<reponame>terrencetec/gtrace
#{{{ Import
import numpy as np
pi = np.pi
#}}}

#{{{ Snell's Law

def deflection_angle(theta, n1, n2, deg=True):
    """Calculate deflection angle according to Snell's law.

    Parameters
    ----------
    theta : float
        Angle of incidence.
    n1 : float
        Refractive index of the first medium.
    n2 : float
        Refraction index of the second medium.
    deg : boolean, optional
        True if theta is specified in degrees.
    """
    if deg:
        factor = pi/180.0
    else:
        factor = 1.0

    return np.arcsin(n1*np.sin(theta*factor)/n2)/factor

#}}}

#{{{ Geometry utilities

#{{{ line_plane_intersection

def line_plane_intersection(pos,
                            dirVect,
                            plane_center,
                            normalVector,
                            diameter):
    '''
    Compute the intersection point between a line
    and a plane

    Parameters
    ----------
    pos : array
        The position of the end point of the line.
    dirVert : array
        The directional vector specifying the line.
    plane_center : array
        The position of the center of the plane.
    normalVector: array
        The normal vector of the plane.
    diameter: float
        The diameter of the plane.

    Returns
    -------
    dict
        The returned value is a dictionary with the following keys:
        "Intersection Point": numpy array of the coordinates of the intersection point.
        "isHit": A boolean value of whether the line intersects with the plane or not.
        "distance": Distance between the origin of the line and the intersection point.
        "distance from center": Distance between the center of the plane and the intersection point.
    '''

    #Make sure the inputs are ndarrays
    pos = np.array(pos, dtype=np.float64)
    dirVect = np.array(dirVect, dtype=np.float64)
    plane_center = np.array(plane_center, dtype=np.float64)
    normalVector = np.array(normalVector, dtype=np.float64)
    diameter = float(diameter)

    #Get a normalized vector along the plane
    plVect = np.array([-normalVector[1], normalVector[0]])
    plVect = plVect/np.linalg.norm(plVect)

    #Normalize
    dirVect = dirVect/np.linalg.norm(dirVect)

    #Make sure that the plVect and dirVect are not parallel
    if np.abs(np.dot(dirVect, plVect)) > 1 - 1e-10:
        return {'Intersection Point': np.array((0.,0.)), 'isHit': False,
            'distance': 0.0,
            'distance from center': 0.0}


    #Solve line equations to get the intersection point
    M = np.vstack((dirVect, -plVect)).T
    ans = np.linalg.solve(M, plane_center - pos)
    intersection_point = pos + ans[0]*dirVect

    #How far the intersection point is from the center
    #of the plane
    dist_from_center = np.abs(ans[1])
    if dist_from_center > diameter/2.0\
           or ans[0] < 0.\
           or np.dot(dirVect, normalVector) > 0.:

        hit = False
    else:
        hit = True

    return {'Intersection Point': intersection_point, 'isHit': hit,
            'distance': np.abs(ans[0]),
            'distance from center': ans[1]}


#}}}

#{{{ line_arc_intersection

def line_arc_intersection(pos,
                          dirVect,
                          chord_center,
                          chordNormVect,
                          invROC,
                          diameter,
                          verbose=False):
    '''
    Compute the intersection point between a line
    and an arc.

    Parameters
    ----------
    pos : array
        Origin of the line.
    dirVect : array
        Direction of the line.
    chord_center : array
        The center of the chord made by the arc.
    chordNormVect : array
        Normal vector of the chord.
    invROC : float
        Inverse of the ROC of the arc. Positive for concave surface.
    diameter : float
        Length of the chord.
    verbose : boolean, optional
        Prints useful information.

    Returns
    -------
    dict
        The returned value is a dictionary with the following keys:
        "Intersection Point": numpy array of the coordinates of the intersection point.
        "isHit": A boolean value of whether the line intersects with the plane or not.
        "distance": Distance between the origin of the line and the intersection point.
        "localNormVect": localNormVect,
        "localNormAngle": localNormAngle.
    '''
    #Make sure the inputs are ndarrays
    pos = np.array(pos, dtype=np.float64)
    dirVect = np.array(dirVect, dtype=np.float64)
    chord_center = np.array(chord_center, dtype=np.float64)
    chordNormVect = np.array(chordNormVect, dtype=np.float64)
    invROC = float(invROC)
    diameter = float(diameter)

    #Normalize
    dirVect = dirVect/np.linalg.norm(dirVect)
    chordNormVect = chordNormVect/np.linalg.norm(chordNormVect)

    #Check if the ROC is too large.
    if np.abs(invROC) < 1e-5:
        #It is almost a plane
        ans = line_plane_intersection(pos, dirVect, chord_center, chordNormVect, diameter)
        localNormVect = chordNormVect
        localNormAngle = np.mod(np.arctan2(localNormVect[1],
                                           localNormVect[0]), 2*pi)

        ans['localNormVect'] = localNormVect
        ans['localNormAngle'] = localNormAngle

        return ans

    ROC = 1/invROC


    #Compute the center of the arc
    theta = np.arcsin(diameter/(2*ROC))
    l = ROC*np.cos(theta)
    arc_center = chord_center + chordNormVect*l

    #For convex surface, pos has to be outside the circle.
    if ROC < 0 and np.linalg.norm(pos - arc_center) < np.abs(ROC):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}


    #First, decompose the vector connecting from the arc_center
    #to pos into the components parallel to the line and orthogonal to it.
    # s is the component in the orthogonal direction and t is the one along
    #the line.
    #A vector orthogonal to the line
    k = np.array([-dirVect[1], dirVect[0]])
    #Solve the equation to decompose the vector pos-arc_center
    M = np.vstack((k, -dirVect)).T
    ans = np.linalg.solve(M, pos - arc_center)
    s = ans[0]
    t = ans[1]

    if np.abs(s) > np.abs(ROC):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    #Compute two cross points
    #Work with the chord formed by the line and the circle.
    #d is half the length of the chord.
    d = np.sqrt(ROC**2 - s**2)
    if ROC > 0:
        intersection_point = k*s+arc_center + d*dirVect
        localNormVect = arc_center - intersection_point
    else:
        intersection_point = k*s+arc_center - d*dirVect
        localNormVect = intersection_point - arc_center

    #Check if dirVect and the vector connecting from pos to intersection_point
    #are pointing the same direction.
    if np.dot(dirVect, intersection_point - pos) < 0:
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    #Normalize
    localNormVect = localNormVect/np.linalg.norm(localNormVect)
    localNormAngle = np.mod(np.arctan2(localNormVect[1],
                                       localNormVect[0]), 2*pi)

    #Check if the intersection point is within the
    #diameter
    v0 = - np.sign(ROC) * chordNormVect*(1-1e-16)  #(1-1e-16) is necessary to avoid rounding error
    v1 = intersection_point - arc_center
    v1 = v1/np.linalg.norm(v1)*(1-1e-16)
    if np.arccos(np.dot(v0,v1)) > np.abs(theta):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    distance = np.linalg.norm(intersection_point - pos)



    return {'Intersection Point': intersection_point, 'isHit': True,
            'distance': distance, 'localNormVect': localNormVect,
            'localNormAngle': localNormAngle}

#}}}

#{{{ vector_rotation_2D

def vector_rotation_2D(vect, angle):
    """Rotate a 2D vector by an angle.

    Parameters
    ----------
    vect : array
        A 2D vector.
    angle : float
        Angle of rotation in radians.

    Returns
    -------
    array
        The rotated vector.
    """
    vect = np.array(vect)
    angle = float(angle)

    M = np.array([[np.cos(angle), -np.sin(angle)],
                  [np.sin(angle),np.cos(angle)]])
    return np.dot(M, vect)

#}}}

def vector_normalize(vect):
    '''
    Normalize a vector

    Parameters
    ----------
    vect : array
        The vector to be normalized

    Returns
    -------
    array
        The normalized vector.
    '''

    return vect/np.linalg.norm(vect)

#{{{ normSpheric

def normSpheric(normAngle, invROC, dist_from_center):
    '''
    Returns the local normal angle of a spheric mirror
    at a distance from the center.

    Parameters
    ----------
    normAngle : float
        The angle formed by the normal vector of the mirror
        at the center and the x-axis.
    invROC : float
        1/R, where R is the ROC of the mirror.
    dist_from_center: float
        The distance from the center of the point where
        the local normal is requested.
        This is a signed value.
        For a mirror facing +x (the normal vector points
        towards positive x direction), this distance
        is positive for points with positive y coordinate,
        and negative for points with negative y coordinate.

    Returns
    -------
    float
        The local normal angle of a spheric mirror
        at a distance from the center.
    '''

    normAngle = np.mod(normAngle, 2*pi)
    return np.mod(np.arcsin(- dist_from_center * invROC) + normAngle, 2*pi)

#}}}

#{{{ reflection and deflection angle

def refl_defl_angle(beamAngle, normAngle, n1, n2, invROC=None):
    '''
    Returns a tuples of reflection and deflection angles.

    Parameters
    ----------
    beamAngle : float
        The angle formed by the propagation direction vector
        of the incident beam and the x-axis.
    normAngle : float
        The angle formed by the normal vector of the surface
        and the x-axis.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.
    invROC : float or None, optional
        Inverse of the radius of curvature.

    Returns
    -------
    6-tuple or 2-tuple
    (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty) or (reflAngle, deflAngle)
    '''

    beamAngle = np.mod(beamAngle, 2*pi)
    normAngle = np.mod(normAngle, 2*pi)

    incidentAngle = np.mod(beamAngle - normAngle, 2*pi) - pi

    reflAngle = np.mod(normAngle - incidentAngle, 2*pi)

    deflAngle = np.arcsin(n1*np.sin(incidentAngle)/n2)
    deflAngle = np.mod(deflAngle + pi + normAngle, 2*pi)

    if not invROC == None:
        #Calculate ABCD matrices

        #Absolute value of the incident angle
        theta1 = np.abs(incidentAngle)

        #For reflection
        Mrx = np.array([[1., 0.], [-2*n1*invROC/np.cos(theta1), 1.]])
        Mry = np.array([[1., 0.], [-2*n1*invROC*np.cos(theta1), 1.]])

        #For transmission
        theta2 = np.arcsin(n1*np.sin(theta1)/n2)

        nex = (n2*np.cos(theta2)-n1*np.cos(theta1))/(np.cos(theta1)*np.cos(theta2))
        Mtx = np.array([[np.cos(theta2)/np.cos(theta1), 0.],
                        [nex*invROC, np.cos(theta1)/np.cos(theta2)]])

        ney = n2*np.cos(theta2)-n1*np.cos(theta1)
        Mty = np.array([[1., 0.],[ney*invROC, 1.]])

        return (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty)

    else:
        return (reflAngle, deflAngle)


#}}}

#{{{ reflection and deflection angle for cylindrical surface

def cyl_refl_defl_angle(beamAngle, normAngle, n1, n2, invROC=None, curve_direction='h'):
    '''
    Returns a tuples of reflection and deflection angles for incidence of a beam into a cylindrical surface.

    Parameters
    ----------
    beamAngle : float
        The angle formed by the propagation direction vector
        of the incident beam and the x-axis.
    normAngle : float
        The angle formed by the normal vector of the surface
        and the x-axis.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.
    invROC : float or None, optional
        Inverse of the radius of curvature.
    curve_direction : str, optional
        Direction of curvature. Either 'h' or 'v'.
    '''

    beamAngle = np.mod(beamAngle, 2*pi)
    normAngle = np.mod(normAngle, 2*pi)

    incidentAngle = np.mod(beamAngle - normAngle, 2*pi) - pi

    reflAngle = np.mod(normAngle - incidentAngle, 2*pi)

    deflAngle = np.arcsin(n1*np.sin(incidentAngle)/n2)
    deflAngle = np.mod(deflAngle + pi + normAngle, 2*pi)

    if not invROC == None:
        #Calculate ABCD matrices

        #Absolute value of the incident angle
        theta1 = np.abs(incidentAngle)

        #For reflection
        if curve_direction == 'h':
            Mrx = np.array([[1., 0.], [-2*n1*invROC/np.cos(theta1), 1.]])
            Mry = np.array([[1., 0.], [0., 1.]])
        else:
            Mrx = np.array([[1., 0.], [0., 1.]])
            Mry = np.array([[1., 0.], [-2*n1*invROC*np.cos(theta1), 1.]])

        #For transmission
        theta2 = np.arcsin(n1*np.sin(theta1)/n2)

        nex = (n2*np.cos(theta2)-n1*np.cos(theta1))/(np.cos(theta1)*np.cos(theta2))
        Mtx = np.array([[np.cos(theta2)/np.cos(theta1), 0.],
                        [nex*invROC, np.cos(theta1)/np.cos(theta2)]])

        ney = n2*np.cos(theta2)-n1*np.cos(theta1)
        Mty = np.array([[1., 0.],[ney*invROC, 1.]])

        return (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty)

    else:
        return (reflAngle, deflAngle)


#}}}

#}}}

#{{{ VariCAD utility functions

def vc_deflect(theta, theta1, n1, n2):
    '''
    Deflection angle helper function for VariCAD.

    Parameters
    ----------
    theta : float
        Angle of the surface measured from right.
    theta1 : float
        Angle of the incident beam measured from right.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.

    Returns
    -------
    phi2 : float
        Angle of the deflected beam measured from right.

    '''
    #Combert theta and theta1 to 0-360 format
    if theta < 0:
        theta = 360.0 + theta

    if theta > 180:
        theta = theta -180.0

    if theta1 < 0:
        theta1 = 360.0 + theta1

    #Determine the incident angle
    phi = abs(theta - theta1)
    phi1 = 90.0-np.arcsin(np.abs(np.sin(pi*phi/180.0)))*180.0/pi

    #Calculate deflection angle
    phi2 = deflection_angle(phi1, n1, n2)

    #Convert to the 0-360 angle
    s1 = np.sign(np.sin(pi*(theta1 - theta)/180.0))
    s2 = -np.sign(np.cos(pi*(theta1 - theta)/180.0))
    phi2 = theta + s1*90 + s1*s2*phi2
    return phi2


def vc_reflect(theta, theta1):
    """Convert theta and theta1 to 0-360 format.

    Parameters
    ----------
    theta : float
        Angle of the surface measured from right.
    theta1 : float
        Angle of the incident beam measured from right.

    Returns
    -------
    float
    """
    #Combert theta and theta1 to 0-360 format
    if theta < 0:
        theta = 360.0 + theta

    if theta > 180:
        theta = theta -180.0

    if theta1 < 0:
        theta1 = 360.0 + theta1

    return theta - (theta1 - theta)

#}}}

#{{{ Import
import numpy as np
pi = np.pi
#}}}

#{{{ Snell's Law

def deflection_angle(theta, n1, n2, deg=True):
    """Calculate deflection angle according to Snell's law.

    Parameters
    ----------
    theta : float
        Angle of incidence.
    n1 : float
        Refractive index of the first medium.
    n2 : float
        Refraction index of the second medium.
    deg : boolean, optional
        True if theta is specified in degrees.
    """
    if deg:
        factor = pi/180.0
    else:
        factor = 1.0

    return np.arcsin(n1*np.sin(theta*factor)/n2)/factor

#}}}

#{{{ Geometry utilities

#{{{ line_plane_intersection

def line_plane_intersection(pos,
                            dirVect,
                            plane_center,
                            normalVector,
                            diameter):
    '''
    Compute the intersection point between a line
    and a plane

    Parameters
    ----------
    pos : array
        The position of the end point of the line.
    dirVert : array
        The directional vector specifying the line.
    plane_center : array
        The position of the center of the plane.
    normalVector: array
        The normal vector of the plane.
    diameter: float
        The diameter of the plane.

    Returns
    -------
    dict
        The returned value is a dictionary with the following keys:
        "Intersection Point": numpy array of the coordinates of the intersection point.
        "isHit": A boolean value of whether the line intersects with the plane or not.
        "distance": Distance between the origin of the line and the intersection point.
        "distance from center": Distance between the center of the plane and the intersection point.
    '''

    #Make sure the inputs are ndarrays
    pos = np.array(pos, dtype=np.float64)
    dirVect = np.array(dirVect, dtype=np.float64)
    plane_center = np.array(plane_center, dtype=np.float64)
    normalVector = np.array(normalVector, dtype=np.float64)
    diameter = float(diameter)

    #Get a normalized vector along the plane
    plVect = np.array([-normalVector[1], normalVector[0]])
    plVect = plVect/np.linalg.norm(plVect)

    #Normalize
    dirVect = dirVect/np.linalg.norm(dirVect)

    #Make sure that the plVect and dirVect are not parallel
    if np.abs(np.dot(dirVect, plVect)) > 1 - 1e-10:
        return {'Intersection Point': np.array((0.,0.)), 'isHit': False,
            'distance': 0.0,
            'distance from center': 0.0}


    #Solve line equations to get the intersection point
    M = np.vstack((dirVect, -plVect)).T
    ans = np.linalg.solve(M, plane_center - pos)
    intersection_point = pos + ans[0]*dirVect

    #How far the intersection point is from the center
    #of the plane
    dist_from_center = np.abs(ans[1])
    if dist_from_center > diameter/2.0\
           or ans[0] < 0.\
           or np.dot(dirVect, normalVector) > 0.:

        hit = False
    else:
        hit = True

    return {'Intersection Point': intersection_point, 'isHit': hit,
            'distance': np.abs(ans[0]),
            'distance from center': ans[1]}


#}}}

#{{{ line_arc_intersection

def line_arc_intersection(pos,
                          dirVect,
                          chord_center,
                          chordNormVect,
                          invROC,
                          diameter,
                          verbose=False):
    '''
    Compute the intersection point between a line
    and an arc.

    Parameters
    ----------
    pos : array
        Origin of the line.
    dirVect : array
        Direction of the line.
    chord_center : array
        The center of the chord made by the arc.
    chordNormVect : array
        Normal vector of the chord.
    invROC : float
        Inverse of the ROC of the arc. Positive for concave surface.
    diameter : float
        Length of the chord.
    verbose : boolean, optional
        Prints useful information.

    Returns
    -------
    dict
        The returned value is a dictionary with the following keys:
        "Intersection Point": numpy array of the coordinates of the intersection point.
        "isHit": A boolean value of whether the line intersects with the plane or not.
        "distance": Distance between the origin of the line and the intersection point.
        "localNormVect": localNormVect,
        "localNormAngle": localNormAngle.
    '''
    #Make sure the inputs are ndarrays
    pos = np.array(pos, dtype=np.float64)
    dirVect = np.array(dirVect, dtype=np.float64)
    chord_center = np.array(chord_center, dtype=np.float64)
    chordNormVect = np.array(chordNormVect, dtype=np.float64)
    invROC = float(invROC)
    diameter = float(diameter)

    #Normalize
    dirVect = dirVect/np.linalg.norm(dirVect)
    chordNormVect = chordNormVect/np.linalg.norm(chordNormVect)

    #Check if the ROC is too large.
    if np.abs(invROC) < 1e-5:
        #It is almost a plane
        ans = line_plane_intersection(pos, dirVect, chord_center, chordNormVect, diameter)
        localNormVect = chordNormVect
        localNormAngle = np.mod(np.arctan2(localNormVect[1],
                                           localNormVect[0]), 2*pi)

        ans['localNormVect'] = localNormVect
        ans['localNormAngle'] = localNormAngle

        return ans

    ROC = 1/invROC


    #Compute the center of the arc
    theta = np.arcsin(diameter/(2*ROC))
    l = ROC*np.cos(theta)
    arc_center = chord_center + chordNormVect*l

    #For convex surface, pos has to be outside the circle.
    if ROC < 0 and np.linalg.norm(pos - arc_center) < np.abs(ROC):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}


    #First, decompose the vector connecting from the arc_center
    #to pos into the components parallel to the line and orthogonal to it.
    # s is the component in the orthogonal direction and t is the one along
    #the line.
    #A vector orthogonal to the line
    k = np.array([-dirVect[1], dirVect[0]])
    #Solve the equation to decompose the vector pos-arc_center
    M = np.vstack((k, -dirVect)).T
    ans = np.linalg.solve(M, pos - arc_center)
    s = ans[0]
    t = ans[1]

    if np.abs(s) > np.abs(ROC):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    #Compute two cross points
    #Work with the chord formed by the line and the circle.
    #d is half the length of the chord.
    d = np.sqrt(ROC**2 - s**2)
    if ROC > 0:
        intersection_point = k*s+arc_center + d*dirVect
        localNormVect = arc_center - intersection_point
    else:
        intersection_point = k*s+arc_center - d*dirVect
        localNormVect = intersection_point - arc_center

    #Check if dirVect and the vector connecting from pos to intersection_point
    #are pointing the same direction.
    if np.dot(dirVect, intersection_point - pos) < 0:
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    #Normalize
    localNormVect = localNormVect/np.linalg.norm(localNormVect)
    localNormAngle = np.mod(np.arctan2(localNormVect[1],
                                       localNormVect[0]), 2*pi)

    #Check if the intersection point is within the
    #diameter
    v0 = - np.sign(ROC) * chordNormVect*(1-1e-16)  #(1-1e-16) is necessary to avoid rounding error
    v1 = intersection_point - arc_center
    v1 = v1/np.linalg.norm(v1)*(1-1e-16)
    if np.arccos(np.dot(v0,v1)) > np.abs(theta):
        if verbose:
            print('The line does not hit the arc.')
        return {'isHit': False}

    distance = np.linalg.norm(intersection_point - pos)



    return {'Intersection Point': intersection_point, 'isHit': True,
            'distance': distance, 'localNormVect': localNormVect,
            'localNormAngle': localNormAngle}

#}}}

#{{{ vector_rotation_2D

def vector_rotation_2D(vect, angle):
    """Rotate a 2D vector by an angle.

    Parameters
    ----------
    vect : array
        A 2D vector.
    angle : float
        Angle of rotation in radians.

    Returns
    -------
    array
        The rotated vector.
    """
    vect = np.array(vect)
    angle = float(angle)

    M = np.array([[np.cos(angle), -np.sin(angle)],
                  [np.sin(angle),np.cos(angle)]])
    return np.dot(M, vect)

#}}}

def vector_normalize(vect):
    '''
    Normalize a vector

    Parameters
    ----------
    vect : array
        The vector to be normalized

    Returns
    -------
    array
        The normalized vector.
    '''

    return vect/np.linalg.norm(vect)

#{{{ normSpheric

def normSpheric(normAngle, invROC, dist_from_center):
    '''
    Returns the local normal angle of a spheric mirror
    at a distance from the center.

    Parameters
    ----------
    normAngle : float
        The angle formed by the normal vector of the mirror
        at the center and the x-axis.
    invROC : float
        1/R, where R is the ROC of the mirror.
    dist_from_center: float
        The distance from the center of the point where
        the local normal is requested.
        This is a signed value.
        For a mirror facing +x (the normal vector points
        towards positive x direction), this distance
        is positive for points with positive y coordinate,
        and negative for points with negative y coordinate.

    Returns
    -------
    float
        The local normal angle of a spheric mirror
        at a distance from the center.
    '''

    normAngle = np.mod(normAngle, 2*pi)
    return np.mod(np.arcsin(- dist_from_center * invROC) + normAngle, 2*pi)

#}}}

#{{{ reflection and deflection angle

def refl_defl_angle(beamAngle, normAngle, n1, n2, invROC=None):
    '''
    Returns a tuples of reflection and deflection angles.

    Parameters
    ----------
    beamAngle : float
        The angle formed by the propagation direction vector
        of the incident beam and the x-axis.
    normAngle : float
        The angle formed by the normal vector of the surface
        and the x-axis.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.
    invROC : float or None, optional
        Inverse of the radius of curvature.

    Returns
    -------
    6-tuple or 2-tuple
    (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty) or (reflAngle, deflAngle)
    '''

    beamAngle = np.mod(beamAngle, 2*pi)
    normAngle = np.mod(normAngle, 2*pi)

    incidentAngle = np.mod(beamAngle - normAngle, 2*pi) - pi

    reflAngle = np.mod(normAngle - incidentAngle, 2*pi)

    deflAngle = np.arcsin(n1*np.sin(incidentAngle)/n2)
    deflAngle = np.mod(deflAngle + pi + normAngle, 2*pi)

    if not invROC == None:
        #Calculate ABCD matrices

        #Absolute value of the incident angle
        theta1 = np.abs(incidentAngle)

        #For reflection
        Mrx = np.array([[1., 0.], [-2*n1*invROC/np.cos(theta1), 1.]])
        Mry = np.array([[1., 0.], [-2*n1*invROC*np.cos(theta1), 1.]])

        #For transmission
        theta2 = np.arcsin(n1*np.sin(theta1)/n2)

        nex = (n2*np.cos(theta2)-n1*np.cos(theta1))/(np.cos(theta1)*np.cos(theta2))
        Mtx = np.array([[np.cos(theta2)/np.cos(theta1), 0.],
                        [nex*invROC, np.cos(theta1)/np.cos(theta2)]])

        ney = n2*np.cos(theta2)-n1*np.cos(theta1)
        Mty = np.array([[1., 0.],[ney*invROC, 1.]])

        return (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty)

    else:
        return (reflAngle, deflAngle)


#}}}

#{{{ reflection and deflection angle for cylindrical surface

def cyl_refl_defl_angle(beamAngle, normAngle, n1, n2, invROC=None, curve_direction='h'):
    '''
    Returns a tuples of reflection and deflection angles for incidence of a beam into a cylindrical surface.

    Parameters
    ----------
    beamAngle : float
        The angle formed by the propagation direction vector
        of the incident beam and the x-axis.
    normAngle : float
        The angle formed by the normal vector of the surface
        and the x-axis.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.
    invROC : float or None, optional
        Inverse of the radius of curvature.
    curve_direction : str, optional
        Direction of curvature. Either 'h' or 'v'.
    '''

    beamAngle = np.mod(beamAngle, 2*pi)
    normAngle = np.mod(normAngle, 2*pi)

    incidentAngle = np.mod(beamAngle - normAngle, 2*pi) - pi

    reflAngle = np.mod(normAngle - incidentAngle, 2*pi)

    deflAngle = np.arcsin(n1*np.sin(incidentAngle)/n2)
    deflAngle = np.mod(deflAngle + pi + normAngle, 2*pi)

    if not invROC == None:
        #Calculate ABCD matrices

        #Absolute value of the incident angle
        theta1 = np.abs(incidentAngle)

        #For reflection
        if curve_direction == 'h':
            Mrx = np.array([[1., 0.], [-2*n1*invROC/np.cos(theta1), 1.]])
            Mry = np.array([[1., 0.], [0., 1.]])
        else:
            Mrx = np.array([[1., 0.], [0., 1.]])
            Mry = np.array([[1., 0.], [-2*n1*invROC*np.cos(theta1), 1.]])

        #For transmission
        theta2 = np.arcsin(n1*np.sin(theta1)/n2)

        nex = (n2*np.cos(theta2)-n1*np.cos(theta1))/(np.cos(theta1)*np.cos(theta2))
        Mtx = np.array([[np.cos(theta2)/np.cos(theta1), 0.],
                        [nex*invROC, np.cos(theta1)/np.cos(theta2)]])

        ney = n2*np.cos(theta2)-n1*np.cos(theta1)
        Mty = np.array([[1., 0.],[ney*invROC, 1.]])

        return (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty)

    else:
        return (reflAngle, deflAngle)


#}}}

#}}}

#{{{ VariCAD utility functions

def vc_deflect(theta, theta1, n1, n2):
    '''
    Deflection angle helper function for VariCAD.

    Parameters
    ----------
    theta : float
        Angle of the surface measured from right.
    theta1 : float
        Angle of the incident beam measured from right.
    n1 : float
        Index of refraction of the incident side medium.
    n2 : float
        Index of refraction of the transmission side medium.

    Returns
    -------
    phi2 : float
        Angle of the deflected beam measured from right.

    '''
    #Combert theta and theta1 to 0-360 format
    if theta < 0:
        theta = 360.0 + theta

    if theta > 180:
        theta = theta -180.0

    if theta1 < 0:
        theta1 = 360.0 + theta1

    #Determine the incident angle
    phi = abs(theta - theta1)
    phi1 = 90.0-np.arcsin(np.abs(np.sin(pi*phi/180.0)))*180.0/pi

    #Calculate deflection angle
    phi2 = deflection_angle(phi1, n1, n2)

    #Convert to the 0-360 angle
    s1 = np.sign(np.sin(pi*(theta1 - theta)/180.0))
    s2 = -np.sign(np.cos(pi*(theta1 - theta)/180.0))
    phi2 = theta + s1*90 + s1*s2*phi2
    return phi2


def vc_reflect(theta, theta1):
    """Convert theta and theta1 to 0-360 format.

    Parameters
    ----------
    theta : float
        Angle of the surface measured from right.
    theta1 : float
        Angle of the incident beam measured from right.

    Returns
    -------
    float
    """
    #Combert theta and theta1 to 0-360 format
    if theta < 0:
        theta = 360.0 + theta

    if theta > 180:
        theta = theta -180.0

    if theta1 < 0:
        theta1 = 360.0 + theta1

    return theta - (theta1 - theta)

#}}}
#{{{ Import #}}} #{{{ Snell's Law Calculate deflection angle according to Snell's law.      Parameters     ----------     theta : float         Angle of incidence.     n1 : float         Refractive index of the first medium.     n2 : float         Refraction index of the second medium.     deg : boolean, optional         True if theta is specified in degrees. #}}} #{{{ Geometry utilities #{{{ line_plane_intersection Compute the intersection point between a line     and a plane      Parameters     ----------     pos : array         The position of the end point of the line.     dirVert : array         The directional vector specifying the line.     plane_center : array         The position of the center of the plane.     normalVector: array         The normal vector of the plane.     diameter: float         The diameter of the plane.      Returns     -------     dict         The returned value is a dictionary with the following keys:         "Intersection Point": numpy array of the coordinates of the intersection point.         "isHit": A boolean value of whether the line intersects with the plane or not.         "distance": Distance between the origin of the line and the intersection point.         "distance from center": Distance between the center of the plane and the intersection point. #Make sure the inputs are ndarrays #Get a normalized vector along the plane #Normalize #Make sure that the plVect and dirVect are not parallel #Solve line equations to get the intersection point #How far the intersection point is from the center #of the plane #}}} #{{{ line_arc_intersection Compute the intersection point between a line     and an arc.      Parameters     ----------     pos : array         Origin of the line.     dirVect : array         Direction of the line.     chord_center : array         The center of the chord made by the arc.     chordNormVect : array         Normal vector of the chord.     invROC : float         Inverse of the ROC of the arc. Positive for concave surface.     diameter : float         Length of the chord.     verbose : boolean, optional         Prints useful information.      Returns     -------     dict         The returned value is a dictionary with the following keys:         "Intersection Point": numpy array of the coordinates of the intersection point.         "isHit": A boolean value of whether the line intersects with the plane or not.         "distance": Distance between the origin of the line and the intersection point.         "localNormVect": localNormVect,         "localNormAngle": localNormAngle. #Make sure the inputs are ndarrays #Normalize #Check if the ROC is too large. #It is almost a plane #Compute the center of the arc #For convex surface, pos has to be outside the circle. #First, decompose the vector connecting from the arc_center #to pos into the components parallel to the line and orthogonal to it. # s is the component in the orthogonal direction and t is the one along #the line. #A vector orthogonal to the line #Solve the equation to decompose the vector pos-arc_center #Compute two cross points #Work with the chord formed by the line and the circle. #d is half the length of the chord. #Check if dirVect and the vector connecting from pos to intersection_point #are pointing the same direction. #Normalize #Check if the intersection point is within the #diameter #(1-1e-16) is necessary to avoid rounding error #}}} #{{{ vector_rotation_2D Rotate a 2D vector by an angle.      Parameters     ----------     vect : array         A 2D vector.     angle : float         Angle of rotation in radians.      Returns     -------     array         The rotated vector. #}}} Normalize a vector      Parameters     ----------     vect : array         The vector to be normalized      Returns     -------     array         The normalized vector. #{{{ normSpheric Returns the local normal angle of a spheric mirror     at a distance from the center.      Parameters     ----------     normAngle : float         The angle formed by the normal vector of the mirror         at the center and the x-axis.     invROC : float         1/R, where R is the ROC of the mirror.     dist_from_center: float         The distance from the center of the point where         the local normal is requested.         This is a signed value.         For a mirror facing +x (the normal vector points         towards positive x direction), this distance         is positive for points with positive y coordinate,         and negative for points with negative y coordinate.      Returns     -------     float         The local normal angle of a spheric mirror         at a distance from the center. #}}} #{{{ reflection and deflection angle Returns a tuples of reflection and deflection angles.      Parameters     ----------     beamAngle : float         The angle formed by the propagation direction vector         of the incident beam and the x-axis.     normAngle : float         The angle formed by the normal vector of the surface         and the x-axis.     n1 : float         Index of refraction of the incident side medium.     n2 : float         Index of refraction of the transmission side medium.     invROC : float or None, optional         Inverse of the radius of curvature.      Returns     -------     6-tuple or 2-tuple     (reflAngle, deflAngle, Mrx, Mry, Mtx, Mty) or (reflAngle, deflAngle) #Calculate ABCD matrices #Absolute value of the incident angle #For reflection #For transmission #}}} #{{{ reflection and deflection angle for cylindrical surface Returns a tuples of reflection and deflection angles for incidence of a beam into a cylindrical surface.      Parameters     ----------     beamAngle : float         The angle formed by the propagation direction vector         of the incident beam and the x-axis.     normAngle : float         The angle formed by the normal vector of the surface         and the x-axis.     n1 : float         Index of refraction of the incident side medium.     n2 : float         Index of refraction of the transmission side medium.     invROC : float or None, optional         Inverse of the radius of curvature.     curve_direction : str, optional         Direction of curvature. Either 'h' or 'v'. #Calculate ABCD matrices #Absolute value of the incident angle #For reflection #For transmission #}}} #}}} #{{{ VariCAD utility functions Deflection angle helper function for VariCAD.      Parameters     ----------     theta : float         Angle of the surface measured from right.     theta1 : float         Angle of the incident beam measured from right.     n1 : float         Index of refraction of the incident side medium.     n2 : float         Index of refraction of the transmission side medium.      Returns     -------     phi2 : float         Angle of the deflected beam measured from right. #Combert theta and theta1 to 0-360 format #Determine the incident angle #Calculate deflection angle #Convert to the 0-360 angle Convert theta and theta1 to 0-360 format.      Parameters     ----------     theta : float         Angle of the surface measured from right.     theta1 : float         Angle of the incident beam measured from right.      Returns     -------     float #Combert theta and theta1 to 0-360 format #}}}