  We present a method to compute the magnification of a finite source star
lensed by a triple lens system based on the image boundary (contour
integration) method. We describe a new procedure to obtain continuous image
boundaries from solutions of the tenth-order polynomial obtained from the lens
equation. Contour integration is then applied to calculate the image areas
within the image boundaries, which yields the magnification of a source with
uniform brightness. We extend the magnification calculation to limb-darkened
stars approximated with a linear profile. In principle, this method works for
all multiple lens systems, not just triple lenses. We also include an adaptive
sampling and interpolation method for calculating densely covered light curves.
The C++ source code and a corresponding Python interface are publicly
available.
