def test_intersection():
poly1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1))
poly2 = Polygon(Point(0, 1), Point(-5, 0),
Point(0, -4), Point(0, Rational(1, 5)),
Point(S.Half, -0.1), Point(1, 0), Point(0, 1))
assert poly1.intersection(poly2) == [Point2D(Rational(1, 3), 0),
Segment(Point(0, Rational(1, 5)), Point(0, 0)),
Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(poly1) == [Point(Rational(1, 3), 0),
Segment(Point(0, 0), Point(0, Rational(1, 5))),
Segment(Point(1, 0), Point(0, 1))]
assert poly1.intersection(Point(0, 0)) == [Point(0, 0)]
assert poly1.intersection(Point(-12, -43)) == []
assert poly2.intersection(Line((-12, 0), (12, 0))) == [Point(-5, 0),
Point(0, 0), Point(Rational(1, 3), 0), Point(1, 0)]
assert poly2.intersection(Line((-12, 12), (12, 12))) == []
assert poly2.intersection(Ray((-3, 4), (1, 0))) == [Segment(Point(1, 0),
Point(0, 1))]
assert poly2.intersection(Circle((0, -1), 1)) == [Point(0, -2),
Point(0, 0)]
assert poly1.intersection(poly1) == [Segment(Point(0, 0), Point(1, 0)),
Segment(Point(0, 1), Point(0, 0)), Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(poly2) == [Segment(Point(-5, 0), Point(0, -4)),
Segment(Point(0, -4), Point(0, Rational(1, 5))),
Segment(Point(0, Rational(1, 5)), Point(S.Half, Rational(-1, 10))),
Segment(Point(0, 1), Point(-5, 0)),
Segment(Point(S.Half, Rational(-1, 10)), Point(1, 0)),
Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(Triangle(Point(0, 1), Point(1, 0), Point(-1, 1))) \
== [Point(Rational(-5, 7), Rational(6, 7)), Segment(Point2D(0, 1), Point(1, 0))]
assert poly1.intersection(RegularPolygon((-12, -15), 3, 3)) == []
def test_eulerline():
assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).eulerline \
== Line(Point2D(0, 0), Point2D(1/2, 1/2))
assert Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))).eulerline \
== Point2D(5, 5*sqrt(3)/3)
assert Triangle(Point(4, -6), Point(4, -1), Point(-3, 3)).eulerline \
== Line(Point2D(64/7, 3), Point2D(-29/14, -7/2))
def test_projection():
p1 = Point(0, 0)
p2 = Point3D(0, 0, 0)
p3 = Point(-x1, x1)
l1 = Line(p1, Point(1, 1))
l2 = Line3D(Point3D(0, 0, 0), Point3D(1, 0, 0))
l3 = Line3D(p2, Point3D(1, 1, 1))
r1 = Ray(Point(1, 1), Point(2, 2))
s1 = Segment(Point2D(0, 0), Point2D(0, 1))
s2 = Segment(Point2D(1, 0), Point2D(2, 1/2))
assert Line(Point(x1, x1), Point(y1, y1)).projection(Point(y1, y1)) == Point(y1, y1)
assert Line(Point(x1, x1), Point(x1, 1 + x1)).projection(Point(1, 1)) == Point(x1, 1)
assert Segment(Point(-2, 2), Point(0, 4)).projection(r1) == Segment(Point(-1, 3), Point(0, 4))
assert Segment(Point(0, 4), Point(-2, 2)).projection(r1) == Segment(Point(0, 4), Point(-1, 3))
assert s2.projection(s1) == EmptySet
assert l1.projection(p3) == p1
assert l1.projection(Ray(p1, Point(-1, 5))) == Ray(Point(0, 0), Point(2, 2))
assert l1.projection(Ray(p1, Point(-1, 1))) == p1
assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1)
assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2))
assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2))
assert r1.projection(Ray(Point(1, 1), Point(-1, -1))) == Point(1, 1)
assert r1.projection(Ray(Point(0, 4), Point(-1, -5))) == Segment(Point(1, 1), Point(2, 2))
assert r1.projection(Segment(Point(-1, 5), Point(-5, -10))) == Segment(Point(1, 1), Point(2, 2))
assert l3.projection(Ray3D(p2, Point3D(-1, 5, 0))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(4, 3), Rational(4, 3), Rational(4, 3)))
assert l3.projection(Ray3D(p2, Point3D(-1, 1, 1))) == Ray3D(Point3D(0, 0, 0), Point3D(Rational(1, 3), Rational(1, 3), Rational(1, 3)))
assert l2.projection(Point3D(5, 5, 0)) == Point3D(5, 0)
assert l2.projection(Line3D(Point3D(0, 1, 0), Point3D(1, 1, 0))).equals(l2)
def test_eulerline():
assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).eulerline \
== Line(Point2D(0, 0), Point2D(S(1)/2, S(1)/2))
assert Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))).eulerline \
== Point2D(5, 5*sqrt(3)/3)
assert Triangle(Point(4, -6), Point(4, -1), Point(-3, 3)).eulerline \
== Line(Point2D(S(64)/7, 3), Point2D(-S(29)/14, -S(7)/2))
def test_intersection():
poly1 = Triangle(Point(0, 0), Point(1, 0), Point(0, 1))
poly2 = Polygon(Point(0, 1), Point(-5, 0),
Point(0, -4), Point(0, S(1)/5),
Point(S(1)/2, -0.1), Point(1,0), Point(0, 1))
assert poly1.intersection(poly2) == [Point2D(S(1)/3, 0),
Segment(Point(0, S(1)/5), Point(0, 0)),
Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(poly1) == [Point(S(1)/3, 0),
Segment(Point(0, 0), Point(0, S(1)/5)),
Segment(Point(1, 0), Point(0, 1))]
assert poly1.intersection(Point(0, 0)) == [Point(0, 0)]
assert poly1.intersection(Point(-12, -43)) == []
assert poly2.intersection(Line((-12, 0), (12, 0))) == [Point(-5, 0),
Point(0, 0),Point(S(1)/3, 0), Point(1, 0)]
assert poly2.intersection(Line((-12, 12), (12, 12))) == []
assert poly2.intersection(Ray((-3,4), (1,0))) == [Segment(Point(1, 0),
Point(0, 1))]
assert poly2.intersection(Circle((0, -1), 1)) == [Point(0, -2),
Point(0, 0)]
assert poly1.intersection(poly1) == [Segment(Point(0, 0), Point(1, 0)),
Segment(Point(0, 1), Point(0, 0)), Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(poly2) == [Segment(Point(-5, 0), Point(0, -4)),
Segment(Point(0, -4), Point(0, S(1)/5)),
Segment(Point(0, S(1)/5), Point(S(1)/2, -S(1)/10)),
Segment(Point(0, 1), Point(-5, 0)),
Segment(Point(S(1)/2, -S(1)/10), Point(1, 0)),
Segment(Point(1, 0), Point(0, 1))]
assert poly2.intersection(Triangle(Point(0, 1), Point(1, 0), Point(-1, 1))) \
== [Point(-S(5)/7, S(6)/7), Segment(Point2D(0, 1), Point(1, 0))]
assert poly1.intersection(RegularPolygon((-12, -15), 3, 3)) == []
def test_arguments():
"""Functions accepting `Point` objects in `geometry`
should also accept tuples, lists, and generators and
automatically convert them to points."""
from sympy import subsets
singles2d = ((1, 2), [1, 3], Point(1, 5))
doubles2d = subsets(singles2d, 2)
l2d = Line(Point2D(1, 2), Point2D(2, 3))
singles3d = ((1, 2, 3), [1, 2, 4], Point(1, 2, 6))
doubles3d = subsets(singles3d, 2)
l3d = Line(Point3D(1, 2, 3), Point3D(1, 1, 2))
singles4d = ((1, 2, 3, 4), [1, 2, 3, 5], Point(1, 2, 3, 7))
doubles4d = subsets(singles4d, 2)
l4d = Line(Point(1, 2, 3, 4), Point(2, 2, 2, 2))
# test 2D
test_single = ['contains', 'distance', 'equals', 'parallel_line', 'perpendicular_line', 'perpendicular_segment',
'projection', 'intersection']
for p in doubles2d:
Line2D(*p)
for func in test_single:
for p in singles2d:
getattr(l2d, func)(p)
# test 3D
for p in doubles3d:
Line3D(*p)
for func in test_single:
for p in singles3d:
getattr(l3d, func)(p)
# test 4D
for p in doubles4d:
Line(*p)
for func in test_single:
for p in singles4d:
getattr(l4d, func)(p)
def test_eulerline():
assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).eulerline \
== Line(Point2D(0, 0), Point2D(S.Half, S.Half))
assert Triangle(Point(0, 0), Point(10, 0), Point(5, 5*sqrt(3))).eulerline \
== Point2D(5, 5*sqrt(3)/3)
assert Triangle(Point(4, -6), Point(4, -1), Point(-3, 3)).eulerline \
== Line(Point2D(Rational(64, 7), 3), Point2D(Rational(-29, 14), Rational(-7, 2)))
def intersection_with_circle(self, point1, point2):
r = self.r_small_circle
R = self.big_circle[2]
try:
# Point A, B and C
A = Point2D(self.big_circle[0], self.big_circle[1])
B = Point2D(point1[0], point1[1])
C = Point2D(point2[0], point2[1])
# Segment from B to C - line
line = Segment2D(B, C)
c = Circle(A, R + r)
result_of_intersect = c.intersection(line)
# print(result_of_intersect)
temp1 = result_of_intersect[0]
temp2 = result_of_intersect[1]
temp1 = str(temp1)[7:]
temp2 = str(temp2)[7:]
# print(temp1)
# print(temp2)
# print(eval(temp1))
# print(eval(temp2))
p1 = eval(temp1)
p2 = eval(temp2)
# point1 = mlines.Line2D([p1[0], p2[0]], [p1[1], p2[1]], color='b')
# self.figure.gca().add_line(point1)
return p1, p2
except:
return -666
def test_are_coplanar():
a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
d = Line(Point2D(0, 3), Point2D(1, 5))
assert are_coplanar(a, b, c) == False
assert are_coplanar(a, d) == False
def test_Point2D():
# Test Distance
p1 = Point2D(1, 5)
p2 = Point2D(4, 2.5)
p3 = (6, 3)
assert p1.distance(p2) == sqrt(61) / 2
assert p2.distance(p3) == sqrt(17) / 2
def demo(ctx, width, height):
map = Map('demo', width, height, cell_size=CELL_SIZE)
map.add_room(Room('start', Point2D(width / 4, height / 4)))
map.add_room(Room('mid1', Point2D(width / 2 + width / 4, height / 2)))
map.add_room(Room('mid2', Point2D(width / 2, height / 2 + height / 4)))
map.add_room(
Room('end', Point2D(width / 2 + width / 4, height / 2 + height / 4)))
map.add_path('start', 'mid1', flags=['arc'])
map.add_path('start', 'mid2', flags=['door', 'trapped'])
map.add_path('mid1', 'end', flags=['door'])
print(map)
map.draw(ctx)
def getPointOfIntersection(extreme_points):
'''This function returns a unique point of intersection (if it exists)
between four points in 2D plane.
Input:
extreme_points: (4,2) numpy array containing (x,y) coordinates of four points
Output:
intersection_point: A list containing [xint, yint]
NOTE: This function errors out (ValueError) unless the intersection is a unique point. Implement
error catching if this is undesired.'''
assert isinstance(
extreme_points,
np.ndarray), "Exteme points should be passed as an ndarray"
assert extreme_points.shape == (
4, 2), "Extreme point array shape must be (4,2)"
# We try a random pairing based search. We make three attempts
# to try unique pairings of fours points and look for the combination that gives
# a unique intersection point.
pairings = [[0, 1, 2, 3], [0, 2, 1, 3], [0, 3, 1, 2]]
intersection_found = False
i = 0
pairs = []
while intersection_found is not True and i < 3:
pairs = pairings[i]
x1 = Point2D(extreme_points[pairs[0], :])
x2 = Point2D(extreme_points[pairs[1], :])
x3 = Point2D(extreme_points[pairs[2], :])
x4 = Point2D(extreme_points[pairs[3], :])
# We use segment over line to ensure the intersection point lies within
# the bounding box defined by the extreme points
intersection_point = intersection(Segment2D(x1, x2), Segment2D(x3, x4))
# Ensure that intersection point is a unique point and not a line or empty
if not intersection_point == []:
if isinstance(intersection_point[0], Point2D):
intersection_found = True
xint, yint = intersection_point[0]
i = i + 1
if intersection_found is not True:
raise ValueError(
"No intersection point was found for given extreme points using random pairing. Check"
)
intersection_point = np.array(
[np.float128(xint.evalf()),
np.float128(yint.evalf())])
pairs = np.array(pairs)
return intersection_point, pairs
def test_object_from_equation():
from sympy.abc import x, y, a, b
assert Line(3*x + y + 18) == Line2D(Point2D(0, -18), Point2D(1, -21))
assert Line(3*x + 5 * y + 1) == Line2D(Point2D(0, -1/5), Point2D(1, -4/5))
assert Line(3*a + b + 18, x='a', y='b') == Line2D(Point2D(0, -18), Point2D(1, -21))
assert Line(3*x + y) == Line2D(Point2D(0, 0), Point2D(1, -3))
assert Line(x + y) == Line2D(Point2D(0, 0), Point2D(1, -1))
raises(ValueError, lambda: Line(x))
raises(ValueError, lambda: Line(y))
raises(ValueError, lambda: Line(x/y))
raises(ValueError, lambda: Line(a/b, x='a', y='b'))
raises(ValueError, lambda: Line(y/x))
raises(ValueError, lambda: Line(b/a, x='a', y='b'))
raises(ValueError, lambda: Line((x + 1)**2 + y))
def get_rectangular_coordinates(self, pos: geom.Point2D):
"""
Calculate the model coordinates of the pos point inside the init table.
"""
def get_coeff(p, x, x_len, a, b, c, d):
if p is not None:
k = geom.intersection(geom.Line2D(p, pos), self.line)[0]
return x.distance(k) / x_len
k1 = a.distance(d)
k2 = b.distance(c)
ln = geom.Line2D(a, d).parallel_line(pos)
g1 = geom.intersection(ln, geom.Line2D(a, b))[0]
g2 = geom.intersection(ln, geom.Line2D(c, d))[0]
k3 = g1.distance(g2)
return k2 * (k3 - k1) / (k3 * (k2 - k1))
if self.P is None and self.Q is None:
l1 = geom.Line2D(self.A, self.D)
l2 = geom.Line2D(self.C, self.D)
x_coeff = pos.distance(l1) / self.B.distance(l1)
y_coeff = pos.distance(l2) / self.B.distance(l2)
else:
x_coeff = get_coeff(self.Q, self.X1, self.x_len, self.A, self.B,
self.C, self.D)
y_coeff = get_coeff(self.P, self.Y1, self.y_len, self.D, self.A,
self.B, self.C)
x = round(x_coeff * self.img_sz[0])
y = round(y_coeff * self.img_sz[1])
return x, y
def find_intersect_circle_and_line(self, x1, y1, x2, y2, x3, y3, r):
A = Point2D(x1, y1)
B = Point2D(x2, y2)
C = Point2D(x3, y3)
F = Line2D(A, B)
c = Circle(C, sympify(Rational(r), rational=True))
i_0 = F.intersection(c)
temp1 = i_0[0]
temp2 = i_0[1]
temp1 = str(temp1)[7:]
temp2 = str(temp2)[7:]
temp1 = eval(temp1)
temp2 = eval(temp2)
x = (temp1[0] + temp2[0]) / 2
y = (temp1[1] + temp2[1]) / 2
return [x, y]
def test_issue_11617():
p1 = Point3D(1, 0, 2)
p2 = Point2D(2, 0)
with warnings.catch_warnings(record=True) as w:
assert p1.distance(p2) == sqrt(5)
assert len(w) == 1
def get_dist_from_line_segment(x1, c, x2, p, sig1, sig2):
'''Given three colinear points, x1, c, x2 (geometric order), this program
checks if point p and x1 are on the same side of a perpendicular to line segment x1x2 drawn at c.
If p and x1 are on the same side of perpendicular line, the distance of p from line segment x1x2
is divided by sig1 (for scaling) or by sig2 otherwise.
Inputs:
x1, c, x2, p: Np.array of size 2.
sig1, sig2: scaling standard deviation
Output:
l1: Equivalent of l1 distance from the line segment x1x2 (scaled by sigma)'''
assert isinstance_multiple(
[x1, x2, c], np.ndarray), "Either x1,x2 or c isn't a np.ndarray, check"
assert x1.size == x2.size == c.size == 2, "x1, x2, c must contain ony 2 elements"
assert isinstance_multiple(
[sig1, sig2], float), "Either sig1 or sig2 is not of type float, check"
assert not (sig1 < 0.001 or
sig2 < 0.001), "sig1, sig2 is smaller than 0.001 (eps), check"
x1, x2, c, p = [Point2D(i) for i in [x1, x2, c, p]]
S = Segment2D(x1, x2)
L = S.perpendicular_line(c)
Sc = Segment2D(x1, p)
l1 = S.distance(p).evalf()
if isinstance(L.intersect(Sc), EmptySet):
l1 = l1 / sig1
else:
l1 = l1 / sig2
return float(l1)
def test_Point2D():
# Test Distance
p1 = Point2D(1, 5)
p2 = Point2D(4, 2.5)
p3 = (6, 3)
assert p1.distance(p2) == sqrt(61) / 2
assert p2.distance(p3) == sqrt(17) / 2
# Test coordinates
assert p1.x == 1
assert p1.y == 5
assert p2.x == 4
assert p2.y == 2.5
assert p1.coordinates == (1, 5)
assert p2.coordinates == (4, 2.5)
def test_transform():
pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)]
pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)]
assert Triangle(*pts).scale(2, 3, (4, 5)) == Triangle(*pts_out)
assert RegularPolygon((0, 0), 1, 4).scale(2, 3, (4, 5)) == \
Polygon(Point(-2, -10), Point(-4, -7), Point(-6, -10), Point(-4, -13))
# Checks for symmetric scaling
assert RegularPolygon((0, 0), 1, 4).scale(2, 2) == \
RegularPolygon(Point2D(0, 0), 2, 4, 0)
def test_bisectors():
p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
p = Polygon(Point(0, 0), Point(2, 0), Point(1, 1), Point(0, 3))
q = Polygon(Point(1, 0), Point(2, 0), Point(3, 3), Point(-1, 5))
poly = Polygon(Point(3, 4), Point(0, 0), Point(8, 7), Point(-1, 1), Point(19, -19))
t = Triangle(p1, p2, p3)
assert t.bisectors()[p2] == Segment(Point(1, 0), Point(0, sqrt(2) - 1))
assert p.bisectors()[Point2D(0, 3)] == Ray2D(Point2D(0, 3), \
Point2D(sin(acos(2*sqrt(5)/5)/2), 3 - cos(acos(2*sqrt(5)/5)/2)))
assert q.bisectors()[Point2D(-1, 5)] == \
Ray2D(Point2D(-1, 5), Point2D(-1 + sqrt(29)*(5*sin(acos(9*sqrt(145)/145)/2) + \
2*cos(acos(9*sqrt(145)/145)/2))/29, sqrt(29)*(-5*cos(acos(9*sqrt(145)/145)/2) + \
2*sin(acos(9*sqrt(145)/145)/2))/29 + 5))
assert poly.bisectors()[Point2D(-1, 1)] == Ray2D(Point2D(-1, 1), \
Point2D(-1 + sin(acos(sqrt(26)/26)/2 + pi/4), 1 - sin(-acos(sqrt(26)/26)/2 + pi/4)))
def test_geometry():
def do_test(*g, s=GeometrySeries, **kwargs):
s1 = _build_series(*g, pt="g", **kwargs)
assert isinstance(s1, s)
# since the range could be None, it is imperative to test that label
# receive the correct value.
assert s1.label == str(g[0])
s2 = _build_series(*g, **kwargs)
assert isinstance(s2, s)
assert s2.label == str(g[0])
assert np.array_equal(s1.get_data(), s2.get_data(), equal_nan=True)
x, y, z = symbols("x, y, z")
do_test(Point2D(1, 2))
do_test(Point3D(1, 2, 3))
do_test(Ray((1, 2), (3, 4)))
do_test(Segment((1, 2), (3, 4)))
do_test(Line((1, 2), (3, 4)), (x, -5, 5))
do_test(Ray3D((1, 2, 3), (3, 4, 5)))
do_test(Segment3D((1, 2, 3), (3, 4, 5)))
do_test(Line3D((1, 2, 3), (3, 4, 5)))
do_test(Polygon((1, 2), 3, n=10))
do_test(Circle((1, 2), 3))
do_test(Ellipse((1, 2), hradius=3, vradius=2))
do_test(Plane((0, 0, 0), (1, 1, 1)), (x, -5, 5), (y, -4, 4), (z, -3, 3),
s=PlaneSeries)
# Interactive series. Note that GeometryInteractiveSeries is an instance of
# GeometrySeries
do_test(Point2D(x, y), params={x: 1, y: 2})
do_test(
Plane((x, y, z), (1, 1, 1)),
(x, -5, 5),
(y, -4, 4),
(z, -3, 3),
params={
x: 1,
y: 2,
z: 3
},
s=PlaneInteractiveSeries,
)
def test_convex_hull():
raises(TypeError, lambda: convex_hull(Point(0, 0), 3))
points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)]
assert convex_hull(*points, **dict(polygon=False)) == ([
Point2D(-5, -2),
Point2D(1, -1),
Point2D(3, -1),
Point2D(15, -4)
], [Point2D(-5, -2), Point2D(15, -4)])
def test_arguments():
"""Functions accepting `Point` objects in `geometry`
should also accept tuples and lists and
automatically convert them to points."""
singles2d = ((1, 2), [1, 2], Point(1, 2))
singles2d2 = ((1, 3), [1, 3], Point(1, 3))
doubles2d = cartes(singles2d, singles2d2)
p2d = Point2D(1, 2)
singles3d = ((1, 2, 3), [1, 2, 3], Point(1, 2, 3))
doubles3d = subsets(singles3d, 2)
p3d = Point3D(1, 2, 3)
singles4d = ((1, 2, 3, 4), [1, 2, 3, 4], Point(1, 2, 3, 4))
doubles4d = subsets(singles4d, 2)
p4d = Point(1, 2, 3, 4)
# test 2D
test_single = [
'distance', 'is_scalar_multiple', 'taxicab_distance', 'midpoint',
'intersection', 'dot', 'equals', '__add__', '__sub__'
]
test_double = ['is_concyclic', 'is_collinear']
for p in singles2d:
Point2D(p)
for func in test_single:
for p in singles2d:
getattr(p2d, func)(p)
for func in test_double:
for p in doubles2d:
getattr(p2d, func)(*p)
# test 3D
test_double = ['is_collinear']
for p in singles3d:
Point3D(p)
for func in test_single:
for p in singles3d:
getattr(p3d, func)(p)
for func in test_double:
for p in doubles3d:
getattr(p3d, func)(*p)
# test 4D
test_double = ['is_collinear']
for p in singles4d:
Point(p)
for func in test_single:
for p in singles4d:
getattr(p4d, func)(p)
for func in test_double:
for p in doubles4d:
getattr(p4d, func)(*p)
# test evaluate=False for ops
x = Symbol('x')
a = Point(0, 1)
assert a + (0.1, x) == Point(0.1, 1 + x, evaluate=False)
a = Point(0, 1)
assert a / 10.0 == Point(0, 0.1, evaluate=False)
a = Point(0, 1)
assert a * 10.0 == Point(0.0, 10.0, evaluate=False)
# test evaluate=False when changing dimensions
u = Point(.1, .2, evaluate=False)
u4 = Point(u, dim=4, on_morph='ignore')
assert u4.args == (.1, .2, 0, 0)
assert all(i.is_Float for i in u4.args[:2])
# and even when *not* changing dimensions
assert all(i.is_Float for i in Point(u).args)
# never raise error if creating an origin
assert Point(dim=3, on_morph='error')
def test_issue_11617():
p1 = Point3D(1, 0, 2)
p2 = Point2D(2, 0)
with warns(UserWarning):
assert p1.distance(p2) == sqrt(5)
def point_from_str(point_str):
x, y = point_str.split(',')
return Point2D(int(x), int(y))
def test_point3D():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
x3 = Symbol('x3', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
y3 = Symbol('y3', real=True)
half = S.Half
p1 = Point3D(x1, x2, x3)
p2 = Point3D(y1, y2, y3)
p3 = Point3D(0, 0, 0)
p4 = Point3D(1, 1, 1)
p5 = Point3D(0, 1, 2)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3)
assert -p2 == Point3D(-y1, -y2, -y3)
assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
assert Point3D.midpoint(p3, p4) == Point3D(half, half, half)
assert Point3D.midpoint(p1,
p4) == Point3D(half + half * x1, half + half * x2,
half + half * x3)
assert Point3D.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point3D.distance(p3, p4) == sqrt(3)
assert Point3D.distance(p1, p1) == 0
assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2)
p1_1 = Point3D(x1, x1, x1)
p1_2 = Point3D(y2, y2, y2)
p1_3 = Point3D(x1 + 1, x1, x1)
Point3D.are_collinear(p3)
assert Point3D.are_collinear(p3, p4)
assert Point3D.are_collinear(p3, p4, p1_1, p1_2)
assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False
assert Point3D.are_collinear(p3, p3, p4, p5) is False
assert p3.intersection(Point3D(0, 0, 0)) == [p3]
assert p3.intersection(p4) == []
assert p4 * 5 == Point3D(5, 5, 5)
assert p4 / 5 == Point3D(0.2, 0.2, 0.2)
assert 5 * p4 == Point3D(5, 5, 5)
raises(ValueError, lambda: Point3D(0, 0, 0) + 10)
# Test coordinate properties
assert p1.coordinates == (x1, x2, x3)
assert p2.coordinates == (y1, y2, y3)
assert p3.coordinates == (0, 0, 0)
assert p4.coordinates == (1, 1, 1)
assert p5.coordinates == (0, 1, 2)
assert p5.x == 0
assert p5.y == 1
assert p5.z == 2
# Point differences should be simplified
assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \
Point3D(0, -1, 1)
a, b, c = S.Half, Rational(1, 3), Rational(1, 4)
assert Point3D(a, b, c).evalf(2) == \
Point(a.n(2), b.n(2), c.n(2), evaluate=False)
raises(ValueError, lambda: Point3D(1, 2, 3) + 1)
# test transformations
p = Point3D(1, 1, 1)
assert p.scale(2, 3) == Point3D(2, 3, 1)
assert p.translate(1, 2) == Point3D(2, 3, 1)
assert p.translate(1) == Point3D(2, 1, 1)
assert p.translate(z=1) == Point3D(1, 1, 2)
assert p.translate(*p.args) == Point3D(2, 2, 2)
# Test __new__
assert Point3D(0.1, 0.2, evaluate=False,
on_morph='ignore').args[0].is_Float
# Test length property returns correctly
assert p.length == 0
assert p1_1.length == 0
assert p1_2.length == 0
# Test are_colinear type error
raises(TypeError, lambda: Point3D.are_collinear(p, x))
# Test are_coplanar
assert Point.are_coplanar()
assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0))
assert Point.are_coplanar((1, 2, 0), (1, 2, 3))
with warns(UserWarning):
raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3)))
assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3))
assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1),
(1, 2, 1)) is False
planar2 = Point3D(1, -1, 1)
planar3 = Point3D(-1, 1, 1)
assert Point3D.are_coplanar(p, planar2, planar3) == True
assert Point3D.are_coplanar(p, planar2, planar3, p3) == False
assert Point.are_coplanar(p, planar2)
planar2 = Point3D(1, 1, 2)
planar3 = Point3D(1, 1, 3)
assert Point3D.are_coplanar(p, planar2, planar3) # line, not plane
plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2))
assert Point.are_coplanar(
*[plane.projection(((-1)**i, i)) for i in range(4)])
# all 2D points are coplanar
assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(
y, x + 2)) is True
# Test Intersection
assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)]
# Test Scale
assert planar2.scale(1, 1, 1) == planar2
assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1)
assert planar2.scale(1, 1, 1, p3) == planar2
# Test Transform
identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
assert p.transform(identity) == p
trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]])
assert p.transform(trans) == Point3D(2, 2, 2)
raises(ValueError, lambda: p.transform(p))
raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
# Test Equals
assert p.equals(x1) == False
# Test __sub__
p_4d = Point(0, 0, 0, 1)
with warns(UserWarning):
assert p - p_4d == Point(1, 1, 1, -1)
p_4d3d = Point(0, 0, 1, 0)
with warns(UserWarning):
assert p - p_4d3d == Point(1, 1, 0, 0)
def test_object_from_equation():
from sympy.abc import x, y, a, b
assert Line(3 * x + y + 18) == Line2D(Point2D(0, -18), Point2D(1, -21))
assert Line(3 * x + 5 * y + 1) == Line2D(Point2D(0, Rational(-1, 5)),
Point2D(1, Rational(-4, 5)))
assert Line(3 * a + b + 18, x="a",
y="b") == Line2D(Point2D(0, -18), Point2D(1, -21))
assert Line(3 * x + y) == Line2D(Point2D(0, 0), Point2D(1, -3))
assert Line(x + y) == Line2D(Point2D(0, 0), Point2D(1, -1))
assert Line(Eq(3 * a + b, -18), x="a",
y=b) == Line2D(Point2D(0, -18), Point2D(1, -21))
raises(ValueError, lambda: Line(x))
raises(ValueError, lambda: Line(y))
raises(ValueError, lambda: Line(x / y))
raises(ValueError, lambda: Line(a / b, x="a", y="b"))
raises(ValueError, lambda: Line(y / x))
raises(ValueError, lambda: Line(b / a, x="a", y="b"))
raises(ValueError, lambda: Line((x + 1)**2 + y))
def test_point3D():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
x1 = Symbol('x1', real=True)
x2 = Symbol('x2', real=True)
x3 = Symbol('x3', real=True)
y1 = Symbol('y1', real=True)
y2 = Symbol('y2', real=True)
y3 = Symbol('y3', real=True)
half = Rational(1, 2)
p1 = Point3D(x1, x2, x3)
p2 = Point3D(y1, y2, y3)
p3 = Point3D(0, 0, 0)
p4 = Point3D(1, 1, 1)
p5 = Point3D(0, 1, 2)
assert p1 in p1
assert p1 not in p2
assert p2.y == y2
assert (p3 + p4) == p4
assert (p2 - p1) == Point3D(y1 - x1, y2 - x2, y3 - x3)
assert p4*5 == Point3D(5, 5, 5)
assert -p2 == Point3D(-y1, -y2, -y3)
assert Point(34.05, sqrt(3)) == Point(Rational(681, 20), sqrt(3))
assert Point3D.midpoint(p3, p4) == Point3D(half, half, half)
assert Point3D.midpoint(p1, p4) == Point3D(half + half*x1, half + half*x2,
half + half*x3)
assert Point3D.midpoint(p2, p2) == p2
assert p2.midpoint(p2) == p2
assert Point3D.distance(p3, p4) == sqrt(3)
assert Point3D.distance(p1, p1) == 0
assert Point3D.distance(p3, p2) == sqrt(p2.x**2 + p2.y**2 + p2.z**2)
p1_1 = Point3D(x1, x1, x1)
p1_2 = Point3D(y2, y2, y2)
p1_3 = Point3D(x1 + 1, x1, x1)
Point3D.are_collinear(p3)
assert Point3D.are_collinear(p3, p4)
assert Point3D.are_collinear(p3, p4, p1_1, p1_2)
assert Point3D.are_collinear(p3, p4, p1_1, p1_3) is False
assert Point3D.are_collinear(p3, p3, p4, p5) is False
assert p3.intersection(Point3D(0, 0, 0)) == [p3]
assert p3.intersection(p4) == []
assert p4 * 5 == Point3D(5, 5, 5)
assert p4 / 5 == Point3D(0.2, 0.2, 0.2)
raises(ValueError, lambda: Point3D(0, 0, 0) + 10)
# Point differences should be simplified
assert Point3D(x*(x - 1), y, 2) - Point3D(x**2 - x, y + 1, 1) == \
Point3D(0, -1, 1)
a, b = Rational(1, 2), Rational(1, 3)
assert Point(a, b).evalf(2) == \
Point(a.n(2), b.n(2))
raises(ValueError, lambda: Point(1, 2) + 1)
# test transformations
p = Point3D(1, 1, 1)
assert p.scale(2, 3) == Point3D(2, 3, 1)
assert p.translate(1, 2) == Point3D(2, 3, 1)
assert p.translate(1) == Point3D(2, 1, 1)
assert p.translate(z=1) == Point3D(1, 1, 2)
assert p.translate(*p.args) == Point3D(2, 2, 2)
# Test __new__
assert Point3D(0.1, 0.2, evaluate=False, on_morph='ignore').args[0].is_Float
# Test length property returns correctly
assert p.length == 0
assert p1_1.length == 0
assert p1_2.length == 0
# Test are_colinear type error
raises(TypeError, lambda: Point3D.are_collinear(p, x))
# Test are_coplanar
assert Point.are_coplanar()
assert Point.are_coplanar((1, 2, 0), (1, 2, 0), (1, 3, 0))
assert Point.are_coplanar((1, 2, 0), (1, 2, 3))
with warnings.catch_warnings(record=True) as w:
raises(ValueError, lambda: Point2D.are_coplanar((1, 2), (1, 2, 3)))
assert Point3D.are_coplanar((1, 2, 0), (1, 2, 3))
assert Point.are_coplanar((0, 0, 0), (1, 1, 0), (1, 1, 1), (1, 2, 1)) is False
planar2 = Point3D(1, -1, 1)
planar3 = Point3D(-1, 1, 1)
assert Point3D.are_coplanar(p, planar2, planar3) == True
assert Point3D.are_coplanar(p, planar2, planar3, p3) == False
assert Point.are_coplanar(p, planar2)
planar2 = Point3D(1, 1, 2)
planar3 = Point3D(1, 1, 3)
assert Point3D.are_coplanar(p, planar2, planar3) # line, not plane
plane = Plane((1, 2, 1), (2, 1, 0), (3, 1, 2))
assert Point.are_coplanar(*[plane.projection(((-1)**i, i)) for i in range(4)])
# all 2D points are coplanar
assert Point.are_coplanar(Point(x, y), Point(x, x + y), Point(y, x + 2)) is True
# Test Intersection
assert planar2.intersection(Line3D(p, planar3)) == [Point3D(1, 1, 2)]
# Test Scale
assert planar2.scale(1, 1, 1) == planar2
assert planar2.scale(2, 2, 2, planar3) == Point3D(1, 1, 1)
assert planar2.scale(1, 1, 1, p3) == planar2
# Test Transform
identity = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
assert p.transform(identity) == p
trans = Matrix([[1, 0, 0, 1], [0, 1, 0, 1], [0, 0, 1, 1], [0, 0, 0, 1]])
assert p.transform(trans) == Point3D(2, 2, 2)
raises(ValueError, lambda: p.transform(p))
raises(ValueError, lambda: p.transform(Matrix([[1, 0], [0, 1]])))
# Test Equals
assert p.equals(x1) == False
# Test __sub__
p_4d = Point(0, 0, 0, 1)
with warnings.catch_warnings(record=True) as w:
assert p - p_4d == Point(1, 1, 1, -1)
assert len(w) == 1
p_4d3d = Point(0, 0, 1, 0)
with warnings.catch_warnings(record=True) as w:
assert p - p_4d3d == Point(1, 1, 0, 0)
assert len(w) == 1
def test_cross_section():
I = Symbol('I')
l = Symbol('l')
E = Symbol('E')
C3, C4 = symbols('C3, C4')
a, c, g, h, r, n = symbols('a, c, g, h, r, n')
# test for second_moment and cross_section setter
b0 = Beam(l, E, I)
assert b0.second_moment == I
assert b0.cross_section == None
b0.cross_section = Circle((0, 0), 5)
assert b0.second_moment == pi*Rational(625, 4)
assert b0.cross_section == Circle((0, 0), 5)
b0.second_moment = 2*n - 6
assert b0.second_moment == 2*n-6
assert b0.cross_section == None
with raises(ValueError):
b0.second_moment = Circle((0, 0), 5)
# beam with a circular cross-section
b1 = Beam(50, E, Circle((0, 0), r))
assert b1.cross_section == Circle((0, 0), r)
assert b1.second_moment == pi*r*Abs(r)**3/4
b1.apply_load(-10, 0, -1)
b1.apply_load(R1, 5, -1)
b1.apply_load(R2, 50, -1)
b1.apply_load(90, 45, -2)
b1.solve_for_reaction_loads(R1, R2)
assert b1.load == (-10*SingularityFunction(x, 0, -1) + 82*SingularityFunction(x, 5, -1)/S(9)
+ 90*SingularityFunction(x, 45, -2) + 8*SingularityFunction(x, 50, -1)/9)
assert b1.bending_moment() == (-10*SingularityFunction(x, 0, 1) + 82*SingularityFunction(x, 5, 1)/9
+ 90*SingularityFunction(x, 45, 0) + 8*SingularityFunction(x, 50, 1)/9)
q = (-5*SingularityFunction(x, 0, 2) + 41*SingularityFunction(x, 5, 2)/S(9)
+ 90*SingularityFunction(x, 45, 1) + 4*SingularityFunction(x, 50, 2)/S(9))/(pi*E*r*Abs(r)**3)
assert b1.slope() == C3 + 4*q
q = (-5*SingularityFunction(x, 0, 3)/3 + 41*SingularityFunction(x, 5, 3)/27 + 45*SingularityFunction(x, 45, 2)
+ 4*SingularityFunction(x, 50, 3)/27)/(pi*E*r*Abs(r)**3)
assert b1.deflection() == C3*x + C4 + 4*q
# beam with a recatangular cross-section
b2 = Beam(20, E, Polygon((0, 0), (a, 0), (a, c), (0, c)))
assert b2.cross_section == Polygon((0, 0), (a, 0), (a, c), (0, c))
assert b2.second_moment == a*c**3/12
# beam with a triangular cross-section
b3 = Beam(15, E, Triangle((0, 0), (g, 0), (g/2, h)))
assert b3.cross_section == Triangle(Point2D(0, 0), Point2D(g, 0), Point2D(g/2, h))
assert b3.second_moment == g*h**3/36
# composite beam
b = b2.join(b3, "fixed")
b.apply_load(-30, 0, -1)
b.apply_load(65, 0, -2)
b.apply_load(40, 0, -1)
b.bc_slope = [(0, 0)]
b.bc_deflection = [(0, 0)]
assert b.second_moment == Piecewise((a*c**3/12, x <= 20), (g*h**3/36, x <= 35))
assert b.cross_section == None
assert b.length == 35
assert b.slope().subs(x, 7) == 8400/(E*a*c**3)
assert b.slope().subs(x, 25) == 52200/(E*g*h**3) + 39600/(E*a*c**3)
assert b.deflection().subs(x, 30) == 537000/(E*g*h**3) + 712000/(E*a*c**3)
def test_cut_section():
# concave polygon
p = Polygon((-1, -1), (1, S(5)/2), (2, 1), (3, S(5)/2), (4, 2), (5, 3), (-1, 3))
l = Line((0, 0), (S(9)/2, 3))
p1 = p.cut_section(l)[0]
p2 = p.cut_section(l)[1]
assert p1 == Polygon(
Point2D(-S(9)/13, -S(6)/13), Point2D(1, S(5)/2), Point2D(S(24)/13, S(16)/13),
Point2D(S(12)/5, S(8)/5), Point2D(3, S(5)/2), Point2D(S(24)/7, S(16)/7),
Point2D(S(9)/2, 3), Point2D(-1, 3), Point2D(-1, -S(2)/3))
assert p2 == Polygon(Point2D(-1, -1), Point2D(-S(9)/13, -S(6)/13), Point2D(S(24)/13, S(16)/13),
Point2D(2, 1), Point2D(S(12)/5, S(8)/5), Point2D(S(24)/7, S(16)/7), Point2D(4, 2), Point2D(5, 3),
Point2D(S(9)/2, 3), Point2D(-1, -S(2)/3))
# convex polygon
p = RegularPolygon(Point2D(0,0), 6, 6)
s = p.cut_section(Line((0, 0), slope=1))
assert s[0] == Polygon(Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9), Point2D(3, 3*sqrt(3)),
Point2D(-3, 3*sqrt(3)), Point2D(-6, 0), Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3)))
assert s[1] == Polygon(Point2D(6, 0), Point2D(-3*sqrt(3) + 9, -3*sqrt(3) + 9),
Point2D(-9 + 3*sqrt(3), -9 + 3*sqrt(3)), Point2D(-3, -3*sqrt(3)), Point2D(3, -3*sqrt(3)))
# case where line does not intersects but coincides with the edge of polygon
a, b = 20, 10
t1, t2, t3, t4 = [(0, b), (0, 0), (a, 0), (a, b)]
p = Polygon(t1, t2, t3, t4)
p1, p2 = p.cut_section(Line((0, b), slope=0))
assert p1 == None
assert p2 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10))
p3, p4 = p.cut_section(Line((0, 0), slope=0))
assert p3 == Polygon(Point2D(0, 10), Point2D(0, 0), Point2D(20, 0), Point2D(20, 10))
assert p4 == None
def test_nine_point_circle():
assert Triangle(Point(0, 0), Point(1, 0), Point(0, 1)).nine_point_circle \
== Circle(Point2D(S(1)/4, S(1)/4), sqrt(2)/4)
