rayoptics.util.misc_math module

miscellaneous functions for working with numpy vectors and floats

normalize(v)

return normalized version of input vector v

distance_sqr_2d(pt0, pt1)

return distance squared between 2d points pt0 and pt1

perpendicular_distance_2d(pt, pt1, pt2)

return perpendicular distance of pt from the line between pt1 and pt2

perpendicular_to_radial(pt, pt2)

return perpendicular distance of pt from the line between the origin and pt2

perpendicular_to_line(pt, pt1, pt2)

return perpendicular distance of pt from the line between pt1 and pt2

perpendicular_from_origin(pt1, pt2)

return perpendicular distance of the origin from the line between pt1 and pt2

projected_point_on_line(pt, pt1, pt2)

projected_point_on_radial_line(pt, radial_pt)

projected_point_on_radial_line_full(pt, radial_pt)

euler2opt(e)

convert right-handed euler angles to optical design convention, i.e. alpha and beta are left-handed

isanumber(a)

returns true if input a can be converted to floating point number

transpose(mat)

transposes a m x n input list and returns the result

circle_intersection_area(ra, rb, d)

return the area of the intersection of 2 circles

Parameters:

• ra – radius of first circle

• rb – radius of second circle

• d – separation of the circles’ centers of curvature

Returns:

area of the circle intersection

Weisstein, Eric W. “Circle-Circle Intersection.” From MathWorld–A Wolfram Web Resource.

compute_tangent_point_to_circle(CofC, r, pt)

return the area of the intersection of 2 circles

Parameters:

• CofC – center of curvature of circle (2d numpy array)

• r – radius of circle

• pt – 2d numpy array of point outside of circle

Returns:

the 2 tangent points for lines from pt to circle

gboffi. “How to find the equation of a line, tangent to a circle, that passes through a given external point.” StackExchange (version: 2019-05-30)