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152 lines
6.1 KiB
152 lines
6.1 KiB
from sympy.core.function import (Derivative, Function)
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from sympy.core.singleton import S
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from sympy.core.symbol import Symbol
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from sympy.functions import exp, cos, sin, tan, cosh, sinh
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.geometry import Point, Point2D, Line, Polygon, Segment, convex_hull,\
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intersection, centroid, Point3D, Line3D
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from sympy.geometry.util import idiff, closest_points, farthest_points, _ordered_points, are_coplanar
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from sympy.solvers.solvers import solve
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from sympy.testing.pytest import raises
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def test_idiff():
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x = Symbol('x', real=True)
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y = Symbol('y', real=True)
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t = Symbol('t', real=True)
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f = Function('f')
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g = Function('g')
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# the use of idiff in ellipse also provides coverage
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circ = x**2 + y**2 - 4
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ans = -3*x*(x**2/y**2 + 1)/y**3
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assert ans == idiff(circ, y, x, 3), idiff(circ, y, x, 3)
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assert ans == idiff(circ, [y], x, 3)
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assert idiff(circ, y, x, 3) == ans
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explicit = 12*x/sqrt(-x**2 + 4)**5
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assert ans.subs(y, solve(circ, y)[0]).equals(explicit)
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assert True in [sol.diff(x, 3).equals(explicit) for sol in solve(circ, y)]
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assert idiff(x + t + y, [y, t], x) == -Derivative(t, x) - 1
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assert idiff(f(x) * exp(f(x)) - x * exp(x), f(x), x) == (x + 1)*exp(x)*exp(-f(x))/(f(x) + 1)
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assert idiff(f(x) - y * exp(x), [f(x), y], x) == (y + Derivative(y, x))*exp(x)
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assert idiff(f(x) - y * exp(x), [y, f(x)], x) == -y + Derivative(f(x), x)*exp(-x)
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assert idiff(f(x) - g(x), [f(x), g(x)], x) == Derivative(g(x), x)
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# this should be fast
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fxy = y - (-10*(-sin(x) + 1/x)**2 + tan(x)**2 + 2*cosh(x/10))
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assert idiff(fxy, y, x) == -20*sin(x)*cos(x) + 2*tan(x)**3 + \
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2*tan(x) + sinh(x/10)/5 + 20*cos(x)/x - 20*sin(x)/x**2 + 20/x**3
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def test_intersection():
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assert intersection(Point(0, 0)) == []
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raises(TypeError, lambda: intersection(Point(0, 0), 3))
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assert intersection(
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Segment((0, 0), (2, 0)),
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Segment((-1, 0), (1, 0)),
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Line((0, 0), (0, 1)), pairwise=True) == [
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Point(0, 0), Segment((0, 0), (1, 0))]
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assert intersection(
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Line((0, 0), (0, 1)),
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Segment((0, 0), (2, 0)),
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Segment((-1, 0), (1, 0)), pairwise=True) == [
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Point(0, 0), Segment((0, 0), (1, 0))]
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assert intersection(
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Line((0, 0), (0, 1)),
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Segment((0, 0), (2, 0)),
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Segment((-1, 0), (1, 0)),
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Line((0, 0), slope=1), pairwise=True) == [
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Point(0, 0), Segment((0, 0), (1, 0))]
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def test_convex_hull():
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raises(TypeError, lambda: convex_hull(Point(0, 0), 3))
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points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)]
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assert convex_hull(*points, **{"polygon": False}) == (
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[Point2D(-5, -2), Point2D(1, -1), Point2D(3, -1), Point2D(15, -4)],
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[Point2D(-5, -2), Point2D(15, -4)])
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def test_centroid():
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p = Polygon((0, 0), (10, 0), (10, 10))
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q = p.translate(0, 20)
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assert centroid(p, q) == Point(20, 40)/3
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p = Segment((0, 0), (2, 0))
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q = Segment((0, 0), (2, 2))
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assert centroid(p, q) == Point(1, -sqrt(2) + 2)
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assert centroid(Point(0, 0), Point(2, 0)) == Point(2, 0)/2
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assert centroid(Point(0, 0), Point(0, 0), Point(2, 0)) == Point(2, 0)/3
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def test_farthest_points_closest_points():
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from sympy.core.random import randint
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from sympy.utilities.iterables import subsets
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for how in (min, max):
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if how == min:
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func = closest_points
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else:
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func = farthest_points
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raises(ValueError, lambda: func(Point2D(0, 0), Point2D(0, 0)))
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# 3rd pt dx is close and pt is closer to 1st pt
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p1 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 1)]
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# 3rd pt dx is close and pt is closer to 2nd pt
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p2 = [Point2D(0, 0), Point2D(3, 0), Point2D(2, 1)]
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# 3rd pt dx is close and but pt is not closer
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p3 = [Point2D(0, 0), Point2D(3, 0), Point2D(1, 10)]
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# 3rd pt dx is not closer and it's closer to 2nd pt
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p4 = [Point2D(0, 0), Point2D(3, 0), Point2D(4, 0)]
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# 3rd pt dx is not closer and it's closer to 1st pt
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p5 = [Point2D(0, 0), Point2D(3, 0), Point2D(-1, 0)]
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# duplicate point doesn't affect outcome
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dup = [Point2D(0, 0), Point2D(3, 0), Point2D(3, 0), Point2D(-1, 0)]
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# symbolic
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x = Symbol('x', positive=True)
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s = [Point2D(a) for a in ((x, 1), (x + 3, 2), (x + 2, 2))]
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for points in (p1, p2, p3, p4, p5, dup, s):
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d = how(i.distance(j) for i, j in subsets(set(points), 2))
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ans = a, b = list(func(*points))[0]
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assert a.distance(b) == d
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assert ans == _ordered_points(ans)
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# if the following ever fails, the above tests were not sufficient
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# and the logical error in the routine should be fixed
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points = set()
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while len(points) != 7:
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points.add(Point2D(randint(1, 100), randint(1, 100)))
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points = list(points)
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d = how(i.distance(j) for i, j in subsets(points, 2))
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ans = a, b = list(func(*points))[0]
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assert a.distance(b) == d
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assert ans == _ordered_points(ans)
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# equidistant points
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a, b, c = (
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Point2D(0, 0), Point2D(1, 0), Point2D(S.Half, sqrt(3)/2))
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ans = {_ordered_points((i, j))
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for i, j in subsets((a, b, c), 2)}
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assert closest_points(b, c, a) == ans
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assert farthest_points(b, c, a) == ans
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# unique to farthest
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points = [(1, 1), (1, 2), (3, 1), (-5, 2), (15, 4)]
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assert farthest_points(*points) == {
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(Point2D(-5, 2), Point2D(15, 4))}
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points = [(1, -1), (1, -2), (3, -1), (-5, -2), (15, -4)]
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assert farthest_points(*points) == {
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(Point2D(-5, -2), Point2D(15, -4))}
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assert farthest_points((1, 1), (0, 0)) == {
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(Point2D(0, 0), Point2D(1, 1))}
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raises(ValueError, lambda: farthest_points((1, 1)))
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def test_are_coplanar():
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a = Line3D(Point3D(5, 0, 0), Point3D(1, -1, 1))
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b = Line3D(Point3D(0, -2, 0), Point3D(3, 1, 1))
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c = Line3D(Point3D(0, -1, 0), Point3D(5, -1, 9))
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d = Line(Point2D(0, 3), Point2D(1, 5))
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assert are_coplanar(a, b, c) == False
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assert are_coplanar(a, d) == False
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