def __new__(cls, focus=None, directrix=None, **kwargs): if focus: focus = Point(focus, dim=2) else: focus = Point(0, 0) directrix = Line(directrix) if directrix.contains(focus): raise ValueError('The focus must not be a point of directrix') return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
def __new__(cls, focus=None, directrix=None, **kwargs): if focus: focus = Point(focus, dim=2) else: focus = Point(0, 0) directrix = Line(directrix) if (directrix.slope != 0 and directrix.slope != S.Infinity): raise NotImplementedError('The directrix must be a horizontal' ' or vertical line') if directrix.contains(focus): raise ValueError('The focus must not be a point of directrix') return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
def __new__(cls, focus=None, directrix=None, **kwargs): if focus: focus = Point(focus, dim=2) else: focus = Point(0, 0) directrix = Line(directrix) if (directrix.slope != 0 and directrix.slope != S.Infinity): raise NotImplementedError('The directrix must be a horizontal' ' or vertical line') if directrix.contains(focus): raise ValueError('The focus must not be a point of directrix') return GeometryEntity.__new__(cls, focus, directrix, **kwargs)
def test_geometry(): p1 = Point(1, 2) p2 = Point(2, 3) p3 = Point(0, 0) p4 = Point(0, 1) for c in ( GeometryEntity, GeometryEntity(), Point, p1, Circle, Circle(p1, 2), Ellipse, Ellipse(p1, 3, 4), Line, Line(p1, p2), LinearEntity, LinearEntity(p1, p2), Ray, Ray(p1, p2), Segment, Segment(p1, p2), Polygon, Polygon(p1, p2, p3, p4), RegularPolygon, RegularPolygon(p1, 4, 5), Triangle, Triangle(p1, p2, p3), ): check(c, check_attr=False)
def test_parabola_intersection(): l1 = Line(Point(1, -2), Point(-1, -2)) l2 = Line(Point(1, 2), Point(-1, 2)) l3 = Line(Point(1, 0), Point(-1, 0)) p1 = Point(0, 0) p2 = Point(0, -2) p3 = Point(120, -12) parabola1 = Parabola(p1, l1) # parabola with parabola assert parabola1.intersection(parabola1) == [parabola1] assert parabola1.intersection(Parabola( p1, l2)) == [Point2D(-2, 0), Point2D(2, 0)] assert parabola1.intersection(Parabola(p2, l3)) == [Point2D(0, -1)] assert parabola1.intersection(Parabola(Point(16, 0), l1)) == [Point2D(8, 15)] assert parabola1.intersection(Parabola(Point( 0, 16), l1)) == [Point2D(-6, 8), Point2D(6, 8)] assert parabola1.intersection(Parabola(p3, l3)) == [] # parabola with point assert parabola1.intersection(p1) == [] assert parabola1.intersection(Point2D(0, -1)) == [Point2D(0, -1)] assert parabola1.intersection(Point2D(4, 3)) == [Point2D(4, 3)] # parabola with line assert parabola1.intersection(Line(Point2D(-7, 3), Point( 12, 3))) == [Point2D(-4, 3), Point2D(4, 3)] assert parabola1.intersection(Line(Point(-4, -1), Point(4, -1))) == [Point(0, -1)] assert parabola1.intersection(Line(Point(2, 0), Point(0, -2))) == [Point2D(2, 0)] raises( TypeError, lambda: parabola1.intersection(Line(Point(0, 0, 0), Point(1, 1, 1)))) # parabola with segment assert parabola1.intersection(Segment2D( (-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)] assert parabola1.intersection(Segment2D((0, -5), (0, 6))) == [Point2D(0, -1)] assert parabola1.intersection(Segment2D((-12, -65), (14, -68))) == [] # parabola with ray assert parabola1.intersection(Ray2D( (-4, -5), (4, 3))) == [Point2D(0, -1), Point2D(4, 3)] assert parabola1.intersection(Ray2D( (0, 7), (1, 14))) == [Point2D(14 + 2 * sqrt(57), 105 + 14 * sqrt(57))] assert parabola1.intersection(Ray2D((0, 7), (0, 14))) == [] # parabola with ellipse/circle assert parabola1.intersection(Circle( p1, 2)) == [Point2D(-2, 0), Point2D(2, 0)] assert parabola1.intersection(Circle( p2, 1)) == [Point2D(0, -1), Point2D(0, -1)] assert parabola1.intersection(Ellipse( p2, 2, 1)) == [Point2D(0, -1), Point2D(0, -1)] assert parabola1.intersection(Ellipse(Point(0, 19), 5, 7)) == [] assert parabola1.intersection(Ellipse((0, 3), 12, 4)) == \ [Point2D(0, -1), Point2D(0, -1), Point2D(-4*sqrt(17)/3, Rational(59, 9)), Point2D(4*sqrt(17)/3, Rational(59, 9))] # parabola with unsupported type raises(TypeError, lambda: parabola1.intersection(2))
def test_geometry(): p1 = Point(1, 2) p2 = Point(2, 3) p3 = Point(0, 0) p4 = Point(0, 1) for c in (GeometryEntity, GeometryEntity(), Point, p1, Circle, Circle(p1, 2), Ellipse, Ellipse(p1, 3, 4), Line, Line(p1, p2), LinearEntity, LinearEntity(p1, p2), Ray, Ray(p1, p2), Segment, Segment(p1, p2), Polygon, Polygon(p1, p2, p3, p4), RegularPolygon, RegularPolygon(p1, 4, 5), Triangle): # XXX: Instance of Triangle hangs because of hasattr in check(). # Triangle(p1,p2,p3) check(c) pass
def test_parabola_geom(): a, b = symbols('a b') p1 = Point(0, 0) p2 = Point(3, 7) p3 = Point(0, 4) p4 = Point(6, 0) p5 = Point(a, a) d1 = Line(Point(4, 0), Point(4, 9)) d2 = Line(Point(7, 6), Point(3, 6)) d3 = Line(Point(4, 0), slope=oo) d4 = Line(Point(7, 6), slope=0) d5 = Line(Point(b, a), slope=oo) d6 = Line(Point(a, b), slope=0) half = S.Half pa1 = Parabola(None, d2) pa2 = Parabola(directrix=d1) pa3 = Parabola(p1, d1) pa4 = Parabola(p2, d2) pa5 = Parabola(p2, d4) pa6 = Parabola(p3, d2) pa7 = Parabola(p2, d1) pa8 = Parabola(p4, d1) pa9 = Parabola(p4, d3) pa10 = Parabola(p5, d5) pa11 = Parabola(p5, d6) d = Line(Point(3, 7), Point(2, 9)) pa12 = Parabola(Point(7, 8), d) pa12r = Parabola(Point(7, 8).reflect(d), d) raises(ValueError, lambda: Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7)))) raises(ValueError, lambda: Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2)))) raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8))) # Basic Stuff assert pa1.focus == Point(0, 0) assert pa1.ambient_dimension == S(2) assert pa2 == pa3 assert pa4 != pa7 assert pa6 != pa7 assert pa6.focus == Point2D(0, 4) assert pa6.focal_length == 1 assert pa6.p_parameter == -1 assert pa6.vertex == Point2D(0, 5) assert pa6.eccentricity == 1 assert pa7.focus == Point2D(3, 7) assert pa7.focal_length == half assert pa7.p_parameter == -half assert pa7.vertex == Point2D(7 * half, 7) assert pa4.focal_length == half assert pa4.p_parameter == half assert pa4.vertex == Point2D(3, 13 * half) assert pa8.focal_length == 1 assert pa8.p_parameter == 1 assert pa8.vertex == Point2D(5, 0) assert pa4.focal_length == pa5.focal_length assert pa4.p_parameter == pa5.p_parameter assert pa4.vertex == pa5.vertex assert pa4.equation() == pa5.equation() assert pa8.focal_length == pa9.focal_length assert pa8.p_parameter == pa9.p_parameter assert pa8.vertex == pa9.vertex assert pa8.equation() == pa9.equation() assert pa10.focal_length == pa11.focal_length == sqrt( (a - b)**2) / 2 # if a, b real == abs(a - b)/2 assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point( a, a - sqrt( (a - b)**2) * sign(a - b) / 2) # change axis x->y, y->x on pa10 aos = pa12.axis_of_symmetry assert aos == Line(Point(7, 8), Point(5, 7)) assert pa12.directrix == Line(Point(3, 7), Point(2, 9)) assert pa12.directrix.angle_between(aos) == S.Pi / 2 assert pa12.eccentricity == 1 assert pa12.equation( x, y) == (x - 7)**2 + (y - 8)**2 - (-2 * x - y + 13)**2 / 5 assert pa12.focal_length == 9 * sqrt(5) / 10 assert pa12.focus == Point(7, 8) assert pa12.p_parameter == 9 * sqrt(5) / 10 assert pa12.vertex == Point2D(S(26) / 5, S(71) / 10) assert pa12r.focal_length == 9 * sqrt(5) / 10 assert pa12r.focus == Point(-S(1) / 5, S(22) / 5) assert pa12r.p_parameter == -9 * sqrt(5) / 10 assert pa12r.vertex == Point(S(8) / 5, S(53) / 10)
def test_parabola_geom(): a, b = symbols('a b') p1 = Point(0, 0) p2 = Point(3, 7) p3 = Point(0, 4) p4 = Point(6, 0) p5 = Point(a, a) d1 = Line(Point(4, 0), Point(4, 9)) d2 = Line(Point(7, 6), Point(3, 6)) d3 = Line(Point(4, 0), slope=oo) d4 = Line(Point(7, 6), slope=0) d5 = Line(Point(b, a), slope=oo) d6 = Line(Point(a, b), slope=0) half = S.Half pa1 = Parabola(None, d2) pa2 = Parabola(directrix=d1) pa3 = Parabola(p1, d1) pa4 = Parabola(p2, d2) pa5 = Parabola(p2, d4) pa6 = Parabola(p3, d2) pa7 = Parabola(p2, d1) pa8 = Parabola(p4, d1) pa9 = Parabola(p4, d3) pa10 = Parabola(p5, d5) pa11 = Parabola(p5, d6) raises(ValueError, lambda: Parabola(Point(7, 8, 9), Line(Point(6, 7), Point(7, 7)))) raises(NotImplementedError, lambda: Parabola(Point(7, 8), Line(Point(3, 7), Point(2, 9)))) raises(ValueError, lambda: Parabola(Point(0, 2), Line(Point(7, 2), Point(6, 2)))) raises(ValueError, lambda: Parabola(Point(7, 8), Point(3, 8))) # Basic Stuff assert pa1.focus == Point(0, 0) assert pa1.ambient_dimension == S(2) assert pa2 == pa3 assert pa4 != pa7 assert pa6 != pa7 assert pa6.focus == Point2D(0, 4) assert pa6.focal_length == 1 assert pa6.p_parameter == -1 assert pa6.vertex == Point2D(0, 5) assert pa6.eccentricity == 1 assert pa7.focus == Point2D(3, 7) assert pa7.focal_length == half assert pa7.p_parameter == -half assert pa7.vertex == Point2D(7 * half, 7) assert pa4.focal_length == half assert pa4.p_parameter == half assert pa4.vertex == Point2D(3, 13 * half) assert pa8.focal_length == 1 assert pa8.p_parameter == 1 assert pa8.vertex == Point2D(5, 0) assert pa4.focal_length == pa5.focal_length assert pa4.p_parameter == pa5.p_parameter assert pa4.vertex == pa5.vertex assert pa4.equation() == pa5.equation() assert pa8.focal_length == pa9.focal_length assert pa8.p_parameter == pa9.p_parameter assert pa8.vertex == pa9.vertex assert pa8.equation() == pa9.equation() assert pa10.focal_length == pa11.focal_length == sqrt( (a - b)**2) / 2 # if a, b real == abs(a - b)/2 assert pa11.vertex == Point(*pa10.vertex[::-1]) == Point( a, a - sqrt( (a - b)**2) * sign(a - b) / 2) # change axis x->y, y->x on pa10