Ejemplo n.º 1
0
    def eval(cls, arg):
        arg = sympify(arg)

        if arg.is_Number:
            if arg is S.NaN:
                return S.NaN
            elif arg is S.Infinity:
                return S.Infinity
            elif arg is S.NegativeInfinity:
                return S.NegativeInfinity
            elif arg is S.Zero:
                return S.Zero
            elif arg is S.One:
                return C.log(2**S.Half + 1)
            elif arg is S.NegativeOne:
                return C.log(2**S.Half - 1)
            elif arg.is_negative:
                return -cls(-arg)
        else:
            i_coeff = arg.as_coefficient(S.ImaginaryUnit)

            if i_coeff is not None:
                return S.ImaginaryUnit * C.asin(i_coeff)
            else:
                if arg.as_coeff_mul()[0].is_negative:
                    return -cls(-arg)
Ejemplo n.º 2
0
    def eval(cls, arg):
        arg = sympify(arg)

        if arg.is_Number:
            if arg is S.NaN:
                return S.NaN
            elif arg is S.Infinity:
                return S.Infinity
            elif arg is S.NegativeInfinity:
                return S.NegativeInfinity
            elif arg is S.Zero:
                return S.Zero
            elif arg is S.One:
                return C.log(2**S.Half + 1)
            elif arg is S.NegativeOne:
                return C.log(2**S.Half - 1)
            elif arg.is_negative:
                return -cls(-arg)
        else:
            i_coeff = arg.as_coefficient(S.ImaginaryUnit)

            if i_coeff is not None:
                return S.ImaginaryUnit * C.asin(i_coeff)
            else:
                if arg.as_coeff_mul()[0].is_negative:
                    return -cls(-arg)
Ejemplo n.º 3
0
    def eval(cls, arg):
        arg = sympify(arg)

        if arg.is_Number:
            if arg is S.NaN:
                return S.NaN
            elif arg is S.Infinity:
                return S.Infinity
            elif arg is S.NegativeInfinity:
                return S.NegativeInfinity
            elif arg is S.Zero:
                return S.Zero
            elif arg is S.One:
                return C.log(sqrt(2) + 1)
            elif arg is S.NegativeOne:
                return C.log(sqrt(2) - 1)
            elif arg.is_negative:
                return -cls(-arg)
        else:
            if arg is S.ComplexInfinity:
                return S.ComplexInfinity

            i_coeff = arg.as_coefficient(S.ImaginaryUnit)

            if i_coeff is not None:
                return S.ImaginaryUnit * C.asin(i_coeff)
            else:
                if _coeff_isneg(arg):
                    return -cls(-arg)
Ejemplo n.º 4
0
    def angle_between(self, o):
        """Angle between the plane and other geometric entity.

        Parameters
        ==========

        LinearEntity3D, Plane.

        Returns
        =======

        angle : angle in radians

        Notes
        =====

        This method accepts only 3D entities as it's parameter, but if you want
        to calculate the angle between a 2D entity and a plane you should
        first convert to a 3D entity by projecting onto a desired plane and
        then proceed to calculate the angle.

        Examples
        ========

        >>> from sympy import Point3D, Line3D, Plane
        >>> a = Plane(Point3D(1, 2, 2), normal_vector=[1, 2, 3])
        >>> b = Line3D(Point3D(1, 3, 4), Point3D(2, 2, 2))
        >>> a.angle_between(b)
        -asin(sqrt(21)/6)

        """
        from sympy.geometry.line3d import LinearEntity3D
        if isinstance(o, LinearEntity3D):
            a = Matrix(self.normal_vector)
            b = Matrix(o.direction_ratio)
            c = a.dot(b)
            d = sqrt(sum([i**2 for i in self.normal_vector]))
            e = sqrt(sum([i**2 for i in o.direction_ratio]))
            return C.asin(c/(d*e))
        if isinstance(o, Plane):
            a = Matrix(self.normal_vector)
            b = Matrix(o.normal_vector)
            c = a.dot(b)
            d = sqrt(sum([i**2 for i in self.normal_vector]))
            e = sqrt(sum([i**2 for i in o.normal_vector]))
            return C.acos(c/(d*e))
Ejemplo n.º 5
0
    def angle_between(self, o):
        """Angle between the plane and other geometric entity.

        Parameters
        ==========

        LinearEntity3D, Plane.

        Returns
        =======

        angle : angle in radians

        Notes
        =====

        This method accepts only 3D entities as it's parameter, but if you want
        to calculate the angle between a 2D entity and a plane you should
        first convert to a 3D entity by projecting onto a desired plane and
        then proceed to calculate the angle.

        Examples
        ========

        >>> from sympy import Point3D, Line3D, Plane
        >>> a = Plane(Point3D(1, 2, 2), normal_vector=(1, 2, 3))
        >>> b = Line3D(Point3D(1, 3, 4), Point3D(2, 2, 2))
        >>> a.angle_between(b)
        -asin(sqrt(21)/6)

        """
        from sympy.geometry.line3d import LinearEntity3D
        if isinstance(o, LinearEntity3D):
            a = Matrix(self.normal_vector)
            b = Matrix(o.direction_ratio)
            c = a.dot(b)
            d = sqrt(sum([i**2 for i in self.normal_vector]))
            e = sqrt(sum([i**2 for i in o.direction_ratio]))
            return C.asin(c/(d*e))
        if isinstance(o, Plane):
            a = Matrix(self.normal_vector)
            b = Matrix(o.normal_vector)
            c = a.dot(b)
            d = sqrt(sum([i**2 for i in self.normal_vector]))
            e = sqrt(sum([i**2 for i in o.normal_vector]))
            return C.acos(c/(d*e))