def test_dot_product():
"""Check dot product of two Vectors."""
Ω = Point(0, 0, 'Ω')
A = Point(1, 1, 'A')
with pytest.raises(TypeError) as excinfo:
Vector(0, 1).dot(Bipoint(Ω, A))
assert str(excinfo.value) == 'Can only calculate the dot product of a '\
'Vector by another Vector. '\
'Found Bipoint(Point Ω(0, 0), Point A(1, 1)) instead.'
u = Vector(1, 1)
v = Vector(3, -7)
assert u.dot(v) == -4
u = Vector(2, 5, -7)
v = Vector(3, -7, 2)
assert u.dot(v) == -43
def __init__(self, point, vertex, point_or_measure, decoration=None,
mark_right=False, second_point_name='auto', label=None,
color=None, thickness='thick', armspoints=None,
label_vertex=False, draw_vertex=False,
label_armspoints=False, draw_armspoints=False,
label_endpoints=False, draw_endpoints=False,
naming_mode='from_endpoints', decoration2=None):
"""
:param point: a Point of an arm of the Angle
:type point: Point
:param vertex: the Angle's vertex
:type vertex: Point
:param point_or_measure: either a Point of the other arm of the Angle,
or the measure of the Angle
:type point_or_measure: Point or number
:param decoration: the decoration of the Angle
:type decoration: None or AngleDecoration
:param mark_right: to tell whether to mark the angle as a right angle
:type mark_right: bool
:param second_point_name: Only used if point_or_measure is a measure,
this is the name of the 2d arm's Point. If set to 'auto', then the name
of the first Point will be used, concatenated to a '.
:type second_point_name: str
:param thickness: the Angle's arms' thickness. Available values are
TikZ's ones.
:type thickness: str
:param color: the color of the Angle's arms.
:type color: str
:param naming_mode: how to build the name. Possible modes are:
'from_endpoints', 'from_armspoints', 'from_vertex'. Note that if no
armspoints are defined, then trying to get the Angle.name will raise an
error
:type naming_mode: str
"""
self.color = color
self.thickness = thickness
self.naming_mode = naming_mode
self.decoration = decoration
self.decoration2 = decoration2
# The label must be set *after* the possible decoration, because it
# will actually be handled by self.decoration
if (self.decoration is None
or self.decoration.label in [None, 'default']):
self.label = label
else:
if label is not None:
raise ValueError('The label has been set twice, as Angle\'s '
'keyword argument ({}) and as its '
'AngleDecoration\'s keyword argument ({}).'
.format(repr(label),
repr(self.decoration.label_value)))
self.mark_right = mark_right
self.label_vertex = label_vertex
self.label_endpoints = label_endpoints
self.draw_endpoints = draw_endpoints
self.label_armspoints = label_armspoints
self.draw_armspoints = draw_armspoints
self.draw_vertex = draw_vertex
if not (isinstance(point, Point)
and isinstance(vertex, Point)
and (isinstance(point_or_measure, Point)
or is_number(point_or_measure))):
raise TypeError('Three Points, or two Points and the measure of '
'the angle are required to build an Angle. '
'Found instead: {}, {} and {}.'
.format(type(point), type(vertex),
type(point_or_measure)))
self._points = [point, vertex]
if isinstance(point_or_measure, Point):
self._points.append(point_or_measure)
else:
self._points.append(point.rotate(vertex, point_or_measure,
rename=second_point_name))
if any([p.three_dimensional for p in self._points]):
self._three_dimensional = True
else:
self._three_dimensional = False
# Measure of the angle:
if self._three_dimensional:
u = Vector(self.points[1], self.points[0])
v = Vector(self.points[1], self.points[2])
self._measure = Number(str(degrees(atan2(u.cross(v).length,
u.dot(v)))))
else: # 2D angles measure
p0 = Point(self._points[0].x - self._points[1].x,
self._points[0].y - self._points[1].y,
None)
p2 = Point(self._points[2].x - self._points[1].x,
self._points[2].y - self._points[1].y,
None)
α0 = Number(str(degrees(atan2(p0.y, p0.x))))
α2 = Number(str(degrees(atan2(p2.y, p2.x))))
self._measure = α2 - α0
if self._measure < 0:
self._measure += 360
# This is not like the matching Triangle!
if shoelace_formula(*self.points) > 0:
self.winding = 'clockwise'
else:
self.winding = 'anticlockwise'
arm0 = Bipoint(self._points[1], self._points[0])
arm1 = Bipoint(self._points[1], self._points[2])
self._arms = [arm0, arm1]
self.armspoints = armspoints
# Only 2D: labels positioning
if not self.three_dimensional:
# Vertex' label positioning
bisector = Vector(self._points[0], self.vertex)\
.bisector(Vector(self._points[2], self.vertex),
new_endpoint_name=None)
try:
self._points[1].label_position = \
tikz_approx_position(bisector.slope360)
except ZeroVector:
self._points[1].label_position = \
tikz_approx_position(
Bipoint(self.vertex,
self._points[0].rotate(self.vertex, -90,
rename=None)
).slope360)
# Endpoints labels positioning
direction = 1 if self.winding == 'anticlockwise' else -1
self.endpoints[0].label_position = \
tikz_approx_position(arm0.slope360 - direction * 55)
self.endpoints[1].label_position = \
tikz_approx_position(arm1.slope360 + direction * 55)