1.])
([-0.5, 0.5, -0.5], [ 0., 0.], [ 0., 1., 0.], [ 0., 1., 0., 1.])
([-0.5, 0.5, 0.5], [ 1., 0.], [ 0., 1., 0.], [ 0., 1., 1., 1.])
([-0.5, -0.5, 0.5], [ 0., 1.], [-1., -0., -0.], [ 0., 0., 1., 1.])
([-0.5, 0.5, 0.5], [ 1., 1.], [-1., -0., -0.], [ 0., 1., 1., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-1., -0., -0.], [ 0., 0., 0., 1.])
([-0.5, 0.5, -0.5], [ 1., 0.], [-1., -0., -0.], [ 0., 1., 0., 1.])
([ 0.5, -0.5, 0.5], [ 0., 1.], [ 1., 0., 0.], [ 1., 0., 1., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 1., 0., 0.], [ 1., 1., 1., 1.])
([ 0.5, -0.5, -0.5], [ 0., 0.], [ 1., 0., 0.], [ 1., 0., 0., 1.])
([ 0.5, 0.5, -0.5], [ 1., 0.], [ 1., 0., 0.], [ 1., 1., 0., 1.])]
>>> print(faces)
[[ 1 2 0]
[ 1 3 2]
[ 4 6 5]
[ 6 7 5]
[ 9 10 8]
[ 9 11 10]
[12 14 13]
[14 15 13]
[17 18 16]
[17 19 18]
[20 22 21]
[22 23 21]]
>>> print(outline)
[[ 0 2]
[ 2 3]
[ 3 1]
[ 1 0]
[ 4 6]
[ 6 7]
[ 7 5]
[ 5 4]
[ 8 10]
[10 11]
[11 9]
[ 9 8]
[12 14]
[14 15]
[15 13]
[13 12]
[16 18]
[18 19]
[19 17]
[17 16]
[20 22]
[22 23]
[23 21]
[21 20]]
"""
axis = (
sorted(list(MAPPING_PLANE_TO_AXIS.values()))
if planes is None
else [
MAPPING_PLANE_TO_AXIS.get(plane, plane).lower() for plane in planes
]
)
dtype_vertices = cast(
Type[DTypeFloating], optional(dtype_vertices, DEFAULT_FLOAT_DTYPE)
)
dtype_indexes = cast(
Type[DTypeInteger], optional(dtype_indexes, DEFAULT_INT_DTYPE)
)
w_s, h_s, d_s = width_segments, height_segments, depth_segments
planes_p = []
if "-z" in axis:
planes_p.append(list(primitive_grid(width, depth, w_s, d_s, "-z")))
planes_p[-1][0]["position"][..., 2] -= height / 2
planes_p[-1][1] = np.fliplr(planes_p[-1][1])
if "+z" in axis:
planes_p.append(list(primitive_grid(width, depth, w_s, d_s, "+z")))
planes_p[-1][0]["position"][..., 2] += height / 2
if "-y" in axis:
planes_p.append(list(primitive_grid(height, width, h_s, w_s, "-y")))
planes_p[-1][0]["position"][..., 1] -= depth / 2
planes_p[-1][1] = np.fliplr(planes_p[-1][1])
if "+y" in axis:
planes_p.append(list(primitive_grid(height, width, h_s, w_s, "+y")))
planes_p[-1][0]["position"][..., 1] += depth / 2
if "-x" in axis:
planes_p.append(list(primitive_grid(depth, height, d_s, h_s, "-x")))
planes_p[-1][0]["position"][..., 0] -= width / 2
planes_p[-1][1] = np.fliplr(planes_p[-1][1])
if "+x" in axis:
planes_p.append(list(primitive_grid(depth, height, d_s, h_s, "+x")))
planes_p[-1][0]["position"][..., 0] += width / 2
positions = zeros((0, 3))
uvs = zeros((0, 2))
normals = zeros((0, 3))
faces = zeros((0, 3), dtype=dtype_indexes)
outline = zeros((0, 2), dtype=dtype_indexes)
offset = 0
for vertices_p, faces_p, outline_p in planes_p:
positions = np.vstack([positions, vertices_p["position"]])
uvs = np.vstack([uvs, vertices_p["uv"]])
normals = np.vstack([normals, vertices_p["normal"]])
faces = np.vstack([faces, faces_p + offset])
outline = np.vstack([outline, outline_p + offset])
offset += vertices_p["position"].shape[0]
vertices = zeros(
positions.shape[0],
[
("position", dtype_vertices, 3),
("uv", dtype_vertices, 2),
("normal", dtype_vertices, 3),
("colour", dtype_vertices, 4),
], # type: ignore[arg-type]
)
vertex_colours = np.ravel(positions)
vertex_colours = np.hstack(
[
np.reshape(
np.interp(
vertex_colours,
(np.min(vertex_colours), np.max(vertex_colours)),
(0, 1),
),
positions.shape,
),
ones((positions.shape[0], 1)),
]
)
vertices["position"] = positions
vertices["uv"] = uvs
vertices["normal"] = normals
vertices["colour"] = vertex_colours
return vertices, faces, outline
PRIMITIVE_METHODS: CaseInsensitiveMapping = CaseInsensitiveMapping(
{
"Grid": primitive_grid,
"Cube": primitive_cube,
}
)
PRIMITIVE_METHODS.__doc__ = """
Supported geometry primitive generation methods.
"""
[docs]def primitive(
method: Union[Literal["Cube", "Grid"], str] = "Cube", **kwargs: Any
) -> Tuple[NDArray, NDArray, NDArray]:
"""
Return a geometry primitive using given method.
Parameters
----------
method
Generation method.
Other Parameters
----------------
axis
{:func:`colour.geometry.primitive_grid`},
Axis the primitive will be normal to, or plane the primitive will be
co-planar with.
depth
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive depth.
depth_segments
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive segments count along the depth.
dtype_indexes
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
:class:`numpy.dtype` to use for the grid indexes, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_INT_DTYPE` attribute.
dtype_vertices
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
:class:`numpy.dtype` to use for the grid vertices, default to
the :class:`numpy.dtype` defined by the
:attr:`colour.constant.DEFAULT_FLOAT_DTYPE` attribute.
height
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive height.
planes
{:func:`colour.geometry.primitive_cube`},
Included grid primitives in the cube construction.
width
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive width.
width_segments
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive segments count along the width.
height_segments
{:func:`colour.geometry.primitive_grid`,
:func:`colour.geometry.primitive_cube`},
Primitive segments count along the height.
Returns
-------
:class:`tuple`
Tuple of primitive vertices, face indexes to produce a filled primitive
and outline indexes to produce an outline of the faces of the
primitive.
References
----------
:cite:`Cabello2015`
Examples
--------
>>> vertices, faces, outline = primitive()
>>> print(vertices)
[([-0.5, 0.5, -0.5], [ 0., 1.], [-0., -0., -1.], [ 0., 1., 0., 1.])
([ 0.5, 0.5, -0.5], [ 1., 1.], [-0., -0., -1.], [ 1., 1., 0., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-0., -0., -1.], [ 0., 0., 0., 1.])
([ 0.5, -0.5, -0.5], [ 1., 0.], [-0., -0., -1.], [ 1., 0., 0., 1.])
([-0.5, 0.5, 0.5], [ 0., 1.], [ 0., 0., 1.], [ 0., 1., 1., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 0., 0., 1.], [ 1., 1., 1., 1.])
([-0.5, -0.5, 0.5], [ 0., 0.], [ 0., 0., 1.], [ 0., 0., 1., 1.])
([ 0.5, -0.5, 0.5], [ 1., 0.], [ 0., 0., 1.], [ 1., 0., 1., 1.])
([ 0.5, -0.5, -0.5], [ 0., 1.], [-0., -1., -0.], [ 1., 0., 0., 1.])
([ 0.5, -0.5, 0.5], [ 1., 1.], [-0., -1., -0.], [ 1., 0., 1., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-0., -1., -0.], [ 0., 0., 0., 1.])
([-0.5, -0.5, 0.5], [ 1., 0.], [-0., -1., -0.], [ 0., 0., 1., 1.])
([ 0.5, 0.5, -0.5], [ 0., 1.], [ 0., 1., 0.], [ 1., 1., 0., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 0., 1., 0.], [ 1., 1., 1., 1.])
([-0.5, 0.5, -0.5], [ 0., 0.], [ 0., 1., 0.], [ 0., 1., 0., 1.])
([-0.5, 0.5, 0.5], [ 1., 0.], [ 0., 1., 0.], [ 0., 1., 1., 1.])
([-0.5, -0.5, 0.5], [ 0., 1.], [-1., -0., -0.], [ 0., 0., 1., 1.])
([-0.5, 0.5, 0.5], [ 1., 1.], [-1., -0., -0.], [ 0., 1., 1., 1.])
([-0.5, -0.5, -0.5], [ 0., 0.], [-1., -0., -0.], [ 0., 0., 0., 1.])
([-0.5, 0.5, -0.5], [ 1., 0.], [-1., -0., -0.], [ 0., 1., 0., 1.])
([ 0.5, -0.5, 0.5], [ 0., 1.], [ 1., 0., 0.], [ 1., 0., 1., 1.])
([ 0.5, 0.5, 0.5], [ 1., 1.], [ 1., 0., 0.], [ 1., 1., 1., 1.])
([ 0.5, -0.5, -0.5], [ 0., 0.], [ 1., 0., 0.], [ 1., 0., 0., 1.])
([ 0.5, 0.5, -0.5], [ 1., 0.], [ 1., 0., 0.], [ 1., 1., 0., 1.])]
>>> print(faces)
[[ 1 2 0]
[ 1 3 2]
[ 4 6 5]
[ 6 7 5]
[ 9 10 8]
[ 9 11 10]
[12 14 13]
[14 15 13]
[17 18 16]
[17 19 18]
[20 22 21]
[22 23 21]]
>>> print(outline)
[[ 0 2]
[ 2 3]
[ 3 1]
[ 1 0]
[ 4 6]
[ 6 7]
[ 7 5]
[ 5 4]
[ 8 10]
[10 11]
[11 9]
[ 9 8]
[12 14]
[14 15]
[15 13]
[13 12]
[16 18]
[18 19]
[19 17]
[17 16]
[20 22]
[22 23]
[23 21]
[21 20]]
>>> vertices, faces, outline = primitive('Grid')
>>> print(vertices)
[([-0.5, 0.5, 0. ], [ 0., 1.], [ 0., 0., 1.], [ 0., 1., 0., 1.])
([ 0.5, 0.5, 0. ], [ 1., 1.], [ 0., 0., 1.], [ 1., 1., 0., 1.])
([-0.5, -0.5, 0. ], [ 0., 0.], [ 0., 0., 1.], [ 0., 0., 0., 1.])
([ 0.5, -0.5, 0. ], [ 1., 0.], [ 0., 0., 1.], [ 1., 0., 0., 1.])]
>>> print(faces)
[[0 2 1]
[2 3 1]]
>>> print(outline)
[[0 2]
[2 3]
[3 1]
[1 0]]
"""
method = validate_method(method, PRIMITIVE_METHODS)
function = PRIMITIVE_METHODS[method]
return function(**filter_kwargs(function, **kwargs))