According to one exemplary implementation, a method for use by a global illumination system including a hardware processor includes identifying, using the hardware processor, a first interior vertex of multiple first interior vertices of a light path, the first interior vertices being situated within a volume having a refractive boundary. In addition, the method includes determining, using the hardware processor, a surface vertex of the light path at the refractive boundary, and determining, using the hardware processor, a linear direction from the surface vertex to a light source of the light path. The method also includes determining, using the hardware processor, one or more second interior vertices for completing the light path by constructing a path from the surface vertex to the first interior vertex, based on the linear direction, the surface vertex and the first interior vertex.