Vehicle-cpp/hkpc/software/sympy/geometry/tests/test_curve.py

from sympy.core.containers import Tuple
from sympy.core.numbers import (Rational, pi)
from sympy.core.singleton import S
from sympy.core.symbol import (Symbol, symbols)
from sympy.functions.elementary.hyperbolic import asinh
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon
from sympy.testing.pytest import raises, slow


def test_curve():
    x = Symbol('x', real=True)
    s = Symbol('s')
    z = Symbol('z')

    # this curve is independent of the indicated parameter
    c = Curve([2*s, s**2], (z, 0, 2))

    assert c.parameter == z
    assert c.functions == (2*s, s**2)
    assert c.arbitrary_point() == Point(2*s, s**2)
    assert c.arbitrary_point(z) == Point(2*s, s**2)

    # this is how it is normally used
    c = Curve([2*s, s**2], (s, 0, 2))

    assert c.parameter == s
    assert c.functions == (2*s, s**2)
    t = Symbol('t')
    # the t returned as assumptions
    assert c.arbitrary_point() != Point(2*t, t**2)
    t = Symbol('t', real=True)
    # now t has the same assumptions so the test passes
    assert c.arbitrary_point() == Point(2*t, t**2)
    assert c.arbitrary_point(z) == Point(2*z, z**2)
    assert c.arbitrary_point(c.parameter) == Point(2*s, s**2)
    assert c.arbitrary_point(None) == Point(2*s, s**2)
    assert c.plot_interval() == [t, 0, 2]
    assert c.plot_interval(z) == [z, 0, 2]

    assert Curve([x, x], (x, 0, 1)).rotate(pi/2) == Curve([-x, x], (x, 0, 1))
    assert Curve([x, x], (x, 0, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
        1, 3).arbitrary_point(s) == \
        Line((0, 0), (1, 1)).rotate(pi/2, (1, 2)).scale(2, 3).translate(
            1, 3).arbitrary_point(s) == \
        Point(-2*s + 7, 3*s + 6)

    raises(ValueError, lambda: Curve((s), (s, 1, 2)))
    raises(ValueError, lambda: Curve((x, x * 2), (1, x)))

    raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point())
    raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s))


@slow
def test_free_symbols():
    a, b, c, d, e, f, s = symbols('a:f,s')
    assert Point(a, b).free_symbols == {a, b}
    assert Line((a, b), (c, d)).free_symbols == {a, b, c, d}
    assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d}
    assert Ray((a, b), angle=c).free_symbols == {a, b, c}
    assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d}
    assert Line((a, b), slope=c).free_symbols == {a, b, c}
    assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d}
    assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d}
    assert Ellipse((a, b), c, eccentricity=d).free_symbols == \
        {a, b, c, d}
    assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \
        {a, b, c, d}
    assert Circle((a, b), c).free_symbols == {a, b, c}
    assert Circle((a, b), (c, d), (e, f)).free_symbols == \
        {e, d, c, b, f, a}
    assert Polygon((a, b), (c, d), (e, f)).free_symbols == \
        {e, b, d, f, a, c}
    assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d}


def test_transform():
    x = Symbol('x', real=True)
    y = Symbol('y', real=True)
    c = Curve((x, x**2), (x, 0, 1))
    cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1))
    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 c.scale(2, 3, (4, 5)) == cout
    assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts
    assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out
    assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \
        Curve((x + S.Half, 3*x), (x, 0, 1))
    assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \
        Curve((x + 4, 3*x + 5), (x, 0, 1))


def test_length():
    t = Symbol('t', real=True)

    c1 = Curve((t, 0), (t, 0, 1))
    assert c1.length == 1

    c2 = Curve((t, t), (t, 0, 1))
    assert c2.length == sqrt(2)

    c3 = Curve((t ** 2, t), (t, 2, 5))
    assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2


def test_parameter_value():
    t = Symbol('t')
    C = Curve([2*t, t**2], (t, 0, 2))
    assert C.parameter_value((2, 1), t) == {t: 1}
    raises(ValueError, lambda: C.parameter_value((2, 0), t))


def test_issue_17997():
    t, s = symbols('t s')
    c = Curve((t, t**2), (t, 0, 10))
    p = Curve([2*s, s**2], (s, 0, 2))
    assert c(2) == Point(2, 4)
    assert p(1) == Point(2, 1)