def tikz_declarations(self):
"""Return the Point declaration."""
if self.name is None:
raise RuntimeError('Point at ({}, {}) has no name (None), '
'cannot create TikZ picture using it.')
return r'\coordinate ({}) at ({},{});'\
.format(self.name,
self.x.rounded(Number('0.001')),
self.y.rounded(Number('0.001')))
def _slope(self, offset=0):
if self.length == 0:
msg = 'Cannot calculate the slope of a zero-length {}.'\
.format(type(self).__name__)
raise ZERO_OBJECTS_ERRORS[type(self).__name__](msg)
theta = Number(
str(math.degrees(math.acos(self.x / self.length))))\
.rounded(Number('0.001'))
return theta if self.y >= 0 else Number(offset) - theta
def __init__(self, *args, allow_zero_length=True):
"""
It's possible to create a Vector giving:
- a Bipoint: Bipoint(A, B)
- a pair of Points: A, B
- its coordinates x, y or x, y, z
"""
if not args or len(args) >= 4:
raise TypeError('Vector() takes one, two or three arguments '
'({} given)'.format(len(args)))
if len(args) == 1:
from mathmakerlib.geometry.bipoint import Bipoint
if not isinstance(args[0], Bipoint):
raise TypeError('a Vector can be created from one Bipoint, '
'found {} instead.'.format(repr(args[0])))
self._x = args[0].Δx
self._y = args[0].Δy
if args[0].three_dimensional:
self._z = args[0].Δz
self._three_dimensional = True
else:
self._z = Number(0)
self._three_dimensional = False
elif len(args) == 2:
# Two Points
if isinstance(args[0], Point) and isinstance(args[1], Point):
self._x = args[1].x - args[0].x
self._y = args[1].y - args[0].y
if args[0].three_dimensional or args[1].three_dimensional:
self._three_dimensional = True
self._z = args[1].z - args[0].z
else:
self._three_dimensional = False
self._z = Number(0)
# Two numbers
elif is_number(args[0]) and is_number(args[1]):
self._three_dimensional = False
self._x = Number(args[0])
self._y = Number(args[1])
self._z = Number(0)
else:
raise TypeError('a Vector can be created from two arguments, '
'either two Points or two numbers. '
'Found {} and {} instead.'.format(
repr(args[0]), repr(args[1])))
elif len(args) == 3:
self._three_dimensional = True
self._x = Number(args[0])
self._y = Number(args[1])
self._z = Number(args[2])
self._length = Number(self.x**2 + self.y**2 + self.z**2).sqrt()
if not allow_zero_length and self.length == 0:
msg = 'Explicitly disallowed creation of a zero-length {}.'\
.format(type(self).__name__)
raise ZERO_OBJECTS_ERRORS[type(self).__name__](msg)
def boundingbox(self, value):
if value is not None:
if not isinstance(value, tuple):
raise TypeError('Expected a tuple, found a {} instead.'.format(
type(value).__name__))
if len(value) != 4:
raise ValueError('Expected a tuple of 4 elements, found {} '
'elements instead.'.format(len(value)))
for v in value:
try:
Number(v)
except (TypeError, InvalidOperation):
raise TypeError('Expected a tuple containing only '
'numbers. Found a {} instead.'.format(
type(v).__name__))
setattr(self, '_boundingbox', tuple(Number(v) for v in value))
def tikz_rightangle_mark(self, winding='anticlockwise'):
if self.decoration is None or not self.mark_right:
return ''
check_winding(winding)
# Decimal numbers in TikZ must be written with a dot as decimal point.
# As of now, there is no reliable way to temporarily change the
# locale to 'C' (or 'en_US'), so here's a little patch that will
# replace possibly other decimal points by a '.'.
theta = str(Bipoint(self.vertex, self.points[0])
.slope.rounded(Number('0.01')).printed)
if (locale.localeconv()['decimal_point'] != '.'
and locale.localeconv()['decimal_point'] in theta):
theta = theta.replace(locale.localeconv()['decimal_point'], '.')
rt = 'cm={{cos({θ}), sin({θ}), -sin({θ}), cos({θ}), ({v})}}' \
.format(θ=theta, v=self.vertex.name)
draw_options = tikz_options_list([self.decoration.thickness,
self.decoration.color,
rt])
if winding == 'anticlockwise':
rightangle_shape = '({R}, 0) -- ({R}, {R}) -- (0, {R})'\
.format(R=self.decoration.radius.uiprinted)
elif winding == 'clockwise':
rightangle_shape = '({R}, 0) -- ({R}, -{R}) -- (0, -{R})'\
.format(R=self.decoration.radius.uiprinted)
return '\draw{} {};'.format(draw_options, rightangle_shape)
def generate_tikz(self, *points_names):
if not len(points_names) == 3:
raise RuntimeError('Three Points\' names must be provided to '
'generate the AngleDecoration. Found {} '
'arguments instead.'.format(len(points_names)))
last_layer = {None: 1, 'single': 1, 'double': 2,
'triple': 3}[self.variety]
pic_attr = self.tikz_attributes(do_label=last_layer == 1)
if pic_attr == '[]':
return ''
required.tikz_library['angles'] = True
deco = ['pic {} {{angle = {}--{}--{}}}'
.format(pic_attr, *points_names)]
if self.variety in ['double', 'triple']:
space_sep = Number('0.16')
deco.append('pic {} {{angle = {}--{}--{}}}'
.format(self.tikz_attributes(
radius_coeff=1 + space_sep,
do_label=last_layer == 2),
*points_names))
if self.variety == 'triple':
deco.append('pic {} {{angle = {}--{}--{}}}'
.format(self.tikz_attributes(
radius_coeff=1 + 2 * space_sep,
do_label=last_layer == 3),
*points_names))
return deco
def tikz_attributes(self, radius_coeff=1, do_label=True):
if not is_number(radius_coeff):
raise TypeError('radius_coeff must be a number, found {} instead.'
.format(type(radius_coeff)))
attributes = []
if do_label and self.label not in [None, 'default']:
required.tikz_library['quotes'] = True
attributes.append('"{}"'.format(self.label))
if self.eccentricity is not None:
attributes.append('angle eccentricity={}'
.format(self.eccentricity))
if self.variety is not None:
if self.do_draw:
attributes.append('draw')
if self.arrow_tips is not None:
attributes.append(self.arrow_tips)
if self.thickness is not None:
attributes.append(self.thickness)
if self.radius is not None:
attributes.append('angle radius = {}'
.format((self.radius * radius_coeff)
.rounded(Number('0.01')).uiprinted))
if self.hatchmark is not None:
attributes.append(self.hatchmark)
required.tikz_library['decorations.markings'] = True
required.tikzset[self.hatchmark + '_hatchmark'] = True
if (self.variety is not None
or (do_label and self.label not in [None, 'default'])):
if self.color is not None:
attributes.append(self.color)
return '[{}]'.format(', '.join(attributes))
def radius(self, value):
from mathmakerlib.calculus.number import Number
if is_number(value):
self._radius = Number(value)
else:
raise TypeError(
'Expected a number as radius. Got {} instead.'.format(
str(type(value))))
def lbl_perimeter(self):
if any([not isinstance(s.label_value, Number) for s in self.sides]):
raise RuntimeError('All labels must have been set as Numbers '
'in order to calculate the perimeter from '
'labels.')
else:
return sum([s.label_value for s in self.sides],
Number(0, unit=self.sides[0].label_value.unit))\
.standardized()
def gap(self, value):
if not (is_number(value) or value is None):
raise TypeError('The gap value must be None or a number. '
'Found {} instead (type: {}).'
.format(repr(value), type(value)))
if value is None:
self._gap = None
else:
self._gap = Number(value)
def radius(self, value):
if is_number(value):
self._radius = Number(value)
elif value is None:
self._radius = None
else:
raise TypeError('Expected a number as radius. Got {} instead.'
.format(str(type(value))))
if hasattr(self, '_eccentricity') and hasattr(self, '_gap'):
self.eccentricity = 'automatic'
def z(self, value):
three_dimensional = True
if value is 'undefined':
value = 0
three_dimensional = False
try:
self._z = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as applicate, found {} '
'instead.'.format(repr(value)))
self._three_dimensional = three_dimensional
def eccentricity(self, value):
if value == 'automatic':
if self.gap is None:
raise ValueError('Cannot calculate the eccentricity if gap '
'is None.')
value = (self.gap / self.radius + 1)\
.rounded(Number('0.01')).standardized()
if not (value is None or is_number(value)):
raise TypeError('The eccentricity of an AngleDecoration must be '
'None or a Number. Found {} instead.'
.format(type(value)))
self._eccentricity = value
def __init__(self, color=None, thickness='thick', label='default',
radius=Number('0.25', unit='cm'), variety='single',
gap=Number('0.4', unit='cm'), eccentricity='automatic',
hatchmark=None, do_draw=True, arrow_tips=None):
self.do_draw = do_draw
self.arrow_tips = arrow_tips
self.color = color
self.thickness = thickness
self.label = label
self.radius = radius
self.gap = gap
if gap is None:
self.gap = None
else:
u = self.radius.unit if isinstance(self.radius, Number) else None
self.gap = Number(gap, unit=u)
# Eccentricity must be set *after* radius, in order to be able to
# calculate a reasonable default eccentricity based on the radius
self.eccentricity = eccentricity
self.variety = variety
self.hatchmark = hatchmark
def __new__(cls,
sign=None,
numerator=None,
denominator=None,
from_decimal=None):
"""
Fraction(5, 8) is equivalent to Fraction('+', 5, 8).
"""
if from_decimal is not None:
f = Number(10)**max(1, from_decimal.fracdigits_nb())
sign = Sign(from_decimal)
numerator = (f * from_decimal).standardized()
denominator = f.standardized()
elif sign in ['+', '-']:
if not (is_number(numerator) and is_number(denominator)):
raise TypeError('Numerator and denominator must be numbers. '
'Got {} and {} instead.'.format(
type(numerator), type(denominator)))
if not (is_integer(numerator) and is_integer(denominator)):
raise TypeError('Numerator and denominator must be integers. '
'Got {} and {} instead.'.format(
numerator, denominator))
else:
if not (is_number(sign) and is_number(numerator)):
raise TypeError('Numerator and denominator must be numbers. '
'Got {} and {} instead.'.format(
type(sign), type(numerator)))
elif not (is_integer(sign) and is_integer(numerator)):
raise TypeError('Numerator and denominator must be integers. '
'Got {} and {} instead.'.format(
sign, numerator))
denominator = numerator
numerator = sign
sign = '+'
# some initialization
self = object.__new__(cls)
self._sign = Sign(sign)
self._numerator = Number(numerator)
self._denominator = Number(denominator)
return self
def tikz_approx_position(slope):
slope %= Number(360)
# Caution: modulo on negative Decimals does not behave as on ints.
# So, it's necessary to add 360 in case of a negative result.
if slope < 0:
slope += 360
if (Decimal('337.5') <= slope <= Decimal('360')
or Decimal('0') <= slope < Decimal('22.5')):
return 'right'
elif Decimal('22.5') <= slope < Decimal('67.5'):
return 'above right'
elif Decimal('67.5') <= slope < Decimal('112.5'):
return 'above'
elif Decimal('112.5') <= slope < Decimal('157.5'):
return 'above left'
elif Decimal('157.5') <= slope < Decimal('202.5'):
return 'left'
elif Decimal('202.5') <= slope < Decimal('247.5'):
return 'below left'
elif Decimal('247.5') <= slope < Decimal('292.5'):
return 'below'
elif Decimal('292.5') <= slope < Decimal('337.5'):
return 'below right'
def point_at(self, position, name='automatic'):
"""
A Point aligned with the Bipoint, at provided position.
The Bipoint's length is the length unit of position.
Hence, position 0 matches points[0], position 1 matches points[1],
position 0.5 matches the midpoint, position 0.75 is three quarters
on the way from points[0] to points[1], position 2 is a Point that
makes points[1] the middle between it and points[0], position -1 makes
points[0] the middle between it and points[1].
:param position: a number
:type position: number
:param name: the name to give to the Point
:type name: str
"""
if not is_number(position):
raise TypeError(
'position must be a number, found {} instead.'.format(
type(position)))
k = Number(position)
if k == 0:
return self.points[0]
elif k == 1:
return self.points[1]
else:
if self.three_dimensional:
zval = (self.points[0].z +
(self.points[1].z - self.points[0].z) * k)
else:
zval = 'undefined'
return Point(
(self.points[0].x + (self.points[1].x - self.points[0].x) * k),
(self.points[0].y + (self.points[1].y - self.points[0].y) * k),
z=zval,
name=name)
def rotate(self, center, angle, axis=None, rename='auto'):
"""
Rotate around center (or axis going through center).
:param center: the center of the rotation
:type center: Point
:param angle: the angle of the rotation
:type angle: a number
:param axis: the axis of the rotation for 3D rotation. If left to None,
the rotation happens around the center, in the plane.
:type axis: Vector
:param rename: if set to 'auto', will name the rotated Point after the
original, adding a ' (like A.rotate(...) creates a Point A'). If set
to None, keep the original name. Otherwise, the provided str will be
used as the rotated Point's name.
:type rename: None or str
:rtype: Point
"""
from mathmakerlib.geometry.vector import Vector
if not isinstance(center, Point):
raise TypeError('Expected a Point as rotation center, got {} '
'instead.'.format(type(center)))
if not is_number(angle):
raise TypeError('Expected a number as rotation angle, got {} '
'instead.'.format(type(angle)))
if not (axis is None or isinstance(axis, Vector)):
raise TypeError('Expected either None or a Vector as axis, '
'found {} instead.'.format(repr(axis)))
Δx = self.x - center.x
Δy = self.y - center.y
Δz = self.z - center.z
cosθ = Number(str(cos(radians(angle))))
sinθ = Number(str(sin(radians(angle))))
if axis is None:
rx = (Δx * cosθ - Δy * sinθ + center.x).rounded(Number('1.000'))
ry = (Δx * sinθ + Δy * cosθ + center.y).rounded(Number('1.000'))
rz = 'undefined'
else:
ux, uy, uz = axis.normalized().coordinates
rotation_matrix = [[
cosθ + (1 - cosθ) * ux**2, ux * uy * (1 - cosθ) - uz * sinθ,
ux * uz * (1 - cosθ) + uy * sinθ
],
[
uy * ux * (1 - cosθ) + uz * sinθ,
cosθ + (1 - cosθ) * uy**2,
uy * uz * (1 - cosθ) - ux * sinθ
],
[
uz * ux * (1 - cosθ) - uy * sinθ,
uz * uy * (1 - cosθ) + ux * sinθ,
cosθ + (1 - cosθ) * uz**2
]]
rx = sum([
rc * coord
for rc, coord in zip(rotation_matrix[0], [Δx, Δy, Δz])
])
ry = sum([
rc * coord
for rc, coord in zip(rotation_matrix[1], [Δx, Δy, Δz])
])
rz = sum([
rc * coord
for rc, coord in zip(rotation_matrix[2], [Δx, Δy, Δz])
])
rx += center.x
ry += center.y
rz += center.z
rx = rx.rounded(Number('1.000'))
ry = ry.rounded(Number('1.000'))
rz = rz.rounded(Number('1.000'))
if rename == 'keep_name':
rname = self.name
elif rename == 'auto':
rname = self.name + "'"
else:
rname = rename
return Point(rx, ry, rz, rname)
def mark_scale(self, value):
check_scale(value, 'LineSegment\'s mark')
self._mark_scale = Number(value)
def __init__(self):
self.DEFAULT_ARMSPOINTS_POSITION = Number('0.8')
def shape_scale(self, value):
check_scale(value, 'Point\'s shape')
self._shape_scale = Number(value)
def x(self, value):
try:
self._x = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as abscissa, found {} '
'instead.'.format(repr(value)))
def y(self, value):
try:
self._y = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as ordinate, found {} '
'instead.'.format(repr(value)))
def __init__(self,
start_vertex=None,
name=None,
base_length=Number('1.5'),
equal_legs_length=Number('1'),
mark_equal_sides=True,
use_mark='||',
draw_vertices=False,
label_vertices=True,
thickness='thick',
color=None,
rotation_angle=0,
winding=None,
sloped_sides_labels=True):
r"""
Initialize Isosceles Triangle
:param start_vertex: the vertex to start to draw the Right Triangle
(default (0; 0))
:type start_vertex: Point
:param name: the name of the Triangle, like ABC.
Can be either None (the names will be automatically created), or a
string of the letters to use to name the vertices. Only single letters
are supported as Points' names so far (at Polygon's creation).
See issue #3.
:type name: None or str
:param base_length: the length of the base of the IsoscelesTriangle,
that will be used to calculate the coordinates of its vertices
:type base_length: a number
:param equal_legs_length: the length of the equal legs of the
IsoscelesTriangle, that will be used to calculate the coordinates of
its vertices
:type equal_legs_length: a number
:param mark_equal_sides: if True (default), all three sides will be
automatically marked with the same symbol.
:type mark_equal_sides: bool
:param draw_vertices: whether to actually draw, or not, the vertices
:type draw_vertices: bool
:param label_vertices: whether to label, or not, the vertices
:type label_vertices: bool
:param thickness: the thickness of the Triangle's sides
:type thickness: str
:param color: the color of the Triangle's sides
:type color: str
:param rotate: the angle of rotation around isobarycenter
:type rotate: int
"""
if start_vertex is None:
start_vertex = Point(0, 0)
self._base_length = Number(base_length)
self._equal_legs_length = Number(equal_legs_length)
v1 = Point(base_length + start_vertex.x, start_vertex.y)
v2 = Point(
base_length / 2,
(equal_legs_length**2 -
Number('0.25') * base_length**2).sqrt().rounded(Number('0.001')) +
start_vertex.y)
if (winding == 'clockwise'
or (winding is None
and config.polygons.DEFAULT_WINDING == 'clockwise')):
start_vertex, v1 = v1, start_vertex
Triangle.__init__(self,
start_vertex,
v1,
v2,
name=name,
draw_vertices=draw_vertices,
label_vertices=label_vertices,
thickness=thickness,
color=color,
rotation_angle=rotation_angle,
winding=winding,
sloped_sides_labels=sloped_sides_labels)
self._type = 'IsoscelesTriangle'
if mark_equal_sides:
self.sides[1].mark = self.sides[2].mark = use_mark
class Point(Drawable, Dimensional):
names_in_use = set()
@classmethod
def automatic_names(cls):
use = Point.names_in_use
names = [
letter for letter in string.ascii_uppercase if letter not in use
][::-1]
if not names:
layer = 1
while not names:
names = [
'{}$_{}$'.format(letter, layer)
for letter in string.ascii_uppercase
if '{}$_{}$'.format(letter, layer) not in use
][::-1]
layer += 1
return names
@classmethod
def reset_names(cls):
cls.names_in_use = set()
def __init__(self,
x=None,
y=None,
z='undefined',
name='automatic',
color=None,
shape=r'$\times$',
shape_scale=Number('0.67'),
label='default',
label_position='below'):
r"""
Initialize Point
When not naming the keyword arguments, it is possible to not mention
the applicate, z:
Point(3, 2, 'A') is almost equivalent to Point(3, 2, 0, 'A'):
- all subsequent keyword arguments must be named
- the first version is a 2D Point, the second version a 3D Point.
:param x: the Point's abscissa
:type x: anything that can be turned to a Number
:param y: the Point's ordinate
:type y: anything that can be turned to a Number
:param z: the Point's applicate
:type z: anything that can be turned to a Number
:param name: the Point's name (e.g. 'A'). If it's left to 'automatic',
a yet unused name will be set.
:type name: str
:param shape: the symbol that will be drawn at the Point's position.
Default value is '$\times$', what draws a cross.
:type shape: str
:param label: what will be placed near the Point. The default value
will set the Point's name as label. Setting label at '' will disable
labeling the Point.
:type label: str
:param label_position: if any label is to be drawn, this is where to
draw it. Available values are TikZ's ones ('above', 'below left'...).
:type label_position: str
"""
self._three_dimensional = False
self._name = None
self._x = None
self._y = None
self._z = None
self._shape = None
self._label = None
self._label_position = None
self.x = x
self.y = y
try:
self.z = z
except (TypeError, InvalidOperation):
# The third value cannot be used as z; let's assume it is actually
# 2D geometry and the value is actually simply the name, implying
# z should be set to 0.
self.z = Number(0)
self._three_dimensional = False
self.name = z
else:
self.name = name
self.shape = shape
if label is 'default':
self.label = self.name
else:
self.label = label
self.label_position = label_position
if color is not None:
self.color = color
self.shape_scale = shape_scale
def __str__(self):
if not self.three_dimensional:
s = '{}({}, {})'.format(self.name, self.x, self.y)
else:
s = '{}({}, {}, {})'.format(self.name, self.x, self.y, self.z)
return s
def __repr__(self):
if not self.three_dimensional:
s = 'Point {}({}, {})'.format(self.name, self.x, self.y)
else:
s = 'Point {}({}, {}, {})'.format(self.name, self.x, self.y,
self.z)
return s
def __hash__(self):
if not self.three_dimensional:
s = 'Point ({}, {})'.format(self.x, self.y)
else:
s = 'Point ({}, {}, {})'.format(self.x, self.y, self.z)
return hash(s)
def __eq__(self, other):
if isinstance(other, Point):
p = config.points.DEFAULT_POSITION_PRECISION
return all([
self.x.rounded(p) == other.x.rounded(p),
self.y.rounded(p) == other.y.rounded(p),
self.z.rounded(p) == other.z.rounded(p)
])
else:
return False
@property
def name(self):
return self._name
@name.setter
def name(self, value):
if self._name is not None:
Point.names_in_use.discard(self._name)
if value is None:
self._name = None
else:
value = str(value)
if value == 'automatic':
self._name = Point.automatic_names().pop()
else:
self._name = value
Point.names_in_use.add(self._name)
@property
def x(self):
return self._x
@x.setter
def x(self, value):
try:
self._x = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as abscissa, found {} '
'instead.'.format(repr(value)))
@property
def y(self):
return self._y
@y.setter
def y(self, value):
try:
self._y = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as ordinate, found {} '
'instead.'.format(repr(value)))
@property
def z(self):
return self._z
@z.setter
def z(self, value):
three_dimensional = True
if value is 'undefined':
value = 0
three_dimensional = False
try:
self._z = Number(value)
except (TypeError, InvalidOperation):
raise TypeError('Expected a number as applicate, found {} '
'instead.'.format(repr(value)))
self._three_dimensional = three_dimensional
@property
def coordinates(self):
return (self._x, self._y, self._z)
@property
def shape(self):
return self._shape
@shape.setter
def shape(self, other):
self._shape = str(other)
@property
def shape_scale(self):
return self._shape_scale
@shape_scale.setter
def shape_scale(self, value):
check_scale(value, 'Point\'s shape')
self._shape_scale = Number(value)
@property
def label_position(self):
return self._label_position
@label_position.setter
def label_position(self, other):
if other is None:
self._label_position = None
else:
self._label_position = str(other)
def rotate(self, center, angle, axis=None, rename='auto'):
"""
Rotate around center (or axis going through center).
:param center: the center of the rotation
:type center: Point
:param angle: the angle of the rotation
:type angle: a number
:param axis: the axis of the rotation for 3D rotation. If left to None,
the rotation happens around the center, in the plane.
:type axis: Vector
:param rename: if set to 'auto', will name the rotated Point after the
original, adding a ' (like A.rotate(...) creates a Point A'). If set
to None, keep the original name. Otherwise, the provided str will be
used as the rotated Point's name.
:type rename: None or str
:rtype: Point
"""
from mathmakerlib.geometry.vector import Vector
if not isinstance(center, Point):
raise TypeError('Expected a Point as rotation center, got {} '
'instead.'.format(type(center)))
if not is_number(angle):
raise TypeError('Expected a number as rotation angle, got {} '
'instead.'.format(type(angle)))
if not (axis is None or isinstance(axis, Vector)):
raise TypeError('Expected either None or a Vector as axis, '
'found {} instead.'.format(repr(axis)))
Δx = self.x - center.x
Δy = self.y - center.y
Δz = self.z - center.z
cosθ = Number(str(cos(radians(angle))))
sinθ = Number(str(sin(radians(angle))))
if axis is None:
rx = (Δx * cosθ - Δy * sinθ + center.x).rounded(Number('1.000'))
ry = (Δx * sinθ + Δy * cosθ + center.y).rounded(Number('1.000'))
rz = 'undefined'
else:
ux, uy, uz = axis.normalized().coordinates
rotation_matrix = [[
cosθ + (1 - cosθ) * ux**2, ux * uy * (1 - cosθ) - uz * sinθ,
ux * uz * (1 - cosθ) + uy * sinθ
],
[
uy * ux * (1 - cosθ) + uz * sinθ,
cosθ + (1 - cosθ) * uy**2,
uy * uz * (1 - cosθ) - ux * sinθ
],
[
uz * ux * (1 - cosθ) - uy * sinθ,
uz * uy * (1 - cosθ) + ux * sinθ,
cosθ + (1 - cosθ) * uz**2
]]
rx = sum([
rc * coord
for rc, coord in zip(rotation_matrix[0], [Δx, Δy, Δz])
])
ry = sum([
rc * coord
for rc, coord in zip(rotation_matrix[1], [Δx, Δy, Δz])
])
rz = sum([
rc * coord
for rc, coord in zip(rotation_matrix[2], [Δx, Δy, Δz])
])
rx += center.x
ry += center.y
rz += center.z
rx = rx.rounded(Number('1.000'))
ry = ry.rounded(Number('1.000'))
rz = rz.rounded(Number('1.000'))
if rename == 'keep_name':
rname = self.name
elif rename == 'auto':
rname = self.name + "'"
else:
rname = rename
return Point(rx, ry, rz, rname)
def belongs_to(self, other):
"""Check if the Point belongs to a LineSegment."""
# This could be extended to Lines and Rays, later.
# Then check if self is different from the 2 known Points, and
# if it belongs to the Line, then:
# (x - x1) / (x2 - x1) = (y - y1) / (y2 - y1)
# also, if three_dimensional, all this = (z - z1) / (z2 - z1)
from mathmakerlib.geometry import LineSegment
if not isinstance(other, LineSegment):
raise TypeError('Argument \'other\' must be a LineSegment. '
'Found {} instead.'.format(repr(other)))
d1 = LineSegment(self, other.endpoints[0]).length
d2 = LineSegment(self, other.endpoints[1]).length
return d1 + d2 == other.length
def tikz_declaring_comment(self):
"""
Replace plural by singular in the declaring comment.
:rtype: str
"""
return '% Declare Point'
def tikz_declarations(self):
"""Return the Point declaration."""
if self.name is None:
raise RuntimeError('Point at ({}, {}) has no name (None), '
'cannot create TikZ picture using it.')
return r'\coordinate ({}) at ({},{});'\
.format(self.name,
self.x.rounded(Number('0.001')),
self.y.rounded(Number('0.001')))
def tikz_drawing_comment(self):
"""Return the comment preceding the Point's drawing."""
return ['% Draw Point']
def _tikz_draw_options(self):
return [self.color]
def tikz_draw(self):
"""Return the command to actually draw the Point."""
sh_scale = ''
if self.shape_scale != 1:
sh_scale = '[scale={}]'.format(self.shape_scale)
return [
r'\draw{} ({}) node{} {};'.format(tikz_options_list('draw', self),
self.name, sh_scale,
'{' + self.shape + '}')
]
def tikz_labeling_comment(self):
"""
Replace plural by singular in the labeling comment.
:rtype: str
"""
return '% Label Point'
def tikz_points_labels(self):
return self.tikz_label()
def tikz_label(self):
"""Return the command to write the Point's label."""
if self.label is None:
return ''
else:
if self.label_position is None:
label_position = ''
else:
label_position = '[' + self.label_position + ']'
return r'\draw ({}) node{} {};'\
.format(self.label, label_position, '{' + self.label + '}')
def __init__(self,
*points,
thickness='thick',
dashpattern='solid',
label=None,
label_mask=None,
label_winding='anticlockwise',
label_position=None,
label_scale=None,
mark=None,
mark_scale=Number('0.5'),
color=None,
draw_endpoints=True,
label_endpoints=True,
locked_label=False,
allow_zero_length=True,
sloped_label=True):
"""
Initialize LineSegment
:param points: either one LineSegment to copy, or two Points
:type points: another LineSegment or a list or tuple of two Points
:param thickness: the LineSegment's thickness. Available values are
TikZ's ones.
:type thickness: str
:param label: what will be written along the LineSegment, about its
middle. A None value will disable the LineSegment's labeling.
:type label: None or str
:param label_mask: if not None (default), hide the label with ' '
or '?'
:type label_mask: None or str (' ' or '?')
:param label_position: tells where to put the LineSegment's label.
Can be a value used by TikZ or 'clockwise' or 'anticlockwise'.
'anticlockwise' (default) will automatically set the label_position to
'above' if Δx < 0 and to 'below' if Δx > 0. This is useful to
put all LineSegments' labels outside a Polygon that is drawn in an
anticlockwise manner. Same for 'clockwise', in the reversed direction.
:type label_position: str
:param label_scale: the label's scale
:type label_scale: None or anything that is accepted to create a Number
:param draw_endpoints: whether or not actually draw the endpoints.
Defaults to True.
:type draw_endpoints: bool
:param label_endpoints: whether or not label the endpoints.
Defaults to True.
:type label_endpoints: bool
:param mark: the mark to print on the line segment
:type mark: str
:param mark_scale: the scale (size) of the mark. Defaults to 0.5
:type mark_scale: any number
:param locked_label: to allow or prevent, by default, modifications of
the LineSegment's label.
:type locked_label: bool
"""
if len(points) != 2:
raise TypeError('Two Points are required to create a '
'LineSegment. Got {} object(s) instead.'.format(
len(points)))
Bipoint.__init__(self, *points, allow_zero_length=allow_zero_length)
self._label = None
self._thickness = None
self._label_mask = None
self._label_scale = None
self._draw_endpoints = None
self._label_endpoints = None
self._locked_label = False # Only temporary, in order to be able to
self.label = label # use the label setter.
self.label_mask = label_mask
self.label_scale = label_scale
self.thickness = thickness
self.dashpattern = dashpattern
self.draw_endpoints = draw_endpoints
self.sloped_label = sloped_label
self.label_winding = label_winding
self.label_endpoints = label_endpoints
self.mark = mark
self.mark_scale = mark_scale
try:
self.endpoints[1].label_position = \
tikz_approx_position(self.slope360)
except ZeroLengthLineSegment:
self.endpoints[1].label_position = 'below left'
self.endpoints[0].label_position = \
OPPOSITE_LABEL_POSITIONS[self.endpoints[1].label_position]
if label_position is None:
label_position = 'automatic'
self.label_position = label_position
if color is not None:
self.color = color
self._comment_designation = 'Line Segment'
if not isinstance(locked_label, bool):
raise TypeError('Expected bool type for \'locked_label\' keyword '
'argument. Found {}.'.format(type(locked_label)))
self._locked_label = locked_label
def __init__(self,
start_vertex=None,
name=None,
side_length=Number('1'),
build_angle=60,
mark_equal_sides=True,
use_mark='||',
draw_vertices=False,
label_vertices=True,
thickness='thick',
color=None,
rotation_angle=0,
winding=None,
sloped_sides_labels=True):
r"""
Initialize Rhombus
:param start_vertex: the vertex to start to draw the Rhombus
(default (0; 0))
:type start_vertex: Point
:param name: the name of the Rhombus, like ABCD.
Can be either None (the names will be automatically created), or a
string of the letters to use to name the vertices. Only single letters
are supported as Points' names so far (at Polygon's creation).
See issue #3.
:type name: None or str
:param side_length: the length that will be used to calculate the
coordinates of the vertices used to build the Rhombus
:type side_length: a number
:param build_angle: one of the interior angles of the Rhombus.
:type build_angle: any number
:param mark_equal_sides: if True (default), all four sides will be
automatically marked with the same symbol.
:type mark_equal_sides: bool
:param draw_vertices: whether to actually draw, or not, the vertices
:type draw_vertices: bool
:param label_vertices: whether to label, or not, the vertices
:type label_vertices: bool
:param thickness: the thickness of the Quadrilateral's sides
:type thickness: str
:param color: the color of the Quadrilateral's sides
:type color: str
:param rotate: the angle of rotation around isobarycenter
:type rotate: int
"""
if start_vertex is None:
start_vertex = Point(0, 0)
self._side_length = Number(side_length)
if is_number(build_angle):
self._build_angle = build_angle
else:
raise TypeError(
'Expected an integer as build_angle, found {}.'.format(
type(build_angle)))
x = (side_length * Number(str(cos(radians(build_angle / 2)))))\
.rounded(Number('0.001'))
y = (side_length * Number(str(sin(radians(build_angle / 2)))))\
.rounded(Number('0.001'))
v1 = Point(x + start_vertex.x, -y + start_vertex.y)
v2 = Point(2 * x + start_vertex.x, start_vertex.y)
v3 = Point(x + start_vertex.x, y + start_vertex.y)
Quadrilateral.__init__(self,
start_vertex,
v1,
v2,
v3,
name=name,
draw_vertices=draw_vertices,
label_vertices=label_vertices,
thickness=thickness,
color=color,
rotation_angle=rotation_angle,
winding=winding,
sloped_sides_labels=sloped_sides_labels)
self._type = 'Rhombus'
Equilateral.__init__(self,
mark_equal_sides=mark_equal_sides,
use_mark=use_mark)
def __init__(self,
start_vertex=None,
name=None,
side_length=Number('1'),
mark_right_angles=True,
mark_equal_sides=True,
use_mark='||',
draw_vertices=False,
label_vertices=True,
thickness='thick',
color=None,
rotation_angle=0,
winding=None,
sloped_sides_labels=True):
r"""
Initialize Square
:param start_vertex: the vertex to start to draw the Square
(default (0; 0))
:type start_vertex: Point
:param name: the name of the Square, like ABCDE for a pentagon. Can
be either None (the names will be automatically created), or a
string of the letters to use to name the vertices. Only single letters
are supported as Points' names so far (at Polygon's creation).
See issue #3.
:type name: None or str
:param side_length: the length that will be used to calculate the
coordinates of the vertices used to build the Square
:type side_length: a number
:param mark_right_angles: if True (default), all four angles will be
automatically marked as right angles.
:type mark_right_angles: bool
:param mark_equal_sides: if True (default), all four sides will be
automatically marked with the same symbol.
:type mark_equal_sides: bool
:param draw_vertices: whether to actually draw, or not, the vertices
:type draw_vertices: bool
:param label_vertices: whether to label, or not, the vertices
:type label_vertices: bool
:param thickness: the thickness of the Polygon's sides
:type thickness: str
:param color: the color of the Polygon's sides
:type color: str
:param rotate: the angle of rotation around isobarycenter
:type rotate: int
"""
Rectangle.__init__(self,
start_vertex=start_vertex,
name=name,
width=side_length,
length=side_length,
mark_right_angles=mark_right_angles,
draw_vertices=draw_vertices,
label_vertices=label_vertices,
thickness=thickness,
color=color,
rotation_angle=rotation_angle,
winding=winding,
sloped_sides_labels=sloped_sides_labels)
# TODO: see issue #5
# Accepted type for side_length is number, already checked at
# vertices' instanciations (in Rectangle.__init__() call).
self._side_length = Number(side_length)
Equilateral.__init__(self,
mark_equal_sides=mark_equal_sides,
use_mark=use_mark)
self._type = 'Square'
def __init__(self,
x=None,
y=None,
z='undefined',
name='automatic',
color=None,
shape=r'$\times$',
shape_scale=Number('0.67'),
label='default',
label_position='below'):
r"""
Initialize Point
When not naming the keyword arguments, it is possible to not mention
the applicate, z:
Point(3, 2, 'A') is almost equivalent to Point(3, 2, 0, 'A'):
- all subsequent keyword arguments must be named
- the first version is a 2D Point, the second version a 3D Point.
:param x: the Point's abscissa
:type x: anything that can be turned to a Number
:param y: the Point's ordinate
:type y: anything that can be turned to a Number
:param z: the Point's applicate
:type z: anything that can be turned to a Number
:param name: the Point's name (e.g. 'A'). If it's left to 'automatic',
a yet unused name will be set.
:type name: str
:param shape: the symbol that will be drawn at the Point's position.
Default value is '$\times$', what draws a cross.
:type shape: str
:param label: what will be placed near the Point. The default value
will set the Point's name as label. Setting label at '' will disable
labeling the Point.
:type label: str
:param label_position: if any label is to be drawn, this is where to
draw it. Available values are TikZ's ones ('above', 'below left'...).
:type label_position: str
"""
self._three_dimensional = False
self._name = None
self._x = None
self._y = None
self._z = None
self._shape = None
self._label = None
self._label_position = None
self.x = x
self.y = y
try:
self.z = z
except (TypeError, InvalidOperation):
# The third value cannot be used as z; let's assume it is actually
# 2D geometry and the value is actually simply the name, implying
# z should be set to 0.
self.z = Number(0)
self._three_dimensional = False
self.name = z
else:
self.name = name
self.shape = shape
if label is 'default':
self.label = self.name
else:
self.label = label
self.label_position = label_position
if color is not None:
self.color = color
self.shape_scale = shape_scale
def label_scale(self, value):
if value is None:
self._label_scale = None
else:
self._label_scale = Number(value)
