121 lines
4.4 KiB
Python
121 lines
4.4 KiB
Python
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from sympy.core.containers import Tuple
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from sympy.core.numbers import (Rational, pi)
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from sympy.core.singleton import S
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.functions.elementary.hyperbolic import asinh
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon
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from sympy.testing.pytest import raises, slow
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def test_curve():
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x = Symbol('x', real=True)
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s = Symbol('s')
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z = Symbol('z')
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# this curve is independent of the indicated parameter
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c = Curve([2*s, s**2], (z, 0, 2))
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assert c.parameter == z
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assert c.functions == (2*s, s**2)
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assert c.arbitrary_point() == Point(2*s, s**2)
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assert c.arbitrary_point(z) == Point(2*s, s**2)
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# this is how it is normally used
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c = Curve([2*s, s**2], (s, 0, 2))
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assert c.parameter == s
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assert c.functions == (2*s, s**2)
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t = Symbol('t')
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# the t returned as assumptions
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assert c.arbitrary_point() != Point(2*t, t**2)
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t = Symbol('t', real=True)
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# now t has the same assumptions so the test passes
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assert c.arbitrary_point() == Point(2*t, t**2)
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assert c.arbitrary_point(z) == Point(2*z, z**2)
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assert c.arbitrary_point(c.parameter) == Point(2*s, s**2)
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assert c.arbitrary_point(None) == Point(2*s, s**2)
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assert c.plot_interval() == [t, 0, 2]
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assert c.plot_interval(z) == [z, 0, 2]
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assert Curve([x, x], (x, 0, 1)).rotate(pi/2) == Curve([-x, x], (x, 0, 1))
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assert Curve([x, x], (x, 0, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
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1, 3).arbitrary_point(s) == \
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Line((0, 0), (1, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
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1, 3).arbitrary_point(s) == \
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Point(-2*s + 7, 3*s + 6)
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raises(ValueError, lambda: Curve((s), (s, 1, 2)))
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raises(ValueError, lambda: Curve((x, x * 2), (1, x)))
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raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point())
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raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s))
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@slow
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def test_free_symbols():
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a, b, c, d, e, f, s = symbols('a:f,s')
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assert Point(a, b).free_symbols == {a, b}
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assert Line((a, b), (c, d)).free_symbols == {a, b, c, d}
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assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d}
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assert Ray((a, b), angle=c).free_symbols == {a, b, c}
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assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d}
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assert Line((a, b), slope=c).free_symbols == {a, b, c}
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assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d}
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assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d}
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assert Ellipse((a, b), c, eccentricity=d).free_symbols == \
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{a, b, c, d}
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assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \
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{a, b, c, d}
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assert Circle((a, b), c).free_symbols == {a, b, c}
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assert Circle((a, b), (c, d), (e, f)).free_symbols == \
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{e, d, c, b, f, a}
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assert Polygon((a, b), (c, d), (e, f)).free_symbols == \
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{e, b, d, f, a, c}
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assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d}
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def test_transform():
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x = Symbol('x', real=True)
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y = Symbol('y', real=True)
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c = Curve((x, x**2), (x, 0, 1))
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cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1))
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pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)]
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pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)]
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assert c.scale(2, 3, (4, 5)) == cout
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assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts
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assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out
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assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \
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Curve((x + S.Half, 3*x), (x, 0, 1))
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assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \
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Curve((x + 4, 3*x + 5), (x, 0, 1))
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def test_length():
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t = Symbol('t', real=True)
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c1 = Curve((t, 0), (t, 0, 1))
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assert c1.length == 1
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c2 = Curve((t, t), (t, 0, 1))
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assert c2.length == sqrt(2)
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c3 = Curve((t ** 2, t), (t, 2, 5))
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assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2
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def test_parameter_value():
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t = Symbol('t')
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C = Curve([2*t, t**2], (t, 0, 2))
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assert C.parameter_value((2, 1), t) == {t: 1}
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raises(ValueError, lambda: C.parameter_value((2, 0), t))
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def test_issue_17997():
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t, s = symbols('t s')
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c = Curve((t, t**2), (t, 0, 10))
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p = Curve([2*s, s**2], (s, 0, 2))
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assert c(2) == Point(2, 4)
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assert p(1) == Point(2, 1)
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