Efficient reflection and transmission dyad multiplication for 3D geometrical optics

Electromagnetic fields are often calculated in indoor environments using geometrical optics and ray tracing. When a ray is reflected from a panel or transmitted through a panel, a ray-fixed coordinate system is used to decompose the field into transverse electric (TE) and transverse magnetic (TM) components, and 2*2 dyads are used to calculate the reflection and the transmission. The paper develops an efficient arrangement of the multiplications associated with multiple reflections and transmissions along a ray path to reduce the overall count of floating-point operations.